What would it have been like to be a student of Leonhard Euler? Until we invent time machines, it will be impossible to answer this question. Still, it is almost impossible not to ask it anyway.

By all accounts, Euler was regarded as an excellent teacher. His eulogists all mention that he was a kind and pious man, a great genius and wonderful teacher. There are stories that students from abroad, particularly from France and Russia, studying in Berlin would rent rooms in Euler's house and that they would talk about science and mathematics at meal times. Accounts of the last day of Euler's life, in September 1783, include the detail that he spent part of that day teaching mathematics to his grandson.

Despite these flowery tributes, we have very few accounts beyond the snippets cited above of Euler actually in the act of teaching.

When Peter the Great founded his Academy of Sciences in St. Petersburg, he intended it to be a comprehensive scholarly institution, doing the latest in scientific research, educating the youth of Russia and promoting the sciences among the general public. Euler supposedly had responsibilities in all three points of this academic mission, but he seems to have left few footprints outside his work in basic research.

The archives of the Academy [SPA 1886, pp. 222–224] reprint a catalog that tells us that in 1732, Euler would teach physics on Monday and Tuesday mornings, and on Saturdays he “will confirm its truth by experiments.” His course seems to be the only one in the catalog (which is only two pages long) that tells us that he will be using a textbook. “In this matter, he will follow the esteemed s'Gravesand's book Physices Elementa Mathematica.”

In 1734, he taught his Course in Mathematics from 2:00 to 3:00 in the afternoon. The catalog [SPA 1886, pp. 554–555] does not tell us which days that course met, nor does it mention a textbook.

These were the only catalogs I could find from Euler's time in St. Petersburg. I found nothing to describe the outcomes of these courses.