Nicole Oresme
Latitude of forms, fractional exponents, harmonic series divergence
Launch PresentationLuca Pacioli
Summa de Arithmetica, double-entry bookkeeping, Divina Proportione
Launch PresentationScipione del Ferro
First solution of the depressed cubic, mathematical secrecy
Launch PresentationNiccolò Tartaglia
General cubic solution, Nova Scientia, ballistics, Italian Euclid
Launch PresentationLodovico Ferrari
Quartic equation solution, mathematical duels, reduction method
Launch PresentationAbraham de Moivre
De Moivre's formula, normal distribution, Doctrine of Chances
Launch PresentationColin Maclaurin
Maclaurin series, Treatise of Fluxions, Euler-Maclaurin formula
Launch PresentationJohann Lambert
Proof π is irrational, hyperbolic functions, Lambert W function
Launch PresentationAdrien-Marie Legendre
Legendre polynomials, least squares, elliptic integrals
Launch PresentationSiméon Denis Poisson
Poisson distribution, Poisson's equation, Poisson bracket
Launch PresentationJoseph Liouville
Transcendental numbers, Liouville's theorem, Sturm-Liouville
Launch PresentationOliver Heaviside
Heaviside step function, operational calculus, Maxwell's equations
Launch PresentationIntellectual Influence Map
Tracing the transmission of mathematical ideas across 2,500 years
Influence Narratives
Eight lineages that shaped the development of mathematics
The Greek Foundations
From Pythagoras's mystical belief that "all is number" through Zeno's paradoxes that interrogated the infinite, to Eudoxus's rigorous method of exhaustion, the Greeks built the first deductive framework for mathematics. Euclid synthesised this tradition into the Elements, the most influential textbook ever written. Archimedes pushed calculation to its limits, while Apollonius gave definitive form to the conic sections that would prove essential two millennia later.
Pythagoras → Zeno → Eudoxus → Euclid → Archimedes → Apollonius
The Eastern Transmission
While Europe stagnated, Brahmagupta formalised zero and negative numbers in 7th-century India. Al-Khwarizmi, working in Baghdad's House of Wisdom, synthesised Indian arithmetic with Greek geometry to create algebra as a discipline — his name giving us the word "algorithm." Through trade routes and translation movements, this knowledge reached Fibonacci, whose Liber Abaci introduced Hindu-Arabic numerals to a Europe still counting with Roman ones.
Brahmagupta → Al-Khwarizmi → Fibonacci → European mathematics
The Renaissance Algebraists
Cardano's Ars Magna (1545) broke open the cubic and quartic equations, revealing for the first time that square roots of negative numbers could be meaningful. Viete introduced systematic symbolic notation, replacing the verbal algebra of the ancients. Descartes then married algebra to geometry through coordinate systems, creating the analytic framework that made calculus possible.
Cardano → Viète → Descartes → Newton & Leibniz
The Analytic Revolution
Newton and Leibniz independently invented calculus in the 1680s, transforming mathematics from the study of static forms to the science of change. Their bitter priority dispute obscured the deeper truth: Leibniz's superior notation, transmitted through the Bernoulli family to Euler, created the continental analysis tradition that dominated the 18th century. Euler's unmatched output touched every branch of mathematics.
Fermat & Descartes → Newton ↔ Leibniz → Bernoullis → Euler
The Continental Analysis Tradition
Euler's influence radiated outward: Lagrange reformulated mechanics analytically, Laplace applied analysis to celestial mechanics and probability, and Fourier decomposed arbitrary functions into infinite sums of sines and cosines. This chain from Euler through the great French analysts created the mathematical physics that would dominate the 19th century and provide the foundation for modern engineering.
Euler → Lagrange → Laplace → Fourier → modern analysis
Geometry Reimagined
Gauss privately explored non-Euclidean geometry but never published; Lobachevsky and Bolyai independently broke the 2,000-year hold of Euclid's parallel postulate. Riemann then generalised geometry to curved spaces of arbitrary dimension. Klein's Erlangen Programme unified geometries through group theory, while Lie developed continuous symmetry groups — ideas that would prove essential for 20th-century physics.
Gauss → Lobachevsky & Bolyai → Riemann → Klein ← Lie
The Algebraic Revolution
Gauss's number theory inspired Abel and Galois to ask not just "can we solve this equation?" but "why can't we?" Galois's group theory, created the night before his fatal duel, became the language of symmetry itself. Through Dedekind's ideal theory and Noether's abstract algebra, this evolved into the modern structural approach. Grothendieck's revolutionary schemes unified algebraic geometry and number theory in the 20th century.
Gauss → Abel & Galois → Dedekind → Noether → Grothendieck
The Rigour Movement
Cauchy began the project of placing analysis on rigorous foundations; Weierstrass completed it with his epsilon-delta definitions. Cantor's set theory revealed the infinite in unexpected depth, but also generated paradoxes. Hilbert's programme to axiomatise all mathematics was shattered by Gödel's incompleteness theorems, while Turing showed the limits of computation itself — and in doing so, conceived the modern computer.
Cauchy → Weierstrass → Cantor → Hilbert → Gödel & Turing