The Founding Problems of the Philosophy of Mathematics: From the Simplest to the Most Complex Problems (Part II) Hilbert and Brouwer had different views on mathematics, with Hilbert seeing mathematics as a formalist game

The Founding Questions of the Philosophy of Mathematics: From the Simplest to the Most Complex (Part II)

Hilbert and Brouwer had different views on mathematics, with Hilbert seeing mathematics as a formalist game, while Brouwer valued mathematical realism more. Hilbert proposed a plan to try to build an axiomatic system that included all mathematics called the Hilbert Project, but Gödel's theorem proved that the plan was impossible, leading to a discussion of mathematical realism. In the logicist approach, mathematical theorems were reduced to logical propositions, but later Russell's paradox and Gödel's incompleteness theorem were discovered, making mathematical realism a controversial topic.