Editing Pure mathematics (section)

===20th century===
At the start of the twentieth century mathematicians took up the [[axiomatic method]], strongly influenced by [[David Hilbert]]'s example. The logical formulation of pure mathematics suggested by [[Bertrand Russell]] in terms of a [[Quantifier (logic)|quantifier]] structure of [[Proposition (mathematics)|proposition]]s seemed more and more plausible, as large parts of mathematics became axiomatised and thus subject to the simple criteria of ''[[rigorous proof]]''.

Pure mathematics, according to a view that can be ascribed to the [[Bourbaki group]], is what is proved. "Pure mathematician" became a recognized vocation, achievable through training. That said, the case has been made pure mathematics is useful in [[engineering education]]:<ref>[[A. S. Hathaway]] (1901) [https://www.ams.org/journals/bull/1901-07-06/S0002-9904-1901-00797-5/S0002-9904-1901-00797-5.pdf "Pure mathematics for engineering students"], [[Bulletin of the American Mathematical Society]] 7(6):266–71.</ref>

:There is a training in habits of thought, points of view, and intellectual comprehension of ordinary engineering problems, which only the study of higher mathematics can give.