Mathematicians — Teacher & Student

Founder of a brotherhood that held number to be the essence of reality; his theorem still anchors geometry.

• → Influenced: Euclid

His Elements made deductive proof from axioms the model of mathematical certainty for two thousand years.

• ← Influenced: Pythagoras
• → Influenced: Archimedes
• → Influenced: René Descartes

The greatest mathematician of antiquity, who anticipated the integral calculus by his method of exhaustion.

• ← Influenced: Euclid
• → Influenced: Fibonacci

Brought the Hindu-Arabic numerals and algebra to Europe in his Liber Abaci, reviving Western mathematics.

• ← Influenced: Archimedes
• → Influenced: René Descartes

Fused algebra and geometry into coordinate geometry, letting curves be studied as equations.

• ← Influenced: Euclid
• ← Influenced: Fibonacci
• ↔ Corresponded: Pierre de Fermat
• → Influenced: Isaac Newton

A magistrate by trade who founded number theory and, with Pascal, the theory of probability.

• ↔ Corresponded: René Descartes
• → Influenced: Isaac Newton
• → Influenced: Gottfried Leibniz

Invented the calculus (his 'method of fluxions') to describe motion and change with mathematical law.

• ← Influenced: René Descartes
• ← Influenced: Pierre de Fermat
• ↔ Corresponded: Gottfried Leibniz

Independently invented the calculus and gave it the notation still used today, sparking a bitter priority dispute.

• ← Influenced: Pierre de Fermat
• ↔ Corresponded: Isaac Newton
• → Taught: Johann Bernoulli

A leading developer of Leibniz's calculus and the private tutor of the young Euler in Basel.

• ← Taught: Gottfried Leibniz
• → Taught: Leonhard Euler

The most prolific mathematician in history, who shaped notation, analysis, graph theory, and much else.

• ← Taught: Johann Bernoulli
• ↔ Corresponded: Joseph-Louis Lagrange

Recast mechanics on a purely analytic footing and advanced the calculus of variations and number theory.

• ↔ Corresponded: Leonhard Euler
• → Influenced: Augustin-Louis Cauchy
• → Influenced: Carl Friedrich Gauss

The 'prince of mathematicians', who transformed number theory, geometry, statistics, and astronomy.

• ← Influenced: Joseph-Louis Lagrange
• → Taught: Bernhard Riemann
• ↔ Corresponded: Augustin-Louis Cauchy

Gave calculus its rigorous foundation with precise limits and continuity, and founded complex analysis.

• ← Influenced: Joseph-Louis Lagrange
• ↔ Corresponded: Carl Friedrich Gauss
• → Influenced: Bernhard Riemann

Gauss's student whose curved geometry, integral, and zeta function reshaped analysis and later physics.

• ← Taught: Carl Friedrich Gauss
• ← Influenced: Augustin-Louis Cauchy
• → Influenced: Henri Poincaré
• → Influenced: Georg Cantor

Created set theory and proved that infinities come in different sizes — a revolution resisted in his lifetime.

• ← Influenced: Bernhard Riemann
• → Influenced: David Hilbert

The last universalist, who founded topology and chaos theory and anticipated relativity.

• ← Influenced: Bernhard Riemann
• → Influenced: David Hilbert

Set the agenda of twentieth-century mathematics with his 23 problems and his programme to formalise all of it.

• ← Influenced: Georg Cantor
• ← Influenced: Henri Poincaré
• → Taught: Emmy Noether
• → Influenced: Kurt Gödel

The founder of modern abstract algebra, whose theorem ties every symmetry to a conservation law in physics.

• ← Taught: David Hilbert

His incompleteness theorems showed that any consistent formal system leaves true statements it cannot prove, ending Hilbert's dream.

• ← Influenced: David Hilbert