  In a series of lectures given in 2003 soon after receiving the Fields Medal
for his results in the Algebraic Geometry Vladimir Voevodsky (1966-2017)
identifies two strategic goals for mathematics, which he plans to pursue in his
further research. The first goal is to develop a "computerised library of
mathematical knowledge", which supports an automated proof-verification. The
second goal is to "bridge pure and applied mathematics". Voevodsky's research
towards the first goal brought about the new Univalent foundations of
mathematics. In view of the second goal Voevodsky in 2004 started to develop a
mathematical theory of Population Dynamics, which involved the Categorical
Probability theory. This latter project did not bring published results and was
abandoned by Voevodsky in 2009 when he decided to focus his efforts on the
Univalent foundations and closely related topics. In the present paper, which
is based on Voevodsky's archival sources, I present Voevodsky's views of
mathematics and its relationships with natural sciences, critically discuss
these views, and suggest how Voevodsky's ideas and approaches in the applied
mathematics can be further developed and pursued. A special attention is given
to Voevodsky's original strategy to bridge the persisting gap between the pure
and applied mathematics where computers and the computer-assisted mathematics
have a major role.
