The science in ancient Greece laid the foundations for modern science. Mathematics, the basis of all scientific knowledge, was cultivated by the philosophical school led by Pythagoras. Excelling in both geometry (the famous Pythagorean theorem, enabling the solution of right-angled triangles) and arithmetic, numbers and lines held a significant place in their speculations. Before the emergence of medicine as a science, the Greeks viewed diseases as punishments from the gods. The Greek gods of medicine were Asclepius and Apollo, and in their temples, the sick offered sacrifices, spending the night with the hope of being cured by morning. Many substances used by the ancient Egyptians in their pharmacopoeia were exported to Greece, and their influence increased after the establishment of a Greek medical school in Alexandria, a city founded by Alexander the Great in Egypt after liberating them from Persia.

Hippocrates, the “father of Medicine,” established his own medical school in Cos and created Hippocratic Medicine. One characteristic of Hippocratic medicine is the theory of the four humors, related to the theory of the four elements proposed by Empedocles. Additionally, Hippocrates and some of his contemporaries agreed that diseases resided in the blood, leading to the practice of extracting a bit of blood from patients’ arms. In most cases, various herbs were prescribed. In all cases, Hippocrates spoke of the benefits of water (hydrotherapy) and plants.

Astronomy was studied by the Greeks in ancient times, typically divided into two periods: **classical Greece** and **Hellenistic Greece**. It received significant influences from other ancient civilizations, with the most notable influences coming from India and Babylon. During the Hellenistic era and the Roman Empire, numerous astronomers devoted their efforts to studying classical astronomical traditions, particularly at the Library of Alexandria and the Mouseion. The ancient Greek calendars were based on lunar and solar cycles. The Hellenic calendar incorporated these cycles, although a lunisolar calendar based on both proved challenging to implement. Consequently, many astronomers focused on developing a calendar based on eclipses.

The ancient Greeks were pioneers in deductive logic and the axiomatic method, but they deemed experimental verification unnecessary and even degrading for their conclusions. It was considered beneath the philosophers of that era to suggest that conclusions derived from logical reasoning needed experimental confirmation. This perspective persisted until the mid-17th century, when figures like Francis Bacon and René Descartes elevated experimental foundations, the bedrock of science, to philosophical respectability.

## Astronomy in Ancient Greece

-> See also: 136 Greek Mythology Figures Behind Asteroid Names

Greek astronomy drew significant influences from other ancient civilizations, primarily India and Babylon. During the Hellenistic era and the Roman Empire, many astronomers engaged in studying classical astronomical traditions, particularly at the Library of Alexandria and the Mouseion.

One of the early astronomers was the scientist **Aristarchus of Samos **(310-230 BC), who calculated the distances between the Earth, the Moon, and the Sun. Additionally, he proposed a heliocentric model of the solar system, where, as the name suggests, the Sun is the center of the universe and all other celestial bodies, including the Earth, orbit around it. This model, imperfect in its time but remarkably close to what we now consider correct, was not widely accepted due to conflicts with everyday observations and the perception of Earth as the center of creation. The heliocentric model is described in the work “The Sand Reckoner” by Archimedes (287-212 BC).

The geocentric model was originally conceived by **Eudoxus of Cnidus **(390-337 BC) and later strongly endorsed by Aristotle and his school. However, this model failed to explain certain observed phenomena, with the most significant being the different behavior of the motion of some celestial bodies compared to that observed for most stars. The latter appeared to move together, maintaining “fixed” positions relative to each other. They were consistently referred to as “fixed stars.”

Nevertheless, certain celestial bodies visible in the night sky, while moving in conjunction with the stars, seemed to do so at a slower pace (direct motion). Indeed, they exhibited a daily lag compared to the fixed stars. Moreover, on specific occasions, they appeared to halt this lag and reverse their motion relative to the “fixed” stars (retrograde motion), only to pause again and resume their original direction of movement, always with a slight daily delay (direct motion). Due to these seemingly irregular changes in their movement among the “fixed stars,” these bodies were labeled as planets (wandering stars) to distinguish them from others.

Ptolemy was the author of a treatise on astronomy known as the Almagest (in Arabic “Al,” followed by a Greek superlative meaning ‘great’). In this work, one can find the star catalog of **Hipparchus** in books VII and VIII. Although Ptolemy claimed to be its observer, many pieces of evidence point to Hipparchus as its true author. The catalog contains the positions of 850 stars in 48 constellations, given in universal ecliptic coordinates. In this work, Ptolemy proposed a geocentric model of the solar system, which was accepted as the model in the Western world and Arab countries for over 1300 years. The Almagest also includes a catalog of 1025 stars and a fixed list of 48 constellations.

**Ptolemy **took on the task of finding a solution to make the geocentric system compatible with all these observations. In the Ptolemaic system, the Earth is the center of the universe, and the Moon, the Sun, planets, and stars are fixed on crystalline spheres revolving around it. To explain the different motions of the planets, he devised a particular system where the Earth was not at the exact center, and the planets orbited in an epicycle around a point located on the circumference of their main orbit or sphere (known as ‘Deferent’).

The concept of epicycles originated with **Apollonius of Perga **(262–190 BC) and was refined by Hipparchus of Nicaea (190-120 BC). As the planet revolves around its epicycle while the center of the epicycle moves simultaneously on the sphere of its deferent, the combination of both movements results in the planet moving in the direction of the ‘fixed’ stars (though with a certain small daily delay). Occasionally, it appears to reverse this motion (lag) and seems to (for a certain period) advance ahead of the fixed stars, thus explaining the retrograde motion of the planets concerning the stars (see figure to the right). The Ptolemaic scheme, with all its intricate epicycles and deferents, was accepted for many centuries for various reasons, primarily for providing humankind with supremacy and a privileged or ‘central’ place in the universe.

Other significant studies during this era included the composition of the Earth, the compilation of the first star catalog, the development of a system for classifying stellar brightness based on the apparent luminosity of different stars, and the determination of the Saros cycle for predicting solar and lunar eclipses, among many others.

## Physics in Ancient Greece

### Speculative Physics

Aristotelian physics encompasses the philosophical, cosmological, physical, and astronomical hypotheses developed by Aristotle and his followers. These theories included the four elements: the ether, motion, the four causes, celestial spheres, geocentrism, etc. Aristotle’s main works where he expounds his physical ideas are Physics, On the Heavens, and On Generation and Corruption. The fundamental principles of his physics are:

**Natural places:**each of the four elements would naturally seek a different position relative to the center of the Earth, which is also the center of the universe. Earth and water are heavy and descend, while fire and air are light and ascend.**Relationship between velocity and density:**velocity is inversely proportional to the density of the medium.**Gravity/levity:**to achieve this position, objects experience a force either upward or downward.**Rectilinear motion:**motion in response to this force is in a straight line at a constant speed.**Circular motion:**planets move in a perfect circular motion.**Time:**the now, the before, and the after are related to motion and space.**Denial of a vacuum:**motion in a vacuum is infinitely fast.**Ether:**all points in space are filled with matter.**Theory of the continuum:**if spherical atoms existed, there would be a vacuum between them, so matter cannot be atomic.**Quintessence:**objects above the sublunary world are not composed of earthly matter.**Incorruptible and eternal cosmos:**the sun and planets are perfect spheres and do not change.**Unmoved mover:**the first cause of the motion of the first celestial sphere and the entire universe.

The reign of Aristotelian physics, the oldest known speculative physics theory, lasted for nearly two millennia. However, there were very few explicit references to experiments in Aristotelian physics, and Aristotle arrived at several conclusions not through experiments and observations but through logical arguments. After the work of many pioneers such as Copernicus, Tycho Brahe, Galileo, Descartes, and Newton, it was widely accepted that Aristotelian physics was neither correct nor viable. A contrasting opinion is presented by Carlo Rovelli, who argues that Aristotle’s physics is correct within its domain of validity—specifically, for objects within the Earth’s gravitational field submerged in a fluid-like air.

### Practical Physics

The use of steam in ancient Greece as the basis for functional, simple machines is a well-known fact. An example is the Aeolipile, which was used in the 1st century by the Greek engineer Hero of Alexandria.

## Mathematics

Greek mathematics, or Hellenic mathematics, refers to mathematics written in Greek from 600 BC to 300 AD. Greek mathematicians lived in cities scattered throughout the Eastern Mediterranean, from Italy to North Africa, but they were united by a common language and culture. Greek mathematics from the period following Alexander the Great is sometimes referred to as Hellenistic mathematics.

Greek mathematics was more sophisticated than the mathematics developed by earlier cultures. All remaining records of pre-Hellenistic mathematics show the use of inductive reasoning, involving repeated observations, to establish general rules. In contrast, Greek mathematicians employed deductive reasoning. The Greeks used logic to derive conclusions or theorems, from definitions and axioms. The concept of mathematics as a system of theorems based on axioms is explicit in Euclid’s Elements (around 300 BC).

Greek mathematics is believed to have started with Thales (around 624 BC – 546 BC) and Pythagoras (around 582 BC – 507 BC). Although the extent of their influence can be debated, they were likely inspired by Egyptian, Mesopotamian, and Indian mathematics. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.

Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. Pythagoras is credited with the first proof of the theorem bearing his name, although the statement of the theorem has a long history. In his commentary on Euclid, Proclus asserts that Pythagoras expressed the theorem bearing his name and constructed Pythagorean triples algebraically before doing so geometrically. Plato’s Academy had the motto “Let no one enter who is not a geometer.”

The Pythagoreans proved the existence of irrational numbers. Eudoxus (408 to 355 BC) developed the method of exhaustion, a precursor to modern integration. Aristotle (384 to 322 BC) was the first to put the laws of logic into writing. Euclid (around 300 BC) provided the earliest example of the mathematical methodology used today, with definitions, axioms, theorems, and proofs. Euclid also studied conics. His book “Elements” encompasses all the mathematics of the time.

Elements” addresses all fundamental problems of mathematics, always in a geometric language. In addition to geometric problems, it also deals with arithmetic, algebraic, and mathematical analysis problems. Besides well-known theorems in geometry, such as the Pythagorean Theorem, the “Elements” include a proof that the square root of two is an irrational number and another on the infinitude of prime numbers. The Sieve of Eratosthenes (around 230 BC) was used for the discovery of prime numbers.

Archimedes of Syracuse (around 287-212 BC) used the method of exhaustion to calculate the area under a parabolic arch with the help of the sum of an infinite series and provided a remarkably accurate approximation of pi. He also studied the spiral, giving it its name, developed formulas for the volume of surfaces of revolution, and devised an ingenious system for expressing very large numbers.

Moreover, many Greek mathematicians conducted their own studies and research, contributing their discoveries and data to the general knowledge of mathematics and other disciplines. They did something fundamentally crucial for mathematics: they transformed it into a rational science, a deductive and rigorous discipline built upon axioms and postulates.

## Medicine

Greek medicine refers to the medical practices developed in ancient Greece, likely influenced by Egyptian medicine. It traces back to the Homeric era, but it truly flourished in the 5th century BC with Hippocrates.

The Iliad mentions Achaean warriors Machaon and Podalirius as physicians, both sons of Asclepius, the god of medicine, along with Pean, the physician of the gods. Machaon, especially, attended to heal Menelaus, wounded by an arrow. He began by examining (Ancient Greek ἰδεῖν/ideĩn, literally “seeing”) the patient and then, after removing the arrow, undressed the wounded, suctioned the blood from the wound, and applied medicines (φάρμακα/phármaka). The specific medications are not detailed, except that they were offered by the centaur Chiron to Asclepius, who then passed them on to Machaon.

Medicine was already recognized as an art to some extent: “A physician, by himself, is worth many loaves of bread,” declares Idomeneus regarding Machaon, a formula that would become proverbial. The Iliad gives more importance to Machaon than to Podalirius. Ancient commentators suggested that Homer saw Machaon as a surgeon and his brother as a simple physician; his name would derive from (μάχαιρα/mákhaira), “knife.” The god Pean himself healed Hades, wounded by an arrow shot by Heracles; he applied medicines (pharmaka) to the wound, specifying that they were analgesics.

The Odyssey mentions professionally trained physicians: swineherd Eumaeus describes the figure of the physician (ἰατήρ/iatếr, literally “he who heals”) as part of the “craftsmen who serve everyone,” resembling the roofer or the singer and the diviner. Elsewhere, the poet pays tribute to the medical knowledge of the Egyptians, whom he calls “sons of Pean.”

## Science Periods in Ancient Greece

### Presocratic Period

According to epistemologist Geoffrey Ernest Richard Lloyd, the scientific method made its appearance in 7th-century BC Greece. Aristotle was one of the first scholars to elaborate on scientific demonstrations. However, philosophers known as Presocratics were the first to inquire about natural phenomena, earning them the designation φυσιολογοι (physiologoi, “physiologists”) by Aristotle because they engaged in rational discourse about nature, investigating the natural causes of phenomena, which became the first objects of the method.

Thales of Miletus (ca. 625-547 BC) and Pythagoras (ca. 570-480 BC) contributed significantly to the birth of some of the earliest sciences, such as mathematics, the Pythagorean theorem in geometry, astronomy, and even music.

Their early investigations were marked by the desire to attribute the constitution of the world (or κόσμος, cosmos) to a single natural (fire for Heraclitus, for example) or divine principle (for Anaximander). The Presocratics introduced the constitutive principles of phenomena, the αρχή (arche).

The Presocratics also initiated a reflection on the theory of knowledge. They observe that reason, on the one hand, and the senses, on the other, lead to contradictory conclusions. Parmenides chooses reason and believes that only reason can lead to knowledge because our senses deceive us. For example, they teach us that motion exists, while reason teaches us that it does not. This example is illustrated by the famous paradoxes of his disciple, Zeno of Elea. If Heraclitus holds an opposing opinion regarding motion, he shares the idea that the senses are deceptive.

### Socratic Period

With Socrates and Plato, concerning words and dialogues, reason (Ancient Greek λόγοσ, lógos) and knowledge become intimately linked. Abstract and constructed reasoning emerge. For Plato, the theories of forms serve as the model for everything that is sensible, with the sensible being a set of geometric combinations of elements. Plato thus paved the way for the mathematization of phenomena.

The sciences find themselves on the path of philosophy, in the sense of discourse about wisdom; conversely, philosophy seeks a secure foundation in the sciences. The use of dialectics, which is the essence of science, then complements philosophy, which holds the primacy of discursive knowledge (through discourse), or διάνοια, diánoia, in Greek.

According to Michel Blay, “the dialectical method is the only one that, successively rejecting hypotheses, rises to the very principle to solidly ensure its conclusions.” Socrates outlines the principles in Theaetetus. For Plato, the pursuit of truth and wisdom (philosophy) is inseparable from scientific dialectics; indeed, this is the meaning of the inscription on the fronton of the Academy in Athens: “Let no one enter here who is not a geometer.”

### Aristotelian Period

It was primarily with Aristotle, who founded physics and zoology, that science acquired a method based on deduction. He is credited with the first formulation of syllogism and inductive reasoning. The notions of “matter,” “form,” “potentiality,” and “actuality” were the first concepts of abstract elaboration. For Aristotle, science is subordinate to philosophy (“it is a secondary philosophy,” he said) and aims to seek the first principles of the first causes, which scientific discourse calls causality and philosophy terms Aristotelianism.

However, Aristotle marks a regression in thought regarding the position of the Earth in space compared to certain Presocratics. Following Eudoxus of Cnidus, he envisions a geocentric system and considers the cosmos to be finite. This view was followed by his successors in astronomy until Copernicus, with the sole exception of Aristarchus, who proposed a heliocentric system.

He also determines that living things are ordered in a hierarchical chain, but his theory is primarily fixist. Aristotle establishes the existence of indemonstrable first principles, precursors to mathematical and logical conjectures. He breaks down propositions into names and verbs, laying the foundation for linguistic science.

### Hellenistic Period

The Hellenistic period (323 BC – 30 BC) is an extension of Greek culture marked by significant progress in astronomy and mathematics, along with some advances in physics. The Egyptian city of Alexandria served as the intellectual center for scholars of the time, predominantly Greek in origin.

The works of Archimedes (292 BC – 212 BC) on hydrostatics (Archimedes’ principle) led to the first known physical law after Eratosthenes (276 BC – 194 BC) determined the Earth’s diameter, and Aristarchus of Samos (310 BC – 240 BC) calculated the distances Earth-Moon and Earth-Sun, showcasing remarkable ingenuity.

Apollonius of Perga constructed a model of planetary movements using eccentric orbits. Hipparchus of Nicaea (194 BC – 120 BC) refined observation instruments such as the dioptra, gnomon, and astrolabe. In algebra and geometry, the circle was divided into 360°, and the first celestial globe (or orb) was created. Hipparchus also authored a treatise in 12 books on the calculation of orders, now known as trigonometry.

Euclid (325 BC – 265 BC) authored The Elements, considered one of the foundational texts of modern mathematics. His postulates, including the “parallel postulate,” stating that “through a given point, there is only one line parallel to a given line,” form the basis of systematic geometry. In astronomy, a “theory of epicycles” was proposed, leading to the development of more accurate astronomical tables. The system proved highly functional, enabling, for instance, the first calculations of lunar and solar eclipses.

References

- Euclid’s Elements – Google Books
- The Works of Archimedes – Google Books
- The Oxford History of Greece and the Hellenistic World – Google Books
- The History of Greece – Google Books