Euler Reshapes Mathematical Notation While Going Blind
The most prolific mathematician in history writes half his life's work after losing his sight completely
Quick facts
- Euler's dates
- 1707-1783
- Berlin period
- 1741-1766, c. 380 articles written
- Notation introduced
- e (1727), f(x) (1734), sigma (1755), i (1777)
- Vision
- One eye lost by 1740; total blindness after return to Russia
What happened
Leonhard Euler, born in 1707 in Basel, Switzerland, worked at the St Petersburg Academy of Sciences, then in Berlin for 25 years starting in 1741, then back in St Petersburg from 1766 until his death in 1783. During his 25 years in Berlin, Euler wrote around 380 articles, and after his return to St Petersburg, despite total blindness, he produced almost half of his entire lifetime output. He had already lost the use of one eye by 1740 and became almost completely blind after an illness soon after returning to Russia. Euler introduced or standardized much of the mathematical notation still in everyday use: the symbol e for the base of natural logarithms in 1727, the notation f(x) for a function in 1734, pi for the ratio of a circle's circumference to its diameter, the summation symbol sigma in 1755, and i for the square root of negative one in 1777.
Why it matters
Euler's notational choices are so deeply embedded in modern mathematics that most students learn them as if they were natural facts rather than one 18th-century mathematician's specific inventions, and his output across analytic geometry, trigonometry, calculus, and number theory makes him, by volume, the most prolific mathematician in history, a record made stranger still by the second half of it being produced after he could no longer see his own writing.
How we know
Euler's collected works run to dozens of volumes still being published by the Euler Commission, and his correspondence and the Berlin and St Petersburg Academy records independently document both his output totals and the timeline of his vision loss.
Sources
- MacTutor History of Mathematics, University of St Andrews. Leonhard Euler · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
- MacTutor History of Mathematics, University of St Andrews. Quadratic, cubic and quartic equations · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry.
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