Archimedes in the context of "Parabola"

Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece) and the 6th century AD (after which there was medieval science). It is typically limited geographically to the Greco-Roman West, Mediterranean basin, and Ancient Near East, thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent.

Ideas regarding nature that were theorized during classical antiquity were not limited to science but included myths as well as religion. Those who are now considered as the first scientists may have thought of themselves as natural philosophers, as practitioners of a skilled profession (e.g., physicians), or as followers of a religious tradition (e.g., temple healers). Some of the more widely known figures active in this period include Hippocrates, Aristotle, Euclid, Archimedes, Hipparchus, Galen, and Ptolemy. Their contributions and commentaries spread throughout the Eastern, Islamic, and Latin worlds and contributed to the birth of modern science. Their works covered many different categories including mathematics, cosmology, medicine, and physics.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

Syracuse (/ˈsaɪrəkjuːs, -kjuːz/ SY-rə-kewss, -⁠kewz; Italian: Siracusa [siraˈkuːza] ; Sicilian: Saragusa [saɾaˈuːsa]) is a city and municipality, capital of the free municipal consortium of the same name, located in the autonomous region Sicily in Italy. As of 2025, with a population of 115,636, it is the fourth most populous city in Sicily, following Palermo, Catania, and Messina.

Situated on the southeastern coast of the island, Syracuse boasts a millennia-long history: counted among the largest metropolises of the classical age, it rivaled Athens in power and splendor, which unsuccessfully attempted to subjugate it. It was the birthplace of the mathematician Archimedes, who led its defense during the Roman siege in 212 BC. Syracuse became the capital of the Byzantine Empire under Constans II. For centuries, it served as the capital of Sicily, until the Muslim invasion of 878, which led to its decline in favor of Palermo. With the Christian reconquest, it became a Norman county within the Kingdom of Sicily.

Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.

Apollonius of Perga (Ancient Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.

Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.

Eutocius of Ascalon (/juːˈtoʊʃəs/; Greek: Εὐτόκιος ὁ Ἀσκαλωνίτης; c. 480s – c. 520s) was a Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian Conics.

The School of Athens (Italian: Scuola di Atene) is a fresco by the Italian Renaissance artist Raphael. It was painted between 1509 and 1511 as part of a commission by Pope Julius II to decorate the rooms now called the Stanze di Raffaello in the Apostolic Palace in Vatican City.

The fresco depicts a congregation of ancient mathematicians, philosophers, and scientists, with Plato and Aristotle featured in the center. The identities of most figures are ambiguous or discernable only through subtle details or allusions; among those commonly identified are Socrates, Pythagoras, Archimedes, Heraclitus, Averroes, and Zarathustra. Additionally, Italian artists Leonardo da Vinci and Michelangelo are believed to be portrayed through Plato and Heraclitus, respectively. Raphael included a self-portrait beside Ptolemy. Hypatia is the only notable character who is looking directly at the viewer in the artwork.

The siege of Syracuse by the Roman Republic took place in 213–212 BC. The Romans successfully stormed the Hellenistic city of Syracuse after a protracted siege, giving them control of the entire island of Sicily. During the siege, the city was protected by weapons developed by the prominent inventor and polymath Archimedes, who was slain at the conclusion of the siege by a Roman soldier, in contravention of the Roman proconsul Marcellus's instructions to spare his life.

Ancient Greek technology developed during the 5th century BC, continuing up to and including the Roman period, and beyond. Inventions that are credited to the ancient Greeks include the gear, screw, rotary mills, bronze casting techniques, water clock, water organ, the torsion catapult, the use of steam to operate some experimental machines and toys, and a chart to find prime numbers. Many of these inventions occurred late in the Greek period, often inspired by the need to improve weapons and tactics in war. However, peaceful uses are shown by their early development of the watermill, a device which pointed to further exploitation on a large scale under the Romans. They developed surveying and mathematics to an advanced state, and many of their technical advances were published by philosophers, like Archimedes and Heron.