Leonhard Euler was born in Basel, Switzerland, on 15 April 1707. Euler's mother was Marguerite (Brucker) Euler, and his father was Paul Euler, a Swiss reform (Calvinist) pastor at St. John's Church in Basel. In 1708, Paul received a call to serve as pastor in Riehen, a village near Basel. It is here that Euler spent his youth.

Paul Euler had done his theological studies at the University of Basel, where he also received some education in mathematics from Jakob Bernoulli. He took great interest in his son's intellectual development, and educated young Euler himself, at home in Riehen. Later, Euler attended schools in Basel, and he entered the University of Basel in 1720. His father wanted Euler to enter the ministry, and so persuaded his son to pursue theological studies. After three years of study, Euler matriculated into the Theology Department.

During this time, however, Euler's thoughts were not devoted exclusively to his theological studies. He was also tutored by Jakob Bernoulli's brother, Johann, then-chair of mathematics at the university. In 1724, Euler was awarded his Master of Arts degree, and gave a lecture comparing the philosophies of Isaac Newton and René Descartes. His father, still desiring for Euler to become a minister, exerted some pressure in this direction, but soon relented and allowed his son to pursue a career in mathematics.

While in Basel, Euler submitted his first paper to the Paris Academy, competing in the Academy's annual prize competition. This piece, Meditationes super problemate nautico (Thoughts on a nautical problem), earned Euler the Academy's prize. This was the first of 15 prizes Euler would be awarded for this competition.

The conclusion of Euler's time in Basel was precipitated by the move of his friends, brothers Daniel and Nicolaus Bernoulli, to the new St. Petersburg Academy in Russia. Shortly after their arrival in St. Petersburg, Daniel sent a letter to Euler from the Academy's president, Laurentius Blumentrost, inviting Euler to join the Academy faculty. Unfortunately, the position offered to Euler was in physiology, a field with which he was unaquainted. Considering his options, Euler decided to study medicine at Basel, in preparation for a move to St. Petersburg.

During this period, a position in physics became available at the University of Basel. Euler applied for this position, and contributed a paper in the course of the application process. However, This paper, Dissertatio physica de sono (Physical dissertation on sound), while notable, was insufficient to earn him the position.

This removed any remaining obstacle regarding the St. Petersburg offer. He left Basel in April 1727. Of the cross-European journey, du Pasquier notes that

"... [Euler] traveled down the Rhine by boat to Mayence. From there, the trip continued on foot through Fankfurt am Main, Kassel, Hanover, Hamburg, Lübeck, and then again by boat to Reval and Kronstadt."

• du Pasquier, L. Gustave; John Glaus, tr. Leonhard Euler and his Friends. Draft translation. Original French publication: Saint-Amand-Montrond, France, 1927.
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