In this post, let’s take a moment to witness the glory of some of the great mathematicians who have left an indelible mark on our lives and the world at large.
Pythagoras was an Ionian Greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and traveled, visiting Egypt and Greece, and maybe India, and in 520 BC returned to Samos.
Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.
Pythagoras was also credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. As a mystical symbol, it was very important to the worship of the Pythagoreans who would swear oaths by it.
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for Fermat’s Last Theorem, which he described in a note at the margin of a copy of Diophantus‘ Arithmetica.
Sir Isaac Newton was an English physicist and mathematician (described in his own day as a “natural philosopher“) who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), first published in 1687, laid the foundations forclassical mechanics. Newton made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for the development of calculus.
Newton’s Principia formulated the laws of motion and universal gravitation, which dominated scientists’ view of the physical universe for the next three centuries. By deriving Kepler’s laws of planetary motion from his mathematical description of gravity, and then using the same principles to account for the trajectories of comets, the tides, the precession of the equinoxes, and other phenomena, Newton removed the last doubts about the validity of theheliocentric model of the Solar System. This work also demonstrated that the motion of objects on Earth and of celestial bodies could be described by the same principles. His prediction that Earth should be shaped as an oblate spheroid was later vindicated by the measurements of Maupertuis, La Condamine, and others, which helped convince most Continental European scientists of the superiority of Newtonian mechanics over the earlier system of Descartes.
Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum. He formulated an empirical law of cooling, studied the speed of sound, and introduced the notion of a Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study of power series, generalised the binomial theoremto non-integer exponents, developed a method for approximating the roots of a function, and classified most of the cubic plane curves.
Johannes Kepler was a German mathematician, astronomer, and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton‘s theory of universal gravitation.
Kepler was a mathematics teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe, and eventually he was the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian telescope), and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei.
Gottfried Wilhelm (von) Leibniz was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton. Leibniz’s notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis). He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal’s calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of virtually all digital computers.
René Descartes was a French philosopher, mathematician, and scientist. Dubbed the father of modern western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. He spent about 20 years of his life in the Dutch Republic.
Descartes’s Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes’s influence in mathematics is equally apparent; the Cartesian coordinate system—allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two- or three-dimensional coordinate system (and conversely, shapes to be described as equations)—was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the scientific revolution.
Leonhard Euler was a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.
Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field. He spent most of his adult life in St. Petersburg, Russia, and in Berlin, then the capital of Prussia.
A statement attributed to Pierre-Simon Laplace expresses Euler’s influence on mathematics: “Read Euler, read Euler, he is the master of us all.”
Daniel Bernoulli FRS was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli’s principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.
Évariste Galois was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He died at age 20 from wounds suffered in a duel.
Johann Carl Friedrich Gauss was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics,electrostatics, astronomy, matrix theory, and optics.
Sometimes referred to as the Princeps mathematicorum (Latin, “the foremost of mathematicians”) and “greatest mathematician since antiquity”, Gauss had an exceptional influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.
Augustin-Louis Cauchy was a French mathematician reputed as a pioneer of analysis. He was one of the first to state and prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost single-handedly founded complex analysis and the study of permutation groups in abstract algebra. A profound mathematician, Cauchy had a great influence over his contemporaries and successors. His writings range widely in mathematics and mathematical physics.
“More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy).” Cauchy was a prolific writer; he wrote approximately eight hundred research articles and five complete textbooks.
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondencebetween the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor’s method of proof of this theorem implies the existence of an “infinity of infinities”. He defined the cardinal and ordinal numbers and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware.
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded, although it is his only paper in the field, as one of the most influential papers in analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity.
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theoryand the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Hilbert adopted and warmly defended Georg Cantor‘s set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
Karl Theodor Wilhelm Weierstrass was a German mathematician often cited as the “father of modern analysis“. Despite leaving university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnastics.
Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals.
Srinivasa Ramanujan FRS was an Indian mathematician and autodidact. Though he had almost no formal training in pure mathematics, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. When his skills became obvious and known to the wider mathematical community, centered in Europe at the time, he began a famous partnership with the English mathematician G. H. Hardy. The Cambridge professor realized that Ramanujan had rediscovered previously known theorems in addition to producing new ones.
During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities andequations). Nearly all his claims have now been proven correct, although some were already known. His original and highly unconventional results, such as the Ramanujan prime and the Ramanujan theta function, have inspired a vast amount of further research. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work.
Of notably deep religious conviction, Ramanujan credited his substantial mathematical capacities to divinity: ‘”An equation for me has no meaning,” he once said, “unless it expresses a thought of God.”‘
Kurt Friedrich Gödel was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.
Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursiveaxiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.
John von Neumann was a Hungarian-American pure and applied mathematician, physicist, inventor, computer scientist, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics,functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics(quantum mechanics, hydrodynamics and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines,stochastic computing), and statistics.
He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer. He published 150 papers in his life: 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. His last work, an unfinished manuscript written while in the hospital, was later published in book form as The Computer and the Brain.
Sir Andrew John Wiles is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is most notable for proving Fermat’s Last Theorem, for which he received the 2016 Abel Prize. Wiles has received numerous other honours.
Want to see one giant after another? Here you go…