History of Mathematics

A Babylonian clay tablet listing Pythagorean triples in base-60, showing sophisticated number work a thousand years before Pythagoras.

Egypt's great problem-book taught fractions, areas, and linear equations, preserving the practical mathematics of the Nile scribes.

The first to prove geometric statements by reasoning rather than measurement, founding the idea of the mathematical theorem.

His school made number the key to the cosmos and gave geometry its most famous theorem, binding mathematics to philosophy and music.

Working in Alexandria, Euclid organised geometry into a deductive system of axioms and proofs that defined rigour for two millennia.

The most influential textbook ever written: thirteen books deriving geometry and number theory from a handful of postulates.

The greatest mathematician of antiquity approximated π, found areas and volumes by exhaustion, and anticipated the integral calculus.

His treatise on conic sections — ellipse, parabola, hyperbola — gave astronomy and later physics the curves of orbits and trajectories.

The 'father of algebra' studied equations in whole numbers; his Arithmetica seeded number theory and Fermat's famous marginal note.

The last great scholar of the Alexandrian school edited and taught geometry and astronomy before her murder closed an age.

The Baghdad scholar who gave us the words 'algebra' and 'algorithm', turning the solving of equations into a systematic art.

Al-Khwarizmi's treatise codified the systematic solution of linear and quadratic equations — the birth certificate of algebra.

He freed algebra from geometry, worked with powers and polynomials, and gave an early form of proof by mathematical induction.

The poet-mathematician solved cubic equations geometrically and probed the parallel postulate, foreshadowing non-Euclidean geometry.

His Liber Abaci introduced Hindu-Arabic numerals and place value to Europe, transforming commerce, accounting, and mathematics.

He graphed quantities against time, summed infinite series, and glimpsed coordinate geometry three centuries before Descartes.

His Ars Magna published the solution of the cubic and quartic and first reckoned with the 'impossible' square roots of negatives.

By using letters for both knowns and unknowns, Viète created symbolic algebra and turned equations into a general calculus of form.

By joining algebra to geometry through coordinates, Descartes created analytic geometry and a new mathematical language for physics.

The founder of modern number theory also co-founded probability and analytic geometry, leaving a margin note that haunted math for 350 years.

John Napier's logarithms turned multiplication into addition, slashing the labour of astronomy, navigation, and finance for centuries.

Prodigy, inventor of a mechanical calculator, and — with Fermat — co-founder of the mathematical theory of probability.

Newton's method of fluxions gave a calculus of motion and change, welded to a physics that explained the heavens and the tides.

Leibniz invented the calculus independently and gave it the elegant ∫ and d notation that mathematicians still use today.

Newton's masterwork derived the laws of motion and universal gravitation, proving that one mathematics governs earth and sky alike.

A dynasty of Swiss mathematicians spread and extended the new calculus, founding the calculus of variations and early probability.

The most prolific mathematician in history reshaped notation, founded graph theory and topology, and united e, i, and π in one identity.

He recast mechanics in pure analysis and advanced the calculus of variations, number theory, and the theory of equations.

The 'Newton of France' perfected celestial mechanics and built the analytic theory of probability into a mathematical science.

His theory of heat showed any signal can be built from waves, giving science and engineering the indispensable Fourier series.

The 'prince of mathematics' revolutionised number theory, gave the first rigorous proof of algebra's fundamental theorem, and touched every field.

Cauchy put the calculus on firm ground with rigorous limits and continuity, and founded complex analysis as a systematic theory.

Gauss's book at twenty-four organised number theory into a rigorous discipline, introducing modular arithmetic and much more.

Dead at twenty-six, Abel proved the general quintic cannot be solved by radicals and opened the modern theory of groups and functions.

The night before a fatal duel at twenty, Galois sketched group theory, revealing exactly which equations can be solved by radicals.

The 'father of modern analysis' gave the calculus its rigorous ε–δ definitions of limit and continuity that students still learn.

Riemann remade geometry with curved manifolds — the language of general relativity — and posed the hypothesis that still rules number theory.

Lobachevsky and Bolyai independently built consistent geometries denying Euclid's parallel postulate, shattering the idea of one true space.

Cantor created set theory and proved there are different sizes of infinity, giving mathematics a new and controversial foundation.

The last universalist founded algebraic topology and chaos theory and posed the conjecture that would stand unproven for a century.

The founder of modern abstract algebra, she also proved the theorem linking symmetries to conservation laws at the heart of physics.

A self-taught genius from India whose astonishing formulas for partitions, series, and continued fractions still yield new mathematics.

David Hilbert's list of open problems set the agenda for twentieth-century mathematics and dreamed of a complete, provable foundation.

His incompleteness theorems proved that any rich formal system must contain true statements it can never prove — ending Hilbert's dream.

A monumental attempt to derive all mathematics from logic; it took hundreds of pages to prove that 1 + 1 = 2.

By defining an abstract computing machine, Turing settled what is computable, founded computer science, and formalised the algorithm.

Andrey Kolmogorov grounded probability in measure theory, finally turning a study of games into a rigorous branch of mathematics.

A secret collective of French mathematicians rebuilt the whole subject from set-theoretic axioms in a vast, rigorous, abstract treatise.

He named and mapped fractals — infinitely rough shapes with fractional dimension — revealing hidden geometry in coastlines, markets, and clouds.

Appel and Haken proved any map needs only four colours — the first major theorem whose proof relied essentially on a computer.

Dozens of mathematicians across tens of thousands of pages catalogued every 'atom' of symmetry — one of the largest proofs ever made.

Andrew Wiles proved the 350-year-old conjecture using deep tools from elliptic curves and modular forms — a landmark of modern number theory.

Grigori Perelman proved the century-old topology conjecture and then declined both the Fields Medal and a million-dollar prize.