  Kolmogorov's Calculus of Problems is an interpretation of Heyting's
intuitionistic propositional calculus published by A.N. Kolmogorov in 1932.
Unlike Heyting's intended interpretation of this calculus, Kolmogorov's
interpretation does not comply with the philosophical principles of
Mathematical Intuitionism. This philosophical difference between Kolmogorov and
Heyting implies different treatments of problems and propositions: while in
Heyting's view the difference between problems and propositions is merely
linguistic, Kolmogorov keeps the two concepts apart and does not apply his
calculus to propositions. I stress differences between Kolmogorov's and
Heyting's interpretations and show how the two interpretations diverged during
their development. In this context I reconstruct Kolmogorov's philosophical
views on mathematics and analyse his original take on the Hilbert-Brouwer
controversy. Finally, I overview some later works motivated by Kolmogorov's
Calculus of Problems and propose a justification of Kolmogorov's distinction
between problems and propositions in terms of Univalent Mathematics.
