Euler's Universe — 18th-Century Mathematics by One Man

Euler left an enormous body of papers, letters, and textbooks and kept working with family and assistants after losing his sight. He introduced or popularized major notation, within a much wider eighteenth-century network.

About 26 min·7 nodes

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STEP 1 · Mathematician1696Basel· Main activity

Johann Bernoulli

Younger brother of Jakob and teacher of Euler. His 1696 brachistochrone problem opened the calculus of variations. He warred with both his brother and his son Daniel — but his Saturday lessons in Basel discovered the young Euler, perhaps his greatest gift to mathematics.

↓31 years later

STEP 2 · Mathematician1727Saint Petersburg· Main activity

Leonhard Euler

An exceptionally prolific author across analysis, number theory, mechanics, astronomy, and early graph problems. He introduced or popularized major notation and continued working by dictation with family and assistants after losing most of his sight.

↓8 years later

STEP 3 · Concept1735Saint Petersburg· Discovery

Infinite Series

Can you add infinitely many things and get a finite sum? From Zeno to Euler's magical summations.

↓1 year later

STEP 4 · Concept1736Saint Petersburg· Discovery

Graph Theory

The mathematics of connection — born from a Sunday walk puzzle, now the language of social networks and the brain.

↓Same year

STEP 5 · Concept1736Saint Petersburg· Discovery

Modular Arithmetic

The arithmetic of clocks — wrapping around at a modulus. The basic language of number theory and cryptography.

↓2 years later

STEP 6 · Mathematician1738Basel· Main activity

Daniel Bernoulli

A mathematician and physicist who treated fluid pressure, density, and velocity through conservation of energy. Work begun in St Petersburg led to Hydrodynamica, published in 1738, which analyzed fluid flow, pumps, and jets. Under assumptions such as steady, inviscid flow, the modern Bernoulli equation relates pressure, speed, and height and remains an important tool in fluid mechanics. The book also included an early kinetic model explaining gas pressure through moving particles. Bernoulli worked alongside Euler in St Petersburg from 1727 to 1733 and later taught in Basel.

↓10 years later

STEP 7 · Number system1748Berlin· Publication

The Complex Plane

The plane of numbers a + bi, combining real and imaginary axes and supplying roots for every non-constant complex polynomial.

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