Category: Biography

Illuminate your own path by learning about the remarkable lives of the exceptional individuals who have lived on our planet.

Alan Turing: The Father of Modern Computer Science
What were Alan Turing’s major contributions to the field of mathematics?
Alan Turing made significant contributions to the field of mathematics, including his invention of the Universal Turing Machine, a theoretical device that is widely considered to be the precursor to modern computers. He also made important contributions to the fields of logic, computability theory, and artificial intelligence, among others.
How did Alan Turing’s work during World War II impact the outcome of the war?
Alan Turing’s work in breaking the German Enigma code during World War II played a crucial role in Allied victory. His decryption of encrypted messages allowed the Allies to anticipate and disrupt German military movements, ultimately leading to the defeat of Germany.
What was Alan Turing’s role in the development of early computers?
Alan Turing is often considered to be one of the founding fathers of modern computing. His invention of the Universal Turing Machine laid the groundwork for the development of digital computers, and his work on algorithms and machine intelligence helped to shape the field of computer science.
What challenges did Alan Turing face during his lifetime?
Alan Turing faced numerous challenges during his lifetime, including discrimination for his homosexuality, which was illegal in England at the time. He was convicted of homosexuality in 1952 and forced to undergo chemical castration. He died two years later, and it is widely believed that his death by suicide was a result of the treatment he received.
What is the significance of the Turing Test in the field of artificial intelligence?
The Turing Test, which was proposed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behavior that is indistinguishable from that of a human. The test has been widely used in the field of artificial intelligence as a benchmark for evaluating the intelligence of machines. The Turing Test has played a significant role in shaping the development of artificial intelligence, and it remains an important topic of research and debate in the field today.
Alan Turing deserves to be called the father of modern computer science. In the years before World War II, he built the theoretical infrastructure for multipurpose machines that formed models for the computer in its most general shape. His seminal 1936 essay, “On Computable Numbers, with an Application to the Entscheidungsproblem,” was later realized as the way he foretold what modern computers can do. During the war, he helped to develop computing devices that were said to shorten the war by two years by deciphering encrypted enemy messages that were thought to be indecipherable. Unlike some theorists, he was also willing to work on practical issues. Thus, he was happy to use a soldering iron in the same way he was grappling with a math problem: by approaching it from a unique angle.
Who was Alan Turing?
Alan Mathison Turing was born on June 23, 1912. His father was a civil servant in India. His parents returned to Maida Vale, London, England, before his birth. At the age of 14, he was sent to Sherborne School, the traditional public school in Dorset, South England. Alan’s interest in science was noticed by the teachers at the school, but he did not find any support in this conservative institution. For example, before learning calculus, he was able to solve advanced mathematical problems developed with the first principles. At the age of 16, he came across Albert Einstein‘s work and understood it. While at school, he became intimate with a student, but his friend died during their last term at Sherborne. This event had a traumatic effect on Alan, and he lost all religious beliefs quickly. Over time, he became an atheist.
Alan Turing continued his education by attending King’s College, Cambridge, from 1931 to 1934, where he graduated with honors. He was later chosen as an academic member of the college. In 1936, he delivered his groundbreaking article on computable numbers that would form the basis of his career. This article describes the concept of a machine that can perform calculations, especially a universal machine that can calculate a wide variety of mathematical problems. Turing’s idea of universality has transformed into the concept of “programmability in computers” today. In a 1939 article, in the context of the human-computer, he stated, “A man provided with paper, pencil, and eraser and subject to strict discipline is in effect a universal machine.“
Turing’s efforts enhanced German mathematician Kurt Gödel’s research in 1931 and led to the use of the term “Turing machine” for this universal machine. Alan Turing showed that this type of machine can perform any mathematical calculation that can be expressed with an algorithm. The Entscheidungsproblem, which he mentions in his 1936 article, was the mathematical problem of whether there is always an algorithm that could judge the correctness or falsity of a mathematical proposition, put forward by German mathematician David Hilbert in 1928.
Church-Turing thesis
The three-wheel Enigma cipher that the Germans thought produced an unsolvable cipher and therefore used for their military plans.
Alan Turing also demonstrated the unsolvability of the problem by showing the impossibility of algorithmically determining the capabilities of any particular Turing machine. This notion, known today as the stopping problem, is a troubling issue for mathematicians. The Turing machine has remained an important concept in computability theory to this day. Although an abstract concept (Turing did not originally think of making such a machine), it could actually be done, which predicted many aspects of contemporary computer features and processes, such as input, output, memory, and programming. Alan Turing completed his doctorate in a remarkably short period, working from 1936 to 1938 at Princeton University under the supervision of American mathematician Alonzo Crunch.
They had previously developed the Church-Turing thesis, which described the nature of computability apart from Alan’s thesis, arguing that any effectively computable function produced by any means can also be calculated using the Turing machine. Although the thesis cannot be proven, it is generally accepted by mathematicians and theoretical computer scientists. Turing returned to Cambridge and attended the philosopher Ludwig Wittgenstein’s lectures on the fundamentals of mathematics. Wittgenstein said that math didn’t find the truth; it made it up, but Turing didn’t agree with this.
Decryption
Hut 6 machine room in Bletchley Park. This is where the British were trying to decrypt the enigma codes of the German army and air force.
The war brought a radical but accidental change in the direction of Turing’s career. His unique talent in math was spotted while at Cambridge, and he was invited to join Bletchley Park, the secret center of England’s efforts to crack German codes. He first started working part-time at the Government Code and Cypher School (now Government Communication Headquarters, GCHO) and then switched to working full-time.
The manual decryption process was both difficult and lengthy for a country facing an approaching enemy. Alan Turing realized that, when combined with a human’s unlimited creativity, machines could solve problems much faster and more reliably. Before the war, he had already helped try to figure out how the Germans encrypted their messages with the Enigma machine.
A few weeks after joining, he set up a machine that could help decrypt Enigma. His solution was named bombe after the earlier Polish device called bomba. Bombe (called crypt) was taking a possible simple piece of the original text and passing it through the combinations of rotors and plugboards in the Enigma. The most likely arrangements produced contradictions, thus eliminating them and leaving only a few combinations for further investigation. The machine performed a mathematical proof mechanically much more effectively than a human, or even a team, could.
What Kind of a Character was Alan Turing?
Front view of one of Turing’s original bombe machines; The bombe machines were the electromechanical tools Turing designed to decode the Enigma in Bletchley Park in 1939.
Alan Turing chose to work on the decoding of Enigma messages used in the Navy, and the reason for this was that “Nobody else was doing anything about it; it could be my job.” This was very typical for Alan, although he was comfortable cooperating with others. He developed new methods of decryption during his time at Bletchley Park. He often referred to them by slang names. One of them was the “Turingery” or “Turingismus,” which he developed in 1942. It was a manual calculation technique to find the string in the rotors of the Lorenz cipher machine, which the Germans used to encrypt high-level strategic orders. The British also deciphered this machine. The method was especially helpful because the information it gave was still true after a certain amount of time.
Alan Turing’s colleagues at Bletchley Park were aware of his unusual manners. He had chained the coffee mug to the radiator so that it would not be lost or stolen. When he came to work by bicycle, he wore a gas mask to protect him from hay fever, not fear of gas. However, with the help of his contribution to the work in Bletchley Park, he developed the world’s first programmable digital electronic computer, called Colossus. Alan Turing was awarded the OBE, the Order of Chivalry, in 1945 for his efforts during the war, but his contributions remained anonymous for years.
Tough Times for Alan
Pilot ACE’s (Automatic Computing Engine) circuits were among the first computers to store instructions, first operated in 1950 at the National Physical Laboratory, NPL.
After the war, Turing took a post at the National Physical Laboratory in Teddington, West London. Here he worked on one of the first computers, the Automatic Computing Engine, or ACE. Sadly, a simplified version of the Pilot ACE was never completed due to delays and Turing’s return to Cambridge on paid leave for a year.
He joined the University of Manchester in 1948 to study mathematics and was appointed deputy director of the university’s computer laboratory. He worked on the software of the Manchester Mark 1. Alan Turing continued to think about more theoretical and abstract ideas, one of which was artificial intelligence, investigating whether a machine could think. For the possible demonstration of the machine’s intelligence, he prepared the Turing test: for a computer to pass the test, it had to be indistinguishable from real humans when in contact with a human. Despite its presumed feasibility, this test has not yet been passed and has not lost its importance today. In fact, many variants of the test are currently in use.
Alan Turing lived at a time when homosexuality was illegal in England. He was charged in 1952 for obscene behavior and lost his security clearance. He had given him two options: incarceration or taking female hormones for a year in the hopes of “curing.” From this point on, he studied morphogenesis in interdisciplinary mathematical biology, becoming particularly interested in the process that allows organisms to produce their forms. Most of these works were published until 1992, when his articles were compiled.
How Did Alan Turing Die?
Turing was found dead in his home by his maid on June 8, 1954. The cause of death was cyanide poisoning, thought to have been caused by the half-eaten apple sitting beside his bed, but the apple was never tested. It was determined that he committed suicide, but the death was likely to be an accident.
Turing was admitted to the Royal Society in 1951, a year before he fell into disfavor. He was only truly appreciated after his death. Now there are two statues erected—one in Manchester and one in Bletchley Park. There are plaques at his birthplace in London and the house where he died in Wilmslow. The British government officially apologized for the official treatment that led Alan Turing to his death in 2009. But perhaps the most appropriate is the A.M. Turing Award, which is the equivalent of the Nobel Prize awarded each year to a leading computer scientist. Even though Turing died too young at age 41, his ideas will still be used in the field of computers in the near future.
References
Hilton, Peter. “A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park” (PDF).
Hodges, Andrew (2012). Alan Turing: The Enigma. Princeton University Press. p. 87. ISBN 978-0-691-15564-7.
Hilton, Peter. “NOVA | Transcripts | Decoding Nazi Secrets | PBS”.
Andrew Hodges. “The Alan Turing Bibliography”. turing.org.uk. p. morphogenesis.
Olinick, M. (2021). Simply Turing. United States: Simply Charly, ch. 15.
September 5, 2022
Andreas Vesalius: Human Body Anatomist of the Renaissance
What Were Andreas Vesalius’ Major Contributions to the Field of Anatomy?
Andreas Vesalius made several major contributions to the field of anatomy, including the publication of his landmark work “De humani corporis fabrica” (On the Fabric of the Human Body), which revolutionized the study of anatomy by emphasizing the importance of direct observation and dissection. He also made several important discoveries about the human body, including the fact that the heart has four chambers and that the blood circulates through the body.
How Did Vesalius’ Approach to Anatomy Differ From the Approaches of His Predecessors?
Vesalius emphasized the importance of direct observation and dissection of human cadavers, whereas many of his predecessors had relied on the work of ancient Greek and Roman anatomists or on animal dissections. He also encouraged his students to think critically and question established beliefs about the human body.
How Did Vesalius’ Work Influence the Practice of Medicine During His Lifetime?
Andreas Vesalius’ work had a significant impact on the practice of medicine during his lifetime, as it provided doctors with a more accurate and detailed understanding of the human body. His emphasis on observation and dissection also helped to establish a more rigorous and scientific approach to the study of medicine.
What Was Vesalius’ Legacy and How Did His Work Influence Other Anatomists?
Andreas Vesalius’ work had a profound impact on the study of anatomy and medicine, and his approach to scientific investigation helped to establish a foundation for modern medical science. His emphasis on direct observation and dissection continues to be an important aspect of anatomical study, and his work laid the groundwork for many later discoveries and advances in the field.
What Were the Controversies Surrounding Vesalius and His Work, and How Did He Respond to Them?
Andreas Vesalius’ work challenged many established beliefs about the human body, and he faced significant opposition from religious and political authorities who saw his work as a threat to traditional beliefs and practices. He also faced criticism from other anatomists who disagreed with his methods or conclusions. Vesalius responded to these controversies by defending his work in public lectures and by continuing to emphasize the importance of observation and dissection in the study of anatomy.
How Did Andreas Vesalius’ Work Influence the Development of Medicine During the Renaissance?
Andreas Vesalius’ work had a significant impact on the development of medicine during the Renaissance. His detailed and accurate descriptions of human anatomy helped to establish a new standard of anatomical knowledge and understanding. His work also contributed to the decline of reliance on traditional authorities such as Galen and the beginning of empirical observation and experimentation.
In July 1453, Andreas Vesalius published De humani corporis fabrica (On the fabric of the human body), known as Fabrica for short. This work consisted of seven large folio books (chapters) on the skeleton, muscles, veins and arteries, nerves, reproductive and digestive organs in the abdomen, heart and lungs, brain, and sense organs. It included 73 breathtaking, realistic illustrations along with detailed Latin text. From then on, the anatomy would never stay the same.
Who Was Andreas Vesalius?
Rembrandt’s 1632 painting, The Anatomy Lesson of Dr. Nicolaes Tulp, depicts newly appointed public anatomists to The Amsterdam Guild of Surgeons, wealthy members of the guild paid to be featured in the painting; the cadaver was the body of Aris Kint, who was executed for stealing a coat before being punished one last time with dissection.
Vesalius was born in Brussels, then part of the Habsburg Netherlands, into a family with strong formal connections: his father was a court pharmacist of the Holy Roman Emperor Charles V; his mother was the daughter of a wealthy government official. Vesalius received a good education in favorable conditions at the University of Leuven, benefiting from the progressive humanism of Erasmus of Rotterdam. Erasmus favored the study of original texts—which came to Europe at the beginning of the Renaissance—in their primary languages (classical Latin, Greek, and Hebrew) instead of translations filtered through generations of Islamic scholars and medieval scholars. Because the same mistakes were copied over and over, and because people tried to update the language, the meaning was probably changed.
Vesalius’ interest in anatomy continued in Leuven. There he spent the night outside the city walls with an anatomist-inclined friend, collecting the bones of executed bodies and sneaking them into the city. This madness resulted in an extremely valuable skeleton that was almost complete. Excesses like this were necessary as dead bodies were difficult to find, the training centers had no skeletons, and Andreas Vesalius believed the body was the main source of anatomical knowledge. He finished his undergraduate thesis, which was published in 1537, and kept studying anatomy until 1538, when he moved to Italy.
In September 1537, Vesalius arrived in Padua. He received his doctorate on December 5. He was offered to lecture in surgery and anatomy by one of Europe’s most renowned medical schools. Vesalius began dissecting in front of his students the very next day.
The Making of the Fabrica
Andreas Vesalius reveals the human body in all its layers in Fabrica. This entire skeleton is shown leaning against the shovel, which it may have dug its own grave to clean up the remains of the dissection.
Under the protection of the Duchy of Venice, the University of Padova was one of the leading institutions of medical and surgical education. Performing at least one dissection per year in medical school—a process that took three weeks during the winter—attracted students interested in the new observational anatomy. The organs in the abdomen and then the thorax were examined. Then the head and brain, and finally the arms and legs, were studied. This ancient practice was better for the durability of cadavers. Vesalius brought two necessary pedagogical innovations to Padova, which were evident in his Fabrica.
Unlike his contemporaries, Vesalius held the knife himself, combining teaching, showing, and cutting. He refused to teach from the lectern and did not read from any other book than his body. Moreover, he did not avoid obsolete anatomical literature. His humanistic approach led him further back to the well-respected 2nd-century authority Galenos of Pergamon (Galen), rather than interpretations of Galen, such as Mondino de Luzzi’s popular 14th-century Anathomia.
Galen advised his readers to make visual comparisons between what was written and what was directly observed. Vesalius was already experienced enough to realize that Galen had acquired some of his knowledge from animals and therefore contained factual errors; these were topics to be discussed with the students. However, he continues to use animal bodies as he deems necessary.
The Tabulae for Students
Veins and liver from Tabula anatomicae sex, 1538, one of the six auxiliary drawings Andreas Vesalius used in his early lectures.
Among many other difficulties, the systems running throughout the body, such as veins and arteries, had to be reconstructed part by part after dissection (following in the footsteps of Galenos, Vesalius manually picked these up as two different systems based on the liver and heart). Vesalius prepared one-to-one drawings to accompany the dissection to help his students envision the system. These drawings were later used in the Tabulae anatomicae sex of 1538; the six illustrations in the book were published in poster form and accompanied by explanatory texts.
The illustrations of the Tabulae were created by Vesalius and his Dutch friend, the painter Jan van Calcar. Calcar had been a student of the great Italian painter Titian in his studio in Venice. It was a great coincidence that Padova was close to one of the world’s leading art centers. The Tabulae became a great success. This is evident from the extensive and serial plagiarism that follows. What really pleased Vesalius was the proposal that the bodies of executed criminals be delivered to him in Padova.
In January 1540, he was summoned to Bologna to share his new method of teaching anatomy. In a presentation before an audience of about 200 people at the church of San Francesco, Vesalius was cutting the cadaver and clashed with Professor Matteo Corti, who was in charge of anatomy and reading Mondino’s Anathomia. The aging Corti despised such manual work, but Vesalius publicly corrected an error in Corti, Mondino, and Galenos and his Tabulae: the liver lacked five lobes.
Andreas Vesalius spent the next two years working on the Fabrica. He was reading Galenos and had a painter with him while he worked at the anatomy table. The drawings were made into highly detailed woodblock prints, often by gluing and traversing the painting into the wood. Woodblock printing was a great innovation in the field of printing. As it works like printing press letters, it could be printed on a page with ease. Aside from the importance of his classical Latin text, what stood out were the drawings that closely resembled reality and the imagery that gave Fabrica its essential splendor.
The Making of the Epitome
The identity of his painter, known to have come from Titian’s workshop, is unknown, but his contributions were enormous. Fabrica‘s cover page is a powerful symbol of the new Vesalius science of anatomy. The arrays of human skeletons and muscle structures are breathtaking. Each of the fourteen muscular man drawings is shown in an ongoing panoramic view, all skinned and given a stance that makes them appear as if they are still alive, even though they are all cut in layers.
After Andreas Vesalius oversaw the production process and Fabrica‘s pages were being prepared, he left Padova to go to Basel to work with the humanist teacher and publisher Oporinus. Oporinus was known for its print quality. His skill manifested itself when the book finally came out. Fabrica was the triumph of Renaissance humanism. However, it was also an expensive and luxurious piece, not something a student could afford to buy or something an on-the-job anatomist would want to touch with bloody hands. The simultaneous publication of the cheaper and shorter Suorum de humani corporis fabrica librorum epitome filled this market gap.
Some of the epitome’s dynamic leaflets were designed to be cut into pieces, and there were full-length body drawings of organs superimposed on one another. Thus, various pictures could be made in the form of flap anatomy that was popular at the time. The second corrected edition of Fabrica was printed in 1555. Vesalius spent the rest of his life in the service of Emperor Charles V, to whom Fabrica was dedicated, but planned to return to Padova before his death on the island of Zakynthos.
After Andreas Vesalius’ Death
Fabrica was simple to read and understand; this was and continues to be the book’s strength. Earlier anatomy books had few illustrations, and they were usually schematic representations of text. They were not images of what could be seen on the body, but drawings to aid in remembering. Vesalius was part of the Renaissance tradition of developing anatomical knowledge and description, but his work was a dramatic leap forward. Apart from the five-lobed liver, he corrected various anatomical errors: humans do not have rete mirable, unlike some other vertebrates (compounds of veins and arteries very close to each other); the chambers of the heart do not have pores for blood to pass through.
Vesalius’ drawings were often copied and reused in subsequent texts throughout the century. His realistic drawings could easily be corrected as new information became available. Traditionalists vilified the 28-year-old Vesalius for criticizing Galenos, but his encouragement to look at the body to find knowledge instead of the books resonated throughout Europe. Andreas Vesalius introduced the method of studying nature in anatomy, which had only recently been adopted in other observational sciences such as botany and geography. Fabrica has redefined the way we learn, teach, and think about what’s under our skin.
References
O’Malley, Charles Donald. Andreas Vesalius of Brussels, 1514–1564. Berkeley : University of California Press, 1964.
Andreas Vesalius, De humani corporis fabrica (1544), Book II, Ch. 24, 268. ISBN 0-19-858409-1.
Porter, Roy, ed. Vesalius. The Biographical Dictionary of Scientists. 2nd Ed. New York: Oxford University P, 1994.
September 5, 2022
Jan Evangelista Purkinje: Pioneer of Neuroscience, and Research on Vision
September 5, 2022
Jan Ingenhousz: Physiologist and Discoverer of Photosynthesis
September 5, 2022
Croesus: The Last King of Lydia, the Happiest Man Ever Lived
Croesus reigned as the last king of Lydia, an ancient nation located in Asia Minor, sometime between 560 and 546 BC. After a brief conflict with one of his half-brothers, he was able to take control of the majority of the Greek colonies that had been established along the coast. These victories gained him a great deal of loot, which led to his becoming infamously wealthy and giving rise to the well-known idiom “Rich as Croesus.”
The tale states that the wise man from Athens, known as Solon, made a trip to the capital city of Lydia, known as Sardis. Croesus questioned him about whether or not a person who had such riches might be thought of as the happiest of all mankind. The response from Solon was as follows: “Count no man happy until the end is known.” After a rule of around eleven years, Croesus was confronted with the devastating danger of the Persians and the downfall of his kingdom.
The Circumstances Surrounding Croesus’ Rule
Croesus and Solon by Gerard van Honthorst (1592-1656)
The Histories of Herodotus are the primary source for almost all of the information that we have about Croesus. This historian is a contemporary of the last conflicts of the Middle Ages (490–479 before our era). He is an essential witness to the struggle that arose between the Greeks and the Persian Empire of Xerxes, and he sets for himself the objective of tracing the origins of that conflict.
He remembers the life of Croesus, the first king of Asia Minor, who strove to dominate the Greek people by using the tales and testimony he acquired throughout his journeys. He gathered these tales and testimonies.
The “father of history,” Herodotus, suggests that the claim of the Persians to dominate Ionia, which includes the coast of southern Asia Minor (with cities such as Ephesus or Miletus) as well as the islands (Chios and Samos), was the cause of the battles that broke out throughout the Middle Ages. The kingdom of Croesus, which was situated in Lydia, a little farther north and inland, was next to this location. Lydia’s capital was called Sardis.
King Croesus’ ultimate goal was to consolidate even more power in his hands. According to Herodotus, this makes him “the first of the barbarians who had dealings with the Greeks, forcing some of them to become his tributaries, and entering into alliance with others.”
Croesus’ Wealth
The map of Ionia and Lydia around 50 AD. (Credit: Caliniuc, Wikimedia Commons, CC BY 4.0)
The myth’s tale explains this declaration of reality. Croesus was the king of Lydia in the year 561 because it was his great-great-grandfather Gyges, who was the bodyguard of King Candaules, who killed his master and took authority by marrying the queen. Croesus is said to have inherited the throne through Gyges. The Oracle of Delphi, however, predicted that the descendants of Candaules would have their payback in the fifth generation, and Croesus belonged to this generation. He did not appear to be concerned by the prophecy, but he was unable to ignore it.
His overbearing desire is matched only by his abilities, and he immediately begins a series of missions against the Greek towns of Ionia and Insula. These expeditions are met with immediate success. In this way, he was able to successfully annex enormous territory to his state. The wealth that Croesus amassed came from several sources, including plundering, the selling of artifacts and people as slaves, tributes, and taxes.
The city that served as his capital, Sardis, rose to prominence during his rule. He constructed lavish palates there and made uncounted subsidies available to draw in a huge number of poets, thinkers, and painters.
The Lydians’ wealth seemed to have no limit, and Croesus established his rule over the whole Mediterranean basin in financial matters. In the ancient world, the ability to manipulate money was a particularly political privilege that demonstrated the independence of each state. On the other hand, Croesus’ financial situation was incomparably better than that of the other nations, to the point that his monetary standard was universally adopted. As a result, he earned the reputation of being a powerful person, particularly the wealthiest man of his time.
A Warning by Solon
Solon before Croesus, by Nikolaus Knüpfer (1609–1655).
Is it possible that his unending wealth has caused him to lose his mind? Croesus believed that he was the best and happiest man alive, and he once said this about himself. But a warning was given to him when a figure who had been drawn to the splendors of the court emerged in Sardis.
This character was the famed lawmaker Solon, who is believed to be the founding father of the democratic system in Athens. Given that he invited him to his palace and showed him his wealth and jewels, Croesus was not without naivety.
After traveling across all of Anatolia and into Egypt, Solon eventually arrived at the palace of Croesus in Sardis. After that, Croesus asked him, “You have lived long in the world, and have visited many countries. Tell me whom you consider to be the happiest man living?”
The sage Athenian then provided the following response: “You are, I see, very rich, and you rule over many subjects; but I cannot answer you until I hear that your death was a good one. The rich man is by no means happier than the man who lives from day to day, if the favor of fate does not remain faithful enough for him to end his career in full prosperity. In all things we must consider the end, for too many men heaven has shown happiness, only to destroy them altogether.”
The Fall of Croesus
Battle of Thymbra, and the defeat of Croesus, 546 BC.
Following this series of events, it seems that fate dealt Croesus a challenging hand. He received a warning in a dream that his son Atys, the commander of his forces, would perish from an iron spear wound. Despite all of the measures that were taken, the prophecy was certainly carried out: Atys was slain as a result of an accident that occurred while he was hunting.
After that, Croesus was put in a position where he had to make an important choice. When confronted with the expansion of Cyrus’s Persian Empire, he waffled between the options of dialogue and open conflict. In the end, he traveled to Delphi to seek guidance from the legendary oracle there, but not before lavishing the sacred site with gifts beforehand.
These gifts included golden vases and cups, purple garments and tunics, silver jars, and craters, and even 117 bricks made entirely of gold. Croesus was certain that the god Apollo would look favorably upon him as a result of this gesture of generosity. The Oracle, on the other hand, was fraught with a great deal of obscurity since it predicted nothing more than the fall of a tremendous kingdom.
But which one was it? Croesus assumed immediately that it was the Persians, and he launched an attack. However, he suffered a humiliating defeat at the hands of his enemy, the Persians. Not long after the initial Battle of Thymbra, the Persians unexpectedly invaded Sardes, and Croesus was taken prisoner. As he was about to be burned at the stake and saw his city being destroyed, he had time to think about what the wise man Solon had said about how fragile human life is.
Croesus on Pyre, attic red figure amphora, c. 500–490 BC.
Cyrus, however, felt curious to witness Croesus repeating the name of Solon while the flames were growing toward him. As a result, he ordered the fire to be put out so that Croesus might explain the story. Cyrus felt compassion for him, first out of pity and then out of friendship. He was worried by the tale, fearing that if he sacrificed his victim, eventually the same might happen to him. He most likely did not return the king’s throne to Croesus but instead appointed him as an advisor. The abduction committed by the wealthiest man in the world’s great-great-grandfather nearly caused him to pay a terrible price.
FAQs
What was Croesus’ background, and how did he come to power in Lydia?
Croesus was born into the Mermnad dynasty, which had ruled Lydia for several generations. He inherited the throne from his father, Alyattes, and went on to expand the Lydian empire through conquest and diplomacy. Economic growth and cultural exchange with surrounding regions were hallmarks of his reign.
What was the significance of Croesus’ wealth, and how did it contribute to his downfall?
Croesus was famous for his immense wealth, which he accumulated through trade and conquest. However, his riches also made him a target for other rulers, including Cyrus the Great of Persia. When Croesus went to war with the Persian Empire, he was defeated and captured, and his wealth was plundered. This led to the end of the Lydian empire and marked the beginning of Persian dominance in the region.
How did Croesus’ reign influence the development of Greek culture and philosophy?
Croesus was known for his patronage of the arts and his support of intellectual inquiry. He welcomed philosophers, poets, and scholars to his court, and his reign is often seen as a golden age of intellectual and cultural exchange. Many Greek philosophers, including Herodotus and Xenophon, wrote about Croesus and his reign, and his legacy continues to inspire scholarship and artistic expression today.
What was the significance of the Battle of Pteria, and how did it shape the political landscape of the ancient world?
The Battle of Pteria was a key conflict between the Lydian and Persian empires that took place in 547 BCE. It was fought near the border between the two empires, and resulted in a decisive victory for the Persians. This battle marked the end of the Lydian empire and the beginning of Persian domination of the region, which would shape the political and cultural landscape of the ancient world for centuries to come.
References
Jona Lendering, “Alyattes of Lydia”. (2003)
James Allan Stewart Evans. “What Happened to Croesus?”. (1978)
Robert W. Wallace “Redating Croesus: Herodotean Chronologies, and the Dates of the Earliest Coinages”. (2016)
September 4, 2022
Nicolas Fouquet: Lavish Ambition for the Throne Led to a Tragedy
The French politician Nicolas Fouquet (1615–1680) was born into a rich bourgeois family, and his father had become a nobleman with the acquisition of a government post. Cardinal Mazarin, the Chief Minister, named Nicolas Fouquet Superintendent of Finance on February 7, 1653. A few years after reaching the pinnacle of his success, he dramatically fell from grace due to his involvement with personal gain.
Nicolas Fouquet, born in 1615, was originally intended for the church, but he rebelled and chose another route. His father gave in and secured him a seat as a counselor in the Parliament of Metz. When he was sixteen, this was his first job. Then, in 1636, he obtained one of the Master of Requests positions, which were established to raise money for the war that had been proclaimed against Spain. Given that he wasn’t 32 years old yet, Nicolas Fouquet was granted an exemption. Four years later, in 1641, he graduated with a law degree.
Nicolas Fouquet had a quick career: in 1642, he became intendant of justice, police, and finances in the army of Marshal de Châtillon in Flanders; in 1644, intendant of justice, police, and finances in Dauphiné; three years later, intendant in the army of Picardy; in 1648, intendant of the generality of Paris; and in 1650, at the age of thirty-five, he bought the office of attorney general of the Parliament, which he sold in August 1661, on the sneaky advice of Jean-Baptiste Colbert, a trusted man of Jules Mazarin, who was brought to the service of King Louis XIV after Mazarin’s death. So, after that Fouquet was no longer the subject of the Parliament.
To what heights can I not rise?
The Fouquet family motto was “Quo non ascendet?” (To what heights can I not rise?) and in 1653, Nicolas Fouquet became the great treasurer of the kingdom of France, which was the pinnacle of his professional career.
On February 7, 1653, he was named Superintendent of Finances at the age of 38. He could only hope to reach this position, as it was his ultimate goal. Although he was sought for the job after the death of the superintendent, he owed his appointment to his brother Basil, who was considered “a puppet” of Jules Mazarin, the young Louis XIV’s Chief Minister. However, Abel Servien, a more senior man, was chosen by the cardinal Mazarin to counteract Fouquet’s ambition. But Fouquet became the only supervisor when Servien passed away in 1659.
The holder of this high position had to meet the daily requirements of the state, which had been living on credit since 1635 and was deeply in debt. Nicolas Fouquet appealed to groups of creditors and lenders. Those in the financial industry who had faith in Nicolas Fouquet helped him build up a sizable network. Additionally, he made loans to the government at usurious interest rates, using the riches his father left him in 1640.
However, since the requirements of the French state were so crucial, he had to mortgage his possessions in the end. He played the affluent yet racked up significant debt for both the kingdom and his private spending (real estate acquisitions, maritime ambition, etc.). When Cardinal Mazarin passed away in March 1661, he had aspirations of becoming Chief Minister after rising to prominence in the French kingdom. He failed to see that the times had changed: Louis XIV was now preferring to rule without the assistance of a Chief Minister.
The Design of Versailles Was Inspired by His Chateau, Vaux-Le-Vicomte
Engraving showing Nicolas Fouquet’s Vaux-le-Vicomte chateau, which he owned as Louis XIV’s financial administrator.
Between the royal palaces of Vincennes and Fontainebleau, near Vaux-le-Vicomte, Nicolas Fouquet acquired a castle in terrible condition in February 1641. He expanded the estate via purchases in an effort to turn it into a luxurious residence. He commissioned the works from the best artists of the time. Above all, he enlisted the services of a triumvirate with a good reputation: Charles Le Brun (painter, in charge of interior decoration), André Le Nôtre (landscaper), and Louis le Vau (architect).
He pushed them to think beyond the box to create a distinctive ensemble. It was a success. Vaux-le-Vicomte is a marvel of architecture and landscape design, with viewpoints, terraces, waterfalls, basins, statues, the first formal gardens, and lavish interior ornamentation. Their skills would subsequently be put to use at Versailles by King Louis XIV.
France’s finance minister Fouquet had thrown a party in August of 1661 with a gala dinner, fireworks display, stage performance, and raffle to celebrate the opening of his beautiful new château (palace) Vaux-le-Vicomte. The guest of honor, King Louis XIV (1638–1715), envied the château so much that his face changed color from embarrassment, as if he was going to vomit.
Up to that point, Fouquet (1615–1680) had accomplished a significant amount of success in his life. Furthermore, he was just making predictions for the future of the office. Ultimately, he aimed for the position of Chief Minister. He’d be second only to Louis XIV in terms of authority if this happened. But Fouquet’s career came to an unexpected end after he put on the beautiful “fête,” or party, called Fouquet’s Fall today.
Ambitions of Becoming a Chief Minister
During the lavish celebration on August 17, 1661, in his castle of Vaux-le-Vicomte, Nicolas Fouquet welcomes Louis XIV.
On August 17, 1661, Nicolas Fouquet held the famous opening ceremony for his chateau, Vaux-le-Vicomte. He was a very influential figure in France at the time. He had become the government’s top lawyer and attorney general. His expectations were higher, however. In March of that year, Prime Minister Jules Mazarin (1602–1661), who had long ruled over state matters for the infant Louis XIV together with the Queen Mother, passed away. Mazarin’s departure has resulted in a political vacuum and complicated state finances. He and Fouquet were probably the only ones who knew who had authorized which funds, taken out loans, and paid them back. Fouquet’s fortune and the state’s treasury were not always clearly separated.
With Mazarin’s death, a key position in the government was left unfilled. Fouquet strongly suggested that the young monarch, King Louis XIV, name him as his heir, but the King did not agree. Louis had doubts about the self-assured newcomer. The King then announced, to widespread astonishment, that he intended to become a one-man government, eliminating the position of Chief Minister. Fouquet, like many of his fellow courtiers and politicians, thought that the King would soon abandon politics in favor of parties, hunting, and ladies. To be on the safe side, however, Fouquet did all in his power to discourage Louis from going through with it.
He intended to prepare a lavish banquet for the king. He was well aware that the House of Bourbon frequently credited a successful party with a promotion. Fouquet leaned in and gave it his all. A grandiose party was due in three weeks, and he was scrambling to pull it off. Nothing could go wrong since all the artists in his court were participating in the preparations.
The Danger of Wild Animals
Lion and Serpent (Lion au Serpent) (Image: Met Museum)
Fouquet planned a lavish dinner for Louis XIV, complete with 30 buffets, golden dinnerware, a theater, a raffle, and, of course, fireworks. The Sun King, however, was not in the least bit captivated. Only at royal festivities or significant triumphs were pyrotechnics permitted, and Fouquet had two fireworks displays that lit up the night sky. The King felt humiliated and intimidated by the event’s pomp and extravagant wealth. He started to believe that Fouquet was yearning for the throne. The only thing that could be said for sure was that Louis was completely over himself.
The Fronde, an uprising of nobles and parliament against the royal family from 1648 to 1653, occurred during Louis XIV’s childhood. He had dethroned the nobility of the sword and surrounded himself with courtiers to avoid another coup d’état by the nobles. But the bourgeoisie grew stronger because they could now buy offices and rise to the ranks of official nobility. Fouquet was such a citizen; rich, cultured, and ambitious. And to show that his ambition was not yet satisfied, Fouquet did not skimp on meaningful symbolism at his party.
Squirrels, which were important to the Fouquet family, were shown all over the castle, from the outside to the allegorical paintings. The motto “Quo non ascendet?” (To what heights can I not rise?) was inscribed on the family’s coat of arms. A painting of a squirrel interacting with a lion and a snake was perhaps the most intriguing thing for the Sun King.
The lions and snakes were symbols that one had to be careful with. Even before La Fontaine began concealing moral teachings in animal fables, this was common knowledge among contemporary people. The lion had always been seen as a strong leader, while the snake was seen as the lion’s sneaky advisor. The snake and the lion got together to eliminate the squirrel. Since Mazarin’s death, royal adviser Jean-Baptiste Colbert (1619–1683), whose coat of arms depicted a snake, had grown closer to the King. He, too, wanted to be Chief Minister, but Fouquet, a financial juggler and arts patron, was standing in his way.
One day, Colbert presented the King with an allegation that Fouquet had fortified the domain of Belle-Ile. Colbert claimed that his spy, disguised as a merchant, returned with the news and that Fouquet had a garrison of 200 men and a formidable arsenal (400 cannons, 3 or 4 warships, etc.). Louis XIV decided to arrest Fouquet at Nantes in the Estates of Brittany.
Colbert worked as a clerical assistant at the court. He had meticulously documented Fouquet’s misbehavior for quite some time. An opportunity presented itself after the feast when Louis XIV was boiling with jealousy. Colbert then gave the king his list. Nicolas Fouquet was among them.
He was taken into custody six weeks after the Vaux-le-Vicomte fireworks incident. Embezzling state money and committing high treason were the charges. Finally, after a three-year trial, the judges handed down a life sentence for Fouquet. His fortress was sealed up. But before that, the Sun King had the artwork, tapestries, and even trees inside the Vaux-le-Vicomte moved to his court, and he even brought the painters to himself. He was transforming his father’s former hunting lodge at Versailles into a home, and so he required the services of architects and painters like Le Vau, Le Brun, and Le Nôtre to pull it off.
A Protracted Trial That Was More Political Than Legal
Nicolas Fouquet was detained on King Louis XIV’s orders on September 5, 1661, at Nantes by D’Artagnan.
Nicolas Fouquet was accused of both lese-majesty (the insulting of a monarch; treason) and participating in a conspiracy against the royal authority. This included financial misconduct while performing his official duties. He was put on trial before an unusual court. Colbert and Louis XIV wanted this matter to be resolved soon, but more than three years passed due to the inquiry, legal disputes, and public arguments.
Additionally, things were not done in accordance with the rules: following Colbert’s orders, investigators fabricated papers; crucial witnesses were not heard; Nicolas Fouquet was held in isolation as a prisoner. Not to mention that the ingenious financial structures made it difficult to uncover proof. Additionally, since he was a smart, competent jurist, and lawyer, Fouquet defended himself and interfered with the trial.
Despite managing to save his life, Nicolas Fouquet was found guilty of embezzlement of public funds on December 22, 1664. Fouquet received the punishment of exile and property seizure. But Louis XIV raised the punishment to life in prison. For 26 years, Nicolas Fouquet was imprisoned in the Pignerol Fort. While waiting for his release, he died there in 1680.
The Lavish Celebration of August 17, 1661: The Fallacy of Grandeur
Nicolas Fouquet was also a great patron of the arts. And he supported the authors of the time like Madame Sevigne, La Fayette, Molière, Corneille, La Fontaine, and Charles Perrault. They were all affected by the folly of grandeur in his projects and his choices. Influential and powerful, he wanted to impress the gallery and please Louis XIV to win over the monarch. He had planned a celebration of unparalleled splendor just for this in his castle of Vaux-le-Vicomte in the summer of 1661. The feast he had prepared was of a magnificence never equaled until then, which left Louis XIV feeling humiliated.
Water jets shot out of basins and fountains as the carriages went by. He requested the famous majordomo François Vatel for supper, and he provided a meal that contained both savory and sweet foods. Les Fâcheux, an original comedy by Molière, was commissioned just for the occasion. As a result, he produced a comedy-ballet with musical interludes that would become highly popular with Louis XIV a few years later. This piece’s music had the Lully signature. And to cap off this very successful night, Nicolas Fouquet provided enormous fireworks, which were directed by Italian expert Torelli. The event was flawless, and charming for everyone in attendance.
According to legend, Louis XIV’s jealousy led him to decide to remove Fouquet, the director of finance, following this celebration. This is untrue, however, since the King chose to have this strong and troublesome person arrested in May. Jean-Baptiste Colbert, who wished to see Fouquet executed, was successful in persuading the monarch that the superintendent had committed misconduct. This was also because Fouquet was his rival for becoming Chief Minister.
On September 5, 1661, D’Artagnan, the captain lieutenant of the musketeers, captured Nicolas Fouquet in Nantes according to the king’s instructions. And on September 15, Louis XIV disbanded the Superintendence and replaced it with a Royal Council of Finance.
FAQ
What were Nicolas Fouquet’s main achievements as superintendent of finances?
As superintendent of finances, Nicolas Fouquet implemented several reforms that helped to modernize and centralize the French economy. He established a system of tax collection and introduced measures to regulate public spending. He also oversaw the construction of several public works projects, including canals and fortifications.
How did Nicolas Fouquet’s patronage of the arts and architecture influence the cultural life of France?
Nicolas Fouquet was a major patron of the arts and architecture, commissioning works by some of the most celebrated artists of his time. He was especially associated with the development of the classical French style, which was characterized by simplicity, order, and symmetry. His support for the arts helped to promote French cultural identity and establish the country’s reputation as a center of artistic excellence.
What were the circumstances of Nicolas Fouquet’s arrest and trial?
Nicolas Fouquet’s arrest and trial were triggered by his lavish spending on the Château de Vaux-le-Vicomte, which was seen as a challenge to the authority of King Louis XIV. Although there is little evidence to support the charges of embezzlement that were brought against him, Fouquet was found guilty and sentenced to life imprisonment. He spent the rest of his life in prison, where he wrote poetry and continued to receive visitors and correspondence.
How did Nicolas Fouquet’s downfall reflect the political and social tensions of the 17th century?
Nicolas Fouquet’s downfall reflected the political and social tensions of the 17th century, which were characterized by a struggle for power between the monarchy and the nobility. Fouquet was seen as a representative of the old nobility, which was perceived as a threat to the authority of the king. His trial was also influenced by religious and philosophical debates, as he was associated with the libertine movement, which advocated for individual freedom and artistic expression.
What was Nicolas Fouquet’s legacy in French cultural and political history?
Nicolas Fouquet’s legacy in French cultural and political history is complex and contested. On the one hand, he is remembered as a symbol of the excess and corruption of the old regime, whose downfall helped to consolidate the power of King Louis XIV. On the other hand, he is celebrated as a patron of the arts and architecture, whose vision and taste helped to shape the cultural identity of France. His life and career continue to inspire debate and discussion among historians and cultural critics.
What was the significance of the famous “Fête des Vaux” held by Nicolas Fouquet in 1661, and how did it contribute to his downfall?
The “Fête des Vaux” was a lavish party held by Nicolas Fouquet at his estate in Vaux-le-Vicomte in 1661. The party was attended by many members of the French court, and was widely seen as a display of Fouquet’s wealth and power. However, the party also drew the attention of King Louis XIV, who was jealous of Fouquet’s success and began to investigate his finances. This eventually led to Fouquet’s arrest and imprisonment.
References
Andrew Lossky, The Seventeenth Century: 1600-1715 (1967).
Jacques De Maupeou, La Mère De Fouquet (1949).
Inès Murat, Colbert (1980).
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George Dantzig: The Story of The Overlooked Genius
In 1939, George Bernard Dantzig, a doctorate candidate at the University of California, Berkeley, arrived a few minutes late to Jerzy Neyman’s statistics lecture while there were two homework problems posted on the board. He wrote them down and spent many days figuring out the answers. He was unaware that these were really two well-known statistics theorems that had never been proved before, not just regular exercise problems.
Dantzig subsequently said in an interview that:
A few days later I apologized to Neyman for taking so long to do the homework—the problems seemed to be a little harder than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o’clock, we were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.” For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics.
The most renowned statistician in the world at the time, Neyman, was then asked by Dantzig the next year what subject he should choose for his doctoral thesis. Neyman shrugged and said, “Just put your treatments of the two issues in a folder.” He would accept it as a doctoral thesis.
Dantzig’s Early Life
The eldest child of Tobias Dantzig and Anja Ourisson, George Bernard Dantzig was born in Portland, Oregon. The parents had met while attending Henri Poincaré lectures at the Sorbonne in Paris, where they were both students.
They moved to the United States after getting married, where Tobias Dantzig, a native of Lithuania, had to start out by working odd jobs like a road builder and a lumberjack due to language barriers before obtaining a Ph.D. in mathematics from Indiana University; his wife took the master’s degree in French.
The parents thought that their children would have better chances in life if they were given the first names of famous people. Thus, the younger boy was given the first name Henri (after Henri Poincaré) in the hopes that he would one day become a mathematician, while the elder son was given the name George Bernard in the hopes that he would one day become a writer (like George Bernard Shaw).
The father taught mathematics at different institutions, including Johns Hopkins (Baltimore, Maryland), Columbia University (New York), and the University of Maryland, while the mother worked at the Library of Congress in Washington, DC. A book he released in 1930 on the history of the evolution of mathematics, Number – The Language of Science, has been reissued several times (most recently in 2005).
Dantzig continued to struggle with arithmetic in the early grades, but owing to his father’s daily assignment training regimen, particularly in geometry, Dantzig finally received top marks.
George Dantzig started his mathematical studies at the University of Maryland because, despite the fact that both of his parents were employed, the family did not have enough money to finance his studies in physics and mathematics at a prestigious university.
George Dantzig moved to the University of Michigan after receiving a bachelor’s degree, where he went on to complete his graduate studies in 1937. He subsequently accepted a position at the U.S. Bureau of Labor Statistics and participated in research on urban consumers’ purchasing habits after becoming weary of abstract mathematics.
Dantzig Was a Heartfelt Statistician
Dantzig first became interested in statistical concerns and techniques while working in this position. He requested Jerzy Neyman’s permission in 1939 to attend his PhD studies at the University of California, Berkeley (with a “teaching assistantship”). And thus, one day, the event that was described above occurred.
The PhD program was still in progress when the United States joined World War II. Dantzig relocated to Washington, D.C., and accepted a post as the director of the Statistical Control Division at the headquarters of the U.S. Air Force. He discovered that the military’s knowledge of the real inventory of aircraft and equipment was insufficient.
He devised a method to collect the necessary data in detail, particularly to make a thorough contract award, including the need for nuts and bolts.
Dantzig briefly returned to Berkeley after the war, where he eventually received his degree. Not simply for financial reasons but also because he preferred the chances and challenges of working for the Air Force, he declined an offer from the university to continue working there.
Dantzig saw the need to dynamize this rather static model and was motivated by the input-output analysis approach of the Russian-American mathematician Wassily Leontief, who had a position at Harvard University in Cambridge starting in 1931. Additionally, he aimed to improve it to the point where hundreds or even thousands of actions and locations could be recorded and optimized; at the time, this was a fascinating computing hurdle.
Dantzig’s Advancements in Military Planning
George Dantzig, Anne Dantzig, and President Gerald Ford (National Medal of Honor ceremony, 1971).
While employed by the Pentagon, Dantzig came to the conclusion that many planning choices were based solely on experience rather than objective criteria, yielding less than ideal outcomes. Linear inequalities are often used to characterize the requirements (restrictions), and specifying an objective function establishes the purpose of optimization, such as maximizing profit or decreasing resource consumption.
In English, the planning technique created by Dantzig is known as “linear programming,” where “programming” refers not to programming in the modern meaning of the word but rather to the phrase used in the military for the planning of procedures. The selected linear function modeling is referred to as being “linear.”
A half-plane in two dimensions and a half-space in three dimensions are both defined by a linear inequality. Convex polygons or convex polyhedrons are produced when many inequalities are taken into account; in the n-dimensional case, the corresponding convex structure is known as a “simplex”.
The so-called Simplex Algorithm, which Dantzig created in 1947, is a systematic approach for computing the best answer. Dantzig himself said of it: “The tremendous power of the simplex method is a constant surprise to me.”
The creation of the simplex algorithm, a technique for resolving linear programming problems, is widely regarded as one of Dantzig’s most important accomplishments. The goal of linear programming is to maximize a linear objective function within a set of linear constraints using a mathematical approach. The simplex algorithm has had a significant influence on many fields, including business, economics, and engineering, as a tool for tackling problems in linear programming.
His work on duality in linear programming is a cornerstone of modern optimization theory. To describe the association between a dependent variable and one or more independent variables, he also made significant contributions to the statistical procedure known as linear regression. George Dantzig is called “the father of linear programming” for that.
He Wasn’t Seen Worthy of the Nobel Prize
George Dantzig
When Dantzig visited Princeton University to speak with John von Neumann towards the end of the year, the algorithm saw its first refinement. This bright mathematician and computer scientist quickly saw similarities between the methods he and Oskar Morgenstern outlined in their newly released book, “The Theory of Games,” (1944) and the linear optimization approach.
The search techniques have significantly improved over time, notably with the advent of computer use. Although other strategies, such as nonlinear modeling, were also studied, Dantzig’s “linear programming” technique was finally proven to be adequate.
Tjalling C. Koopmans, professor of research in economics at the University of Chicago, realized the value of linear planning from an economic perspective after speaking with Dantzig. His famous theory on the optimal use of exhaustible resources was born out of this. To the surprise of everyone in the field, Dantzig was left unaccomplished when Koopmans received the Nobel Prize in Economics in 1975, together with the Russian mathematician Leonid Vitaliyevich Kantorovich, who had earlier proposed comparable methods in 1939. But it took the West two decades to learn about them. Dantzig, who was always kind to his fellow men, handled this with remarkable perseverance, demonstrating his high degree of expertise.
Dantzig went to the RAND Corporation in Santa Monica in 1952 to continue developing computerized execution of processes after his work with the Air Force. He established the Operations Research Center after accepting a post at Berkeley’s Department of Industrial Engineering in 1960.
When it was first published in 1963 by Princeton University Press, his book Linear Programming and Extensions established the field of linear optimization. Dantzig began working at Stanford in 1966, when he also established the Systems Optimization Lab (SOL). He oversaw a total of 41 PhD students over the course of more than 30 years; all of them had bright futures in academia and the workplace after receiving their degrees from Dantzig.
Dantzig has received multiple honorary degrees and memberships in academies in recognition of his significant scientific accomplishments, including the National Medal of Science and the John von Neumann Theory Prize. The George B. Dantzig Prize is given every three years by the Mathematical Optimization Society (MOS) and the Society for Industrial and Applied Mathematics (SIAM) in recognition of the scientist and his achievements.
His health quickly deteriorated shortly after a celebration of his 90th birthday in 2004; a diabetes condition mixed with cardiovascular issues ultimately caused his death.
The Two Unsolved Homework Problems That George Dantzig Solved
The doctoral student George Bernard Dantzig came late to Jerzy Neyman’s statistics lecture in 1939, when two homework assignments were already written on the board. He put them in writing and spent many days trying to solve them. To him, these seemed like ordinary math exercises, but upon further investigation, he discovered that they were, in fact, proofs of two well-known theorems in statistics that had never been proven previously.
1. “On the Non-Existence of Tests of “Student’s” Hypothesis Having Power Functions Independent of σ”, 1940
In the paper, Dantzig investigates whether or not the power function (i.e., the likelihood of rejecting the null hypothesis) of the statistical test for the “Student’s” hypothesis (commonly known as the t-test) can be designed to be independent of the standard deviation of the population (σ).
The “Student’s” hypothesis is a statistical hypothesis test used to evaluate whether the means of two populations are substantially different from each other; it was named after the statistician William Sealy Gosset, who wrote under the pseudonym “Student.” A common statistical procedure for comparing the means of two samples, the t-test is based on the “Student’s” hypothesis and has extensive use.
Dantzig demonstrated that a power function independent of σ cannot be designed for a statistical test of the “Student’s” hypothesis. He then explained his results and gave evidence for them. The study has received several citations because of its significance for the development of statistical theory.
2. “On the Fundamental Lemma of Neyman and Pearson”, 1951
In 1951, George Dantzig published an article in the Annals of Mathematical Statistics titled “On the Fundamental Lemma of Neyman and Pearson.” As a result of statistical theory, Neyman and Pearson’s fundamental lemma has to do with the power of statistical tests, which Dantzig proves in his article.
Neyman and Pearson’s “fundamental lemma” is a universal conclusion that establishes a connection between the null and alternative hypotheses in a statistical test. If the null hypothesis holds, then the likelihood of detecting a test statistic that is more extreme than a specified value (the critical value) is proportional to the sample size of the test. If the null hypothesis is correct, then the test’s power (the probability of rejecting the null) will be proportional to the test size.
Dantzig provides a demonstration of Neyman and Pearson’s fundamental lemma and examines how this finding has practical consequences for statistical testing in his work. The study has again received a lot of attention for its groundbreaking addition to statistical theory.
George Dantzig, the Real Good Will Hunting
A scene from the Good Will Hunting movie with the character inspired by George Dantzig,
The American drama film “Good Will Hunting,” starring Matt Damon and Robin Williams, was directed by Gus Van Sant and released in 1997. Will Hunting, a young guy from South Boston who is a math prodigy yet works as a janitor at MIT, is the protagonist of this film. An MIT professor sees potential in Will, encourages him to pursue mathematics, and ultimately helps him conquer his own personal issues.
A memorable scene from Good Will Hunting has Matt Damon’s character, a janitor at a university, tackling an almost impossible graph problem on a chalkboard. Certain details were changed for dramatic effect, but the basic tale is based on real events related to George Dantzig. One day, future renowned mathematician George Dantzig was running late to his statistics class when he saw two statistical questions written on the whiteboard and assumed they were homework assignments. Dantzig later casually solved the long-unsolved problems of statistics.
George Dantzig’s Discoveries and Contributions
George Dantzig made important contributions to operations research and mathematical modeling. These are the important discoveries and contributions he made that bear mentioning:
- The simplex algorithm: In particular, Dantzig is lauded for creating the simplex algorithm, a standard technique for resolving linear programming issues. If you have a linear objective function and linear constraints, the simplex method may help you find the best solution.
- The theory of duality in linear programming: Dantzig established a cornerstone notion in optimization theory known as the principle of duality in linear programming. The best solution to a linear programming problem can be found with the help of duality theory, which establishes a link between the original problem and its dual problem.
- Contributions to linear regression: Dantzig’s contributions to the field of linear regression are substantial. Linear regression is a statistical technique for modeling the association between a dependent variable and one or more independent variables, and Dantzig made significant contributions to this area.
- Work on the transportation problem: Dantzig also did important work in the area of transportation problems, a kind of linear programming issue that includes determining the best possible route for resources to take between different points on a map.
When taken as a whole, Dantzig’s contributions to the fields of mathematics and computer science were influential and shaped the manner in which modern corporations and organizations use mathematical modeling to address difficult issues.
References
Joe Holley (2005). “Obituaries of George Dantzig”.
Donald J. Albers. (1990). “More Mathematical People: Contemporary Conversations“
On the Fundamental Lemma of Neyman and Pearson – Projecteuclid.org
On the Non-Existence of Tests of “Student’s” Hypothesis Having Power Functions Independent of σ – Projecteuclid.org
Dantzig, George (1940). “On the non-existence of tests of “Student’s” hypothesis having power functions independent of σ“
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