Mangoldt completed his Doctorate of Philosophy (Ph.D) in 1878 at the University of Berlin, where his supervisors were Ernst Kummer and Karl Weierstrass.[1] He contributed to the solution of the prime number theorem by providing rigorous proofs of two statements in Bernhard Riemann's seminal paper "On the Number of Primes Less Than a Given Magnitude". Riemann himself had only given partial proofs of these statements. Mangoldt worked as professor at the RWTH Aachen and was succeeded by Otto Blumenthal.