Key contributors to the development of formalistic ideas include:
* Gottlob Frege (1848-1925): Laid the foundation for formal logic and attempted to reduce mathematics to logic.
* Giuseppe Peano (1858-1932): Developed a system of axioms for arithmetic, contributing to the idea of formalizing mathematical systems.
* David Hilbert (1862-1943): Strongly advocated for formalization in mathematics, aiming to prove the consistency and completeness of arithmetic. He developed the Hilbert program, a major influence on formalistic thinking.
* Bertrand Russell (1872-1970): His work on logic and set theory, particularly the paradoxes he uncovered, helped to highlight the need for formalization to avoid contradictions.
* Kurt Gödel (1906-1978): His incompleteness theorems, which showed that any sufficiently powerful formal system would contain undecidable propositions, had a significant impact on the formalist program.
Formalism as a philosophical approach to mathematics:
Formalism is a philosophical approach to mathematics that emphasizes the formal structure of mathematical systems. This means that the meaning of mathematical concepts is derived from the way they are represented within a formal system, rather than from any intuitive or empirical understanding.
It is important to note that formalistic approaches have been criticized, with alternative perspectives like constructivism and intuitionism offering different views on the nature of mathematical knowledge.
Overall, the development of formalism in mathematics was a complex and multifaceted process, with contributions from many individuals across several decades. It's not attributed to a single person but rather a culmination of work by mathematicians and logicians.