What did Wilhelm Ackermann contribute to math?

Answer 1

Wilhelm Friedrich Ackermann was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

Ackermann was awarded a Ph.D. in 1925 for a consistency proof of arithmetic apparently without full Peano induction (although it did use e.g. induction over the length of proofs).

In 1928, Ackermann helped David Hilbert turn his 1917 - 22 lectures on introductory mathematical logic into a text, Principles of Mathematical Logic. This text contained the first exposition ever of first-order logic, and posed the problem of its completeness and decidability. Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).