TL;DR
This paper critiques Wittgenstein's view of mathematics as a linguistic game, emphasizing the need to understand the complex, speculative nature of modern mathematical thinking and questioning its philosophical foundations.
Contribution
It offers a new perspective on the philosophy of mathematics by challenging Wittgenstein's linguistic approach and highlighting the importance of complexification and experimental methods.
Findings
Mathematics lacks empirical automatism and physical motricity.
Complexification is essential for understanding mathematical philosophy.
Numerical experiments reveal the depth of mathematical questioning.
Abstract
Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays, philosophy has to face with the growing, exponential ramified tree of speculative mathematical thinking. Our main (problematical) theses are: 1. In mathematics, there is no empirical automatism, and no separate, physical-like motricity. 2: The irreversible-synthetical must force to complexify the exegetical game of philosophy; numerical experiments in algebra and in number theory are a kind of letting blow up all possible problems; 4. The nature of mathematical questioning still remains in question.
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