Plato(427-347 BC)

Plato was born near Athens. There he studied philosophy under Socrates and then traveled to the African coast to study mathematics under Theodorus of Cyrene. When he returned to Athens he founded his famous Academy. His Academy helped continue the feverous study of mathematics began by Pythagoras and his followers. Although Plato made no significant contributions to math himself, his friends and those who studied at his academy made most of the important mathematical contributions of this century. Theodorus of Cyrene, for example, is credited with discovering that other square roots of integers were irrational besides just the square root of 2..

Euclid(lived around the time of 300 BC)Not much is known about Euclid’s life, but he most likely was from Athens and taught at the University of Alexandria. He also founded the prestigious Alexandrian School of Mathematics. One of his crowning achievements was his comprehensive mathematics book called “The Elements” . Enormously influential, Elements was used as the standard textbook on math for thousands of years and is still used as a basis for geometry today . In one of its books Euclid proved that the number of primes was infinite, expressed an statement equivalent to the fundamental theorem of arithmetic, and provided many other proofs in geometry, number theory, and algebra.

Archimedes(287-212 BC)Archimedes of Syracuse was born on the island of Sicily and his father was an astronomer. He is considered one the greatest mathematicians of all time. He seems to have studied at the University of Alexandria and kept many of Euclid’s successors as his friends. In math he is most known for his discoveries in geometry although he is well known for his discoveries in science as well. He was able to calculate a value of pi more accurate than was previously known and found a formula for the volume and surface area of a sphere. He used a method for finding volumes that used ideas of calculus long before the work of Newton or Leibniz. In science Archimedes was credited with a formula describing the upward force of displaced water called the Archimedes principle, and he also made many inventions astonishingly advanced for his time supposedly even including a “death ray” that could ignite ships with focused lenses. He is famous for his quote, “Give me a place to stand on and I will move the earth.”

Eratosthenes (approx. 230-194 BC)

Eratosthenes first lived in Cyrene and was a contemporary of Archimedes. He excelled in many areas but supposedly earned the nickname “Beta” because he was only second best at everything. In math he is credited for the sieve of Eratosthenes which filters out composite numbers by removing mutliples of a number and leaving behind the primes. He also measured the circumference of the earth to be 25000 miles. Its actualy circumference is 24901.55 miles so Eratosthenes was very close.

Apollonius(262-190 BC)Like many of the great scholars of his time, Apollonius studied at Alexandria under the successors of Euclid. He is most known for his work Conic Sections which contains 8 books and 400 propositions and includes study of ellipses, parabolas, hyperbolas, and circles. He also proposed the problem of

Apollonius, which dealt with constructing a circle tangent to three other circles, a problem that fascinated mathematicians for years to come.

Ptolomy(150 AD)Ptolemy was a prominent Greek astronomer and mathematician. He put much of his work and the work of Hipparchus in tables which contributed to the development of trigonometry. The geocentric model of the universe is often given his name, the Ptolemaic system, due to his work in astronomy.

Diophantus(250 AD)Diophantus of Alexandria was an extremely influential mathematician and made important contributions to algebra and number theory. He wrote three books, Arithmetica, On Polygonal Numbers, and Porisms. Arithmetica was his most significant book and the content contained displays his genius. In it he gives the theorem that the difference of two rational cubes is also the sum of two rational cubes and that every integer is the sum of four squares. He proposed several problems involving systems of equations with only integer solutions which became known as Diophantine equations and ones that had only rational solutions which are known as Diophantine problems.

Pappus (300 AD)Pappus of Alexandria was born after the wake of Euclid and Archimedes died down to a ripple. He reintroduced excitement into the field. His greatest work was his book Mathematical Collection which combined previous work with his own original material. He discovered the Isoperimetric Theorem by considering the hive patterns of bees and noticing that a hexagon held more honey than other shapes such as triangles with the same perimeter.

Aryabhata(475-550 AD)Aryabhata was born near modern day Patna on the Ganges River. He wrote a book on astronomy and mathematics. There were two mathematicians with his name during this time so there is some uncertainty as to who wrote the book. In Hindu mathematics, Aryabhata is credited along with Brahmagupta for finding all possible integral solutions to the equation ax+by=c where a,b, and c are integers.

Brahmagupta(628 AD)Of all the Hindu mathematicians of the 7th century, Brahmagupta was the most prominent. His book Brahmasphutasiddhanta was the first to mention zero as a number and employed symbols instead of words inside equations. He also used negative and irrational numbers before they were widely accepted.

Liu Hui (3rd century AD)Liu Hui was known as one of the greatest Chinese mathematicians of ancient China. His book the Sea Island Mathematical Manual contains a very precise approximation of pi between 3.1410 and 3.1427. In his book he showed how to approximate the height of an island using similar triangles.

Li Chunfeng(430-501 AD)Li Chunfeng was a Chinese mathematician who wrote a book containing the most precise approximation of pi for a thousand years. It was expressed as the rational number 355/113 which is correct to six decimal places.

Jia Xian(11th century)Little is known about Jia Xian and his two mathematical books were lost. He is however credited as a source by mathematican Yang Hui for being one of the first to devise a method for finding square and cube roots and for using an idea equivalent to Pascal’s triangle.

Harun al-Rashid(763?-809)Harun al-Rashid was an Arabian caliph who ruled from 786 to 808 AD. His reign was characterized by his interest in science. He had Euclid’s Elements translated into Arabic and he embraced the Hindu mathematics, furthering its integration into Arabic culture. He was also reference in the classic book Arabian Nights.

Al Khowarizmi(825 AD)Al Khowarizmi was an Arabic mathematician during the reign of Harun al-Rashid’s son. He wrote an influential treatise on algebra and Hindu numerals which was later translated into Latin. He emphasized solving problems though explicit steps hence the word algorithm comes from his name.

Omar Khayyam(1050-1123)

Omar Khayyam was an Islamic mathematician. He produced a calendar much better than what was previously used and devised a method of solving cubic equations by intersecting a parabola with a circle.

Fibonacci(1175-1250 AD)

Fibonacci, or Leonardo of Pisa, was the most talented mathematician of his time. His father was a merchant and this allowed Fibonacci to gather knowledge from many different places such as Sicily, Greece, Egypt, and Syria. During his travels he was introduced to Arabic mathematics. When he returned to Itlay in 1202 he wrote his first book, Liber abaci or Book of Calculation. It helped introduce the Hindu-Arabic numeral system into Europe. Fibonacci is most famous for his sequence. It can be producedd by adding two neighboring numbers in the sequence to obtain the next number starting with 1,1. The first few terms of the fibonacci sequence are 1,1,2,3,5,8,13... He is thought to have devised this sequence when considering the offspring of rabbits. Another book he wrote was the Liber Quadratorum or Book of the Square. In it he showed how to solve equations with squares given that the solutions are whole numbers.

Scipione del Ferro(1465-1526)Scipione del Ferro was an Italian mathematician who taught at Bologna. His accomplishments include a method for finding the the exact value of one of the roots of an arbitrary cubic polynomial. His work marked an extension of the math of the ancient Greeks for the first time.

Niccolo Fontana Tartaglia

(1499-1557 AD)

Tartaglia was an Italian mathematician who was famous for his algebraic solution of cubic equations.

Gerolamo Cardano(1501-1576)

Often considered one of the greatest Italian algebraists of the 16th century. He published a method of finding solutions to cubic equations in his work Ars Magna, the first Latin treatise devoted soley to algebra.

Rafael Bombelli(1526-1573) An Italian mathematician, Bombelli's most influential work was his use of negative and complex numbers.

John Napier(1550-1617)John Napier was born in Edinburgh Scottland. Like many of the scholars of his day, Napier not only studied math, but astronomy and physics as well. He is best known for his invention of logarithms which helped to serve Kepler in his study of planetary motion. He also devised a method for making quick calculations with a system of rods called Napier's bones.

Johannes Kepler(1571-1630)Kepler was a German mathematician and astronomer who is most known for his three laws of planetary motion. 1.) The path of the planets around the sun trace out ellipses with the sun located at one of the foci.2.) The line connecting the sun to its orbiting planet sweeps out equal areas in equal amounts of time.3.) The ratio of the squares of the perios of any two planets is equal to the ratio of the cubes of their average distances from the sun.In addition to astronomy, Keplar did important work in optics and geometry as well.

Galileo Galilei(1564-1642)Galileo grew up in a poor but noble family with his father a musician. He studied at the University of Pisa where he experimented with pendulums and devised a formula for falling objects. One of the most famous physicists of all time, Galileo made several discoveries in science. With his invention of the telescope, he found the four moons revolving around Jupiter and was able to study lunar craters. His observations led him to support the Copernican model of the universe which placed the sun at the center. This placed him at odds with the Catholic Church and he was brought to trial where he was sentenced to house arrest.

Blaise Pascal(1623-1662)

Pascal was an influential French mathematician and philosopher. He published an essay on conic sections and invented a rudimentary handcranked calculator called the Pascaline. He experimented in physics as well and fought for his belief in the existance of vaccums with Pascal. The unit of pressure, the pascal, is named after him. Pascal's triangle is also named after him. Although he wasn't the first to use it, his work was the most important on this subject. With Fermat, Pascal laid the foundation for study of the theory of probability.

Pierre de Fermat(1601-1665)Fermat was a lawyer and French government official by trade but enjoyed doing mathematics as a hobby. Most of his remembered work was done in number theory, most notably he authored Fermat's Last Theorem. He supposedly had the proof but did not include it along with the theorem causing it to be lost for centuries. The theorem is as follows:x^n + y^n = z^n has no integer solutions when n>2. As well as his contributions to number theory, Fermat laid the foundations for the development of calculus.

Rene Descartes(1596-1650) Rene Descartes Was a French philosopher most famous for his quote, "I think, therefore I am." His work La geometrie established a link between algebra and geometry and became to basis for Cartesian geometry. He is credited for many modern day notational conventions such as using x,y, and z to symbolize unknowns in equations and using superscripts to represent powers. He is also credited for the Descartes rule of signs which helps determine the number of positive and negative roots of a polynomial.

Isaac Newton(1642-1727)

Gottfried Wilhelm Leibnitz(1646-1716)

Johann Bernoulli(1667-1748)

Born in Switzerland, Bernoulli did work in physics as well as with the orthogonal trajectories of families of curves and quadrature of areas by series.

Leonhard Euler(1707-1783)Euler was a Swiss mathematician who was extremely influential in math and physics. One of his most noted equations links exponential with trigometric terms in a relationship called Euler's formula.

e^(ix)=cos(x)+isin(x)He also made contributions in analytic geometry, trigonometry,geometry, number theory, and calculus.

Carl Friedrich Gauss(1777-1855)Gass was a German mathematician whose potential was noticed very early. His influential book, Disquisitiones Arithmeticae included the construction of a 17-gon with a ruler and compass, a major advancement in his time. Gauss also studied astronomy and wrote on differential equations, conic sections, and elliptic orbits. The list of things he is noted for is impressively long, but some of them include the Gaussian integral, Gaussian primes, and the Gaus-Jordan elimination.

Neils Abel(1802-1829)

Neils Abel had a short lived appearance in mathematics, but he made an impression none-the-less. He was born in Norway and published his first work in 1824 which showed that solving quantic equations with radicals was impossible. He continued to write more papers on infinite series, elliptic functions, and other subjects in mathematics. His name appears often in the study of analysis, series, and abstract algebra with Abel’s integral equation, Abel’s theorem, and Abelian groups.

Evariste Galois(1811-1832)Galois is known for his method of determing whether an equation can be solved by radicals, his work on the development of group theory, and on Abelian integrals.

Joseph Fourier(1768-1830)

Augustin Louis Cauchy(1789-1857)

Karl Weierstrass(1815-1897)

Bernhard Riemann(1826-1866)

David Hilbert(1862-1943)

Srinivasa Ramanujan(1887-1920)

Srinivasa Ramanujan stands apart from the other mathematicians in history. He was never formally trained and was coincidently discovered by British number theorist G. H. Hardy. There are many astonishing stories of his mathematical genius. For instance, he was able to calculate e raised to pi times the square-root of 163 all without a calculator and remark that it was very nearly an integer. He made contributions to mathematical analysis, number theory, and continued fractions.

Andrew Wiles(1953- )

A modern day mathematician, Wiles produced the first proof of Fermat's last theorem.