Leonhard Euler’s relations with Russia and the St. Petersburg Academy certainly played a part in his reputation as the most distinguished mathematician of the eighteenth century. A Swiss mathematician who made extensive contributions in the subjects of geometry, calculus, mechanics, and number theory, Euler set the foundation for the most general branch of mathematics, later named topology. His legacy can be traced directly to Russia, though, ironically, a life in St. Petersburg was not his first choice. Upon his application for a physics scholarship being rejected by the University of Basel, he was instead offered a position as a physiologist at the Russian Academy of Science. His two friends, Nikolaus and Daniel Bernoulli, had already received positions as professors in the same institution, and Euler soon followed, almost immediately switching to the mathematics department. It was during this first period in St. Petersburg that he realised he had entered ‘into the paradise of scholars’.

Founded by Peter the Great in 1724, the Petersburg Academy was a component of the emperor’s plan for modernising Russia. His decision to model the academy on the Parisian Academy of Sciences was not only a way of introducing Russia to the Enlightenment and Western science, but also of ensuring the institution was allied closely with the imperial government. The academy began to attract young scientists who received large incentives for their work: free accommodation, firewood for heat, and a fixed salary to name a few. Euler’s first position was as a student (*é**l**è**ve*), though he quickly became an adjunct and was able to engage in the academy’s meetings and publish papers in its main journal, *Commentarii Academiae Scientiarum Imperialis Petropolitana*. Euler was given full freedom for his research projects, and his extensive mathematical work, particularly in mechanics, is reflected in his impressive publications.

In 1727, his first paper to the academy – concerning the motion of water in inclined tubes – received appraisal by Daniel Bernoulli, who wrote:

The theory of the motion of water, which is very general … [and] had been sought out by the cleverest geometers, but in vain … but what is even more remarkable is that at the same time this theory was found by a different method by Mr. Euler of Basel.

Euler decided to cast aside classical hydrodynamics following his paper, ‘De efflux aquae’ (Of the flow of water), since it was Bernoulli’s primary field, and began to explore differential geometry. Though they did not often collaborate in their works, Bernoulli’s and Euler’s research complemented each other; while Bernoulli opted to avoid mathematics in his scientific thinking, Euler’s scientific thinking emerged *from* mathematical algorithms. The following year, Euler published three articles in the *Commentarii* on the subjects of the elasticity of air, reciprocal geometries, and tautochrone. This was made possible by the academy’s new printing press acquired from Holland, and particularly highlighted Euler’s work on elastic curves. His unification of several curves through a series of differential equations was a mere introduction to his research into the field of mechanics.

Beyond this, Euler participated in the academy’s effort to spread scientific ideas to the wider public. This proved to be a difficult task, considering arithmetic and geometry were labelled as magic in seventeenth century Russia, and such ideas continued to exist in the following century – indeed, efforts to inform literate Russians of Western scientific advances in *Primechaniya k Vedomostyam* did initially fail. Nonetheless, Euler gave the most lectures out of all adjuncts of the academy on scientific discoveries and was appointed the rank of professor soon after. During this period, his field of research was extended to astronomy, geography, and even fields of music, but mathematics remained his strongest suit.

His years in St. Petersburg after 1727 saw him shift away from geometry and toward infinitary analysis as he began to stress the importance of functions in mathematical analysis, which allowed for the simplification of analytical operations. Other key works of this time include his development of the theory of trigonometric and logarithmic functions, and integral calculus, in his manuscript *Calculus Differentialis*. His mathematical research continued for almost fifteen years in St. Petersburg, where he gained an international reputation. This was possible through the political circumstances of Russia that granted him academic freedom, and the *Commentarii *publication programme. Euler, in a letter to fellow scientist Johann Schumacher, expressed his gratitude to the institution:

“I and all others who have had the good fortune to spend some time in the Russian Imperial Academy of Sciences must admit that we owe all that we are to the advantageous circumstances in which we found ourselves here.”

Sadly, the death of Tsarina Anna in 1740 swept Russia into political turmoil, and Euler resorted to accepting the Prussian King Frederick the Great’s earlier offer for him to transfer to The Prussian Academy. The next year, he set off for Berlin.

Euler’s time in Berlin was far from ideal, largely as a result of his strained relations with Frederick. Euler was, at this point, Europe’s most distinguished mathematician, but the king treated him as an unsophisticated lowborn. He grew to criticise Euler’s abstract mathematics, and his overall inability to mesh with the fashions of his own royal court. In 1763, Euler was more than relieved when the newly ascended Catherine the Great invited him back to Russia. Her terms were very generous. She agreed to his demands for salary, and even gave him 10,800 rubles for a house, alongside a title as the noblest of scientists. Euler and his family arrived in St. Petersburg on 28 July 1766, and he began to restore the academy he had once thrived under to its previous splendour. Due to Euler’s deteriorating eyesight around this time, his son also helped with the rehabilitation of the academy. They improved the organisation of academy meetings, ordered new equipment, and appointed new members to conduct scientific research. This aligned with Catherine’s pledge to support further research into various fields of mathematics including mechanics and optics. Thus, Euler’s decade of leadership within the academy, beginning in 1766, was successful in improving its administration.

Euler’s scientific work also continued in his return to St. Petersburg: *Institutionum Calculi Integralis* in 1768, which contained several methods of indefinite integration and differentiation formulas, and *Theoria Motuum Lunae* concerning the theory of lunar motion, are examples of this. By 1771, Euler had completely lost his eyesight, but he continued to publish his works with the help of his young colleagues. He had so many papers that the Petersburg Academy was not able to publish them all. Aside from published papers, he laid out many basic principles of mechanics, astronomy, optics, and acoustics in his letters to the Prussian Princess Friederike Charlotte Brandenburg-Schwedt. It was through these exchanges, both in letter and physical form, that Euler was able to establish himself as one of the largest pedagogical influences in the history of mathematics. Considered the most successful scientist of the modern world, Euler died in 1783 in St. Petersburg at the age of 76.

Euler’s legacy should be remembered in terms of his special connection to Russia. It was at the Petersburg Academy that his professional career first began, and where it ended. Though Euler remained a Swiss citizen for the entirety of his life, Russia was his adopted home. He never felt as comfortable in Berlin as he did in the urban St. Petersburg, and it was inevitable that he would return later in his career. It was in St. Petersburg that Euler was able to delve into the many fields of mathematics under the freedom of the St. Petersburg Academy, and he should undoubtedly be considered as a significant figure of the Russian scientific community.

**Written by Kat Jivkova**

**Bibliography: **

Bradley, Robert E., and Charles Edward Sandifer. *Leonhard Euler: Life, Work and Legacy / Edited by Robert E. Bradley, C. Edward Sandifer.* Amsterdam: Elsevier, 2007.

Calinger, Ronald S. Leonhard Euler: Mathematical Genius in the Enlightenment / Ronald S. Calinger. Princeton, NJ: Princeton University Press, 2015.

European Consortium for Mathematics in Industry. ‘Leonhard Euler and Saint Petersburg.’ [Online]. [Accessed on 23 January 2021].

Schulze, Ludmilla. “The Russification of the St. Petersburg Academy of Sciences and Arts in the Eighteenth Century.” *The British journal for the history of science* 18, no. 3 (1985): 305–335.

Tent, M. B. W. Leonhard Euler and the Bernoullis : Mathematicians from Basel / M.B.W. Tent. Natick, Mass: A.K. Peters, 2009.