Stern became Ordinarius (full professor) at Göttingen University in 1858, succeeding Carl Friedrich Gauss. Stern was the first Jewish full professor at a German university. As a professor, Stern taught Gauss"s student Bernhard Riemann.
Stern was very helpful to Ferdinand Eisenstein in formulating a proof of the quadratic reciprocity theorem.
Stern was interested in primes that cannot be expressed as the sum of a prime and twice a square (now known as Stern primes). He is known for formulating Stern"s diatomic series
1, 1, 2, 1, 3, 2, 3, 1, 4, … (sequence A002487 in OEIS)
that counts the number of ways to write a number as a sum of powers of two with no power used more than twice.
He is also known for the Stern–Brocot tree which he wrote about in 1858 and which Brocot independently discovered in 1861.