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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 structure of propositions 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.

The case was made that pure mathematics is useful in engineering education: