(Greek, c. 625 BC - c. 546 BC). So far as we know, all of science, philosophy, and mathematics begins with him. His notion that everything has a natural - as opposed to mystical - cause is possibly the single most important idea behind scientific thought. He is listed here because his proof that a triangle inscribed in a semicircle must contain a right angle, now known as his theorem, is the earliest known mathematical proof. Name him.

(Greek, c. 570 BC - c. 495 BC). His name is irrevocably attached to a theorem about right triangles, of course. He is more of a legendary figure than anything; if he even existed, he appears to have led a cult whose explorations of music, mathematics, and philosophy were a profound influence on subsequent Greek writers - Plato among them - and thus all of Western thought. One thing's for sure: from what the ancients wrote about him, he was certainly an interesting character. Name him.

(Greek, c. 490 BC - c. 430 BC). Call him a nay-sayer, but his specialty was refuting conventional wisdom via the paradox. His arguments against the possibility of motion, for example, baffled logicians for over two thousand years - until the days of Cauchy and Weierstrass - and, even today, this disciple of Parmenides can inspire many a bright young fellow to scratch his head in confusion. Name him.

(Greek, fl. c. 300 BC). We know almost nothing about his life, but his Elements is one of the most influential books ever written. It was still being used as a standard textbook in logic and geometry as late as the turn of the 20th century. Name him.

(Greek, c. 287 BC - c. 212 BC). One of the most brilliant men who ever lived, he was a master inventor and engineer. He ranks as one of the earliest physicists for his formulation of statics, and his method of exhaustion anticipated the development of integral calculus nearly two millennia before anyone else. He was killed during the Roman siege of Syracuse, against the orders of the invasion's commander. Name him.

(Greek, c. 262 BC - c. 190 BC). Namer of the ellipse, parabola, and hyperbola, he wrote extensively and expertly on the conic sections. Name him.

(Greek, c. 207 - c. 291). He posed a series of problems in number theory and algebra, then solved many of them using a type of analysis he developed. One of his unsolved equations was later remarked upon by Fermat to have no solutions, and this conjecture became known as Fermat's Last Theorem. Name him.

(Indian, 598 - 668). We know him best for a formula involving cyclic quadrilaterals; however, he also figured out an explicit solution to the general quadratic. Moreover, one of his books is the first to treat zero as a number in its own right, rather than a mere placeholder. Name him.

(Italian, c. 1170 - c. 1250). A standout mathematician in a largely dead age, his twin claims to fame are a sequence of positive integers and - less well known but far more important - his introduction of the Hindu-Arabic numeral system to Europe. The numerals were included in his 1202 publication Liber Abaci, which translates literally as "Book of the Abacus." Name him.

(Italian, 1501 - 1576). He published the general solutions to the cubic and quartic, even though he didn't actually come up with them. What really earns him a spot on this list is his extremely early acknowledgement of "imaginary" numbers -- at a time when even negative numbers weren't widely accepted. Name him.

(Scottish, 1550 - 1617). He popularized two very important ideas in mathematics: the decimal point and the logarithm. He also invented a calculating aid known as "______'s bones." Name him.

(French, 1596 - 1650). His Meditations on First Philosophy is recommended reading; as a mathematician, he created the x-y coordinate plane, now named for him, and used it to develop analytic geometry. Name him.

(French, 1601 - 1665). Easily the most accomplished amateur mathematician, he had a hand in the development of analytic geometry, calculus, and especially probability -- but it was in number theory that he really shone. His Last Theorem was finally proven in 1994. Name him.

(French, 1623 - 1662). Also an important physicist, he shares credit with Fermat for the development of probability theory. Among the things named for him are the SI unit of pressure, a useful triangle of numbers, and an interesting philosophical wager. Name him.

(German, 1646 - 1716). His interests and talents were by no means limited to mathematics, and he would be one of the great minds of history had he only been a mathematician. He invented calculus independently of Newton, and it is his notation we use today. Among a legion of other achievements, he also invented binary arithmetic. Name him.

(Swiss, 1654 - 1705). He and his younger brother Johann divided their time between early development of the calculus and bitter feuding; Johann, rest assured, would be furious to know that he was merely lumped into his brother's entry and not accorded one of his own. His masterwork is the posthumously published Ars Conjectandi, a probability treatise containing such staples as the ________ trial and the law of large numbers. Name him.

(French, 1667 - 1754). One of the more underrated names in mathematics, his namesake formula links trigonometry to the complex numbers. He also wrote a book on probability, which he entitled The Doctrine of Chances. Name him.

(Swiss, 1707 - 1783). Enormously prolific, astonishingly diverse, and blind as a bat for the last 17 years of his career, he is a strong contender for the greatest mathematician of them all. He is responsible for much of the notation we use today, and his name is everywhere -- for example, the important transcendental number e was given that initial as an homage to his genius. Name him.

(French, 1736 - 1813). He helped create the calculus of variations and invented the method of variation of parameters. He also did important work in number theory. However, his most lasting mark may be his revision of Newtonian mechanics. Name him.

(French, 1768 - 1830). His namesake transform, which reduces a complicated periodic function to a superposition of simple sines and cosines, is an indispensible tool to physicists. Not many people know, though, that he also discovered the greenhouse effect. Name him.

(German, 1777 - 1855). Here we have Euler's chief competition for the title of greatest mathematician. A child prodigy, he published his masterpiece Disquisitiones Arithmeticae at the age of 24. He proved the fundamental theorem of algebra and improved upon the method of least squares, and let's not forget his countless contributions to number theory. Name him.

(French, 1789 - 1857). A pioneer in the field of complex analysis, what really gets him on this list is his rigorous logical formulation of the basic concepts of calculus. Until his revisions, mathematicians who used calculus had no real understanding of why it worked and studiously avoided the awful truth. Name him.

(German, 1790 - 1868). Here's an easily recognizable surname, thanks to his discovery of a two-dimensional surface with only one side. He did more than that, though; he made several important strides in number theory. Name him.

(Russian, 1792 - 1856). Euclid's fifth postulate, far more complicated than the other four, had long been a subject of some consternation among mathematicians. It was he - and, independently, Janos Bolyai - who showed that the fifth postulate was absolutely necessary to Euclidean geometry -- by messing around with it and creating non-Euclidean geometry. Name him.

(Norwegian, 1802 - 1829). He displayed brilliance from an early age, then lived a sadly short life. He proved the binomial theorem for all numbers - not just rationals - at age 16. He also proved the impossibility of finding a general solution for fifth-degree (or higher) polynomial equations; in order to accomplish this, he invented group theory. Name him.