On A.Ya. Khinchin's paper ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926): A translation with introduction and commentary

A.N. Kolmogorov’s Calculus of Problems and Homotopy Type Theory

“…However, historically the idea of the continuum has been created by idealization of a really observable continuous environment. Now 11 Kolmogorov's rejection of Hilbert's Formalism is shared by his friend and colleague of the time Alexandr Khintichin who in 1926 published a philosophical paper Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics [42], English translation in [89]. The "subject matter" in the title is English translation of Russian "predmet", which can be also translated into English as "object" and into German as "Gegenstand" -notice the same German word used by Kolmogorov in his critique of Hilbert in the above quote.…”

The beginnings of the Soviet encyclopedia. The utopia and misery of mathematics in the political turmoil of the 1920s

“…Khinchin explains how Weyl and Brouwer, when they wanted to "pitilessly expell everything which hides its emptiness under the veil of a perfect logical outside from mathematics" (Khinchin, 1926;p.184) did not wish to prove how some contemporaneous mathematics were pointless but wanted to show "a deep inner illness" of contemporaneous mathematics. In the Soviet society under construction, formalism was beginning to be considered with high suspicion (for details on these questions, see (Verburgt, 2016)). This may partly explain why at the time of the Stalinist turn of the 1930s, even a star mathematician as Kolmogorov felt necessary to make rhetorical efforts to convince his readers that, though deeply involved in probability theory, he was acting as a mathematician and was concerned only with the mathematical aspects, leaving to others the question of interpretation, connection to the real world and practical application of his research.…”