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MASTHEAD: Pictured here are some of the most famous mathematicians in history (or artistic renderings of imagined likenesses) and equations associated with their work. Top row (left to right): Pythagoras of Samos (c. 569 – c. 475 BC), leader of the secret Greek society that bore his name and often described as the first ‘pure’ mathematician, though he also noticed the connection between simple fractions and musical harmony; Euclid of Alexandria (c. 325 – c. 365 BC), whose treatise, The Elements, endured for two millennia as the principle text on geometry; Archimedes of Syracuse (c. 287 – c. 211 BC), whose contributions to geometry revolutionized the subject and anticipated the integral calculus; Pierre de Fermat (1601-1665), renowned for his work in number theory, in particular his last theorem, co-founder (with Pascal) of the theory of probabilities, and anticipator of the differential calculus; Middle row (left to right): Blaise Pascal (1623-1662), who in addition to laying the foundations of probability theory, contributed important theorems in projective geometry and is remembered especially for his work on the arithmetical triangle, bionomial coefficients, and the cycloid; Sir Isaac Newton (1642-1727), one of the foremost scientific intellects of all time and the author of the Principia (a treatise on the mathematical principles of natural history), made contributions to all branches of mathematics, but is especially acclaimed for showing how planetary motions, including the famed Kepler laws, followed from principles of universal gravitation, and is generally regarded as having independently invented the calculus (along with Leibniz), thereby determining, for example, tangents to curves and areas bounded by curves; Gottfried Wilhelm Leibniz (1646-1716), whose invention of the present day notations for differential and integral calculus assured his place in the history of mathematics, also developed the binary system of arithmetic that is the basis of virtually all modern computer architectures, formulated many different approaches to determinants, laid the foundation of a theory of envelopes, and made important contributions to dynamics; Leonhard Euler, (1707-1783), the most prolific writer on mathematics of all time, made major advances in the study of modern analytic geometry and trigonometry as well as calculus and number theory, was responsible for foundational contributions to dynamics, and introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis; Bottom row (left to right): Johann Carl Friedrich Gauss (1777-1855), one of the great prodigies of mathematics, had immense influence on many mathematical fields, including number theory, which he systematized, analysis, differential geometry to which he contributed the idea (named after him) of Gaussian curvature, and geodesy, undertaking a major geodesic survey of the German state of Hanover, and among other achievements introduced the hypergeometric function and made important contributions to approximate integration, mathematical statistics, and the study of terrestrial magnetism, as well as theoretical astronomy; Augusta Ada Byron, Lady Lovelace, (1815-1852), recognized the potential of the calculating machine invented by her friend Charles Babbage and prepared detailed notes for a memoir about his Analytic Engine that specified a method for using it to calculate Bernoulli numbers—a feat recognized by historians as the world’s first computer program; Bernhard Riemann (1826-1866), who made important contributions to complex analysis, real analysis, number theory, and differential geometry, some of which paved the way for the later development of the theory of general relativity, and whose Riemann hypothesis remains the most famous (and arguably the most important) unsolved problem in mathematics to this day; and Georg Ferdinand Ludwig Philipp Cantor (1845-1918), founder of set theory who introduced the concept of infinite numbers (cardinal numbers and ordinal numbers) and advanced the study of trigonometric series.

Photo Credits (Pythagoras, Euclid, de Fermat, Newton, Leibniz, Gauss):
The Granger Collection, New York

All other portraits are part of the public domain.