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Thales is the first known Greek Mathematician. He is said to have been the first person to attempt to solve geometrical theorems. One including that the sum of the angles in any triangle is equal to two right angles. He also studied the sides of similar triangles being proportional and that circles are bisected by any of its diameters.
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Pythagoras is most commonly recognized for the Pythagorean Theorem and the properties of right triangles. Pythagoreans also identified incommensurable ratios, meaning cannot be measured together. This is what we call today and irrational number.
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He is best known for his developments in geometry and fractions, specifically in the volume of a cone.
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He came up with a method for rigorously proving statements about areas and volumes by continuous approximations.
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Plato was inspired by Pythagoras and founded an Academy in Athens where he focused his teachings on the relationship between mathematics and reality. He inspired individuals to study math and posed questions referring to “squaring the circle”, “doubling the cube” and “trisecting the angle”. He is most famous for identifying 5 symmetrical 3D shapes: tetrahedron, octahedron, icosahedron, cube, and dodecahedron.
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Apollonius of Perga (in Turkey) is known for his work with curved objects, specifically cones. He is famously known as the "Great Geometer" of the third century B.B. He put two cones together, touching at the point of each, and took a plane through a section of the cone that did not pass through the cone. He produced 4 kinds of 'conic' sections - circle, eclipse, parabola, and hyperbola.
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Known as the "father of geometry." Euclid wrote The Elements which consisted of all the mathematical revolution that had taken place in Greece up to his time. This book of definitions, proofs, and theories was very influential for future mathematicians. Elements was used as a model of mathematical reasoning and encouraged the work of many future mathematicians. Euclid also studied geometrical figures and divided them into parts in given ratios and looked at spherical astrology.
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Archimedes produced formulas for the area of regular shapes. He wrote about areas and volumes of various curved figures. He studied the surface and volume of a sphere. He discovered that the volume of a sphere is two-thirds the volume of a circumscribed cylinder.
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Claudius Ptolemy was an astronomer who lived in Alexandra around 120 A.D. He wrote the Syntaxis. It includes descriptions of all visual astronomical phenomena. This includes the motion of the sun, moon, and planets.
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Diphantus lived in the early to mid 3rd century. Diophantus wrote a collection of book called Arithmetica. He didn't focus on geometry, he instead focused on rational numbers and solving numerical problems. Diophantus was the first mathematician to use notation that represented unknowns in his work.
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Theon lived in Alexandria in the 4th century. He worked on writing new editions of Euclid's Elements and Ptolemy's Syntaxis. His daughter Hypatia then wrote commentaries on her father's mathematical work.
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Proclus was one of the last important writers of Greek tradition. He used Neoplatonic theories to comment on part of Euclid's Elements. His comments include information on the history of early Greek mathematics.
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Also known as Hippasus, is said to have discovered potential existence of irrational numbers while trying to calculate the value of √2. In the mid-4th century Pappus attributed to mathematical history by his Collection. He discussed "the method of analysis"."Analysis" was the process for discovering proof or a solution.
