Timeline

  1. 1707
    Born on April 15, in Basel, Switzerland.
  2. 1720
    Enters the University of Basel, at 13 years old. He began studying with Johann Bernoulli.
  3. 1727
    Moves to the Academy of Sciences in Saint Petersburg, Russia.
  4. 1735
    Solve the Basel problem and analyze the Königsberg bridges.
  5. 1738
    He loses almost all vision in his right eye.
  6. 1741
    He goes to the Berlin Academy, at the invitation of Frederick II of Prussia.
  7. 1748
    Publishes the Introductio in analysin infiniterum, where $e^{ix} = \cos x + i \sin x$ appears.
  8. 1750
    In a letter to Goldbach, he states the formula for polyhedra $V - A + F = 2$.
  9. 1766
    Returns to Saint Petersburg, at the invitation of Catherine the Great. A cataract affects the left eye.
  10. 1771
    Cataract surgery fails and he is left practically blind. Keep working.
  11. 1783
    Dies in 18 September, in Saint Petersburg.
  1. Born and raised in Switzerland. At 13 he enters the university and starts Saturday lessons with Johann Bernoulli.
  2. He travels down the Rhine by boat, crosses Germany by coach and sets sail from Lübeck for Russia.
  3. He works at the Academy of Sciences. He solves the Basel problem, studies the Königsberg bridges and loses the sight of his right eye.
  4. At the invitation of Frederick II he moves to the Berlin Academy. He publishes the Introductio in analysin infinitorum and the formula $e^{ix}=\cos x+i\sin x$.
  5. He returns at the invitation of Catherine the Great. He goes almost blind but keeps dictating papers until his death in 1783.
Euler’s cities, from Basel to Saint Petersburg. Click a stage or use Follow the journey. Map: © OpenStreetMap contributors
Euler’s changes across Europe. The years mark each trip.

Euler’s life

Basel and the Bernoullis

Basel in 1615, in an engraving by Matthäus Merian: the city where Euler was born and studied.
Basel in 1615, in an engraving by Matthäus Merian: the city where Euler was born and studied.Matthäus Merian · public domain

Euler was born in Basel, the son of Paul Euler, a Protestant pastor who had attended classes by mathematician Jakob Bernoulli. The father wanted his son to also be a pastor, and Leonhard entered the university at 13 years old to study philosophy and theology.

Johann Bernoulli, the Saturday teacher.
Johann Bernoulli, the Saturday teacher.Rijksmuseum · CC0

The talent appeared quickly. Johann Bernoulli, brother of Jakob and one of the greatest mathematicians of Europe, agreed to receive him on Saturdays to answer any questions. Bernoulli did not give private lessons complete: he indicated difficult books and let the young man manage, helping only when he got stuck true. It was Bernoulli who convinced his father that his son was destined for mathematics.

In 1727, Euler competed for the Paris Academy prize with a work on the best position of masts of a ship. It came in second place, which is curious for someone who had never seen one seagoing ship.

Saint Petersburg: the first Russian phase

The building of the Academy of Sciences in Saint Petersburg, on the banks of the Neva River, engraving by 1753.
The building of the Academy of Sciences in Saint Petersburg, on the banks of the Neva River, engraving by 1753.G. Kachalov, according to drawing by M. Makhaev · public domain

Without a place in Basel, Euler accepted in 1727 a position at the new Academy of Sciences in São Paulo. Petersburg, where Daniel and Nicolaus Bernoulli, Johann’s sons, already worked. It is said that he arrived to the city on the same day that Empress Catherine I died, which left the Academy suspended for a while.

In 1733 he took over the professorship of mathematics left by Daniel Bernoulli. The following year he married with Katharina Gsell. They had thirteen children, only five of whom survived childhood. Euler said that Some of his best ideas came with a baby on his lap and children playing around him.

It was during this phase that he resolved the Basel problem and the Königsberg bridges, which we will see forward. It was also at this stage that he lost vision in his right eye, around 1738. Himself He attributed the loss to the effort with the maps he drew for the Academy.

Berlin: twenty-five years of production

Frederick II of Prussia, who took Euler to Berlin.
Frederick II of Prussia, who took Euler to Berlin.Atelier by Antoine Pesne, 1745 · public domain

In 1741, Euler accepted Frederick II’s invitation to the Berlin Academy, where he stayed 25 years. There he wrote some of the books that organized calculus for subsequent generations, such as Introductio in analysin infiniterum (1748) and the Institutiones calculi differentialis (1755).

Title page of *Introductio in analysin infiniterum* (1748), where Euler's formula appears.
Title page of Introductio in analysin infiniterum (1748), where Euler’s formula appears.Public domain

He also wrote more than 200 letters to a young German princess, explaining physics, astronomy, philosophy and mathematics for someone without training in the area. Published as Letters to a Princess of Germany, became a bestseller throughout Europe: one of the first great books on scientific dissemination.

*Letters to a Princess of Germany*, edition of 1768.
Letters to a Princess of Germany, edition of 1768.Imperial Academy of Sciences · public domain

Back to Russia: the work in the dark

Catherine the Great, empress of Russia.
Catherine the Great, empress of Russia.Alexander Roslin public domain

In 1766, Catherine the Great took Euler back to St. Petersburg. Shortly afterwards, a cataract it hit the eye that was still working. A surgery on 1771 was unsuccessful, and in the same year a fire destroyed his house.

What comes next is most impressive: about half of Euler’s work was produced after of that. With an extraordinary memory and mental calculation capacity, he dictated the work to children and assistants, such as Nicolas Fuss. In some years it reached an average of one article per week.

Euler in 1778, at 71 years old and practically blind.
Euler in 1778, at 71 years old and practically blind.Joseph Friedrich August Darbes · public domain

On 18 September 1783, after spending the morning calculating the rise of hot air balloons, new that year, and the orbit of the planet Uranus, discovered shortly before, had a stroke while He had tea with his grandson. The philosopher Condorcet summarized: “he stopped calculating and living”.

He left so much material that the Saint Petersburg Academy continued publishing his unpublished works for about 50 years. His complete works, the Opera Omnia, occupy dozens of volumes.

All topics by Leonhard Euler · The language that Euler left us →

Credits and sources of images.