Re:Some stuff I found interesting about number theory research
by jkhdigital on Monday July 26, 2021 @10:58AM
(#27960198)
I'm a PhD student in computer science, and after spending some time on this subject I'm pretty well convinced that parts of mathematics and CS are converging towards a more unified foundational framework that will benefit both fields tremendously.
In a nutshell, the key challenge is taking the core of complexity theory (which is easy to formalize in terms of state machines) and migrating it into the language(s) of category/type theory (which is much more modular/compositional).
In a nutshell, the key challenge is taking the core of complexity theory (which is easy to formalize in terms of state machines) and migrating it into the language(s) of category/type theory (which is much more modular/compositional).
A couple interesting recent works in this area:
Categorical Complexity: https://www.cambridge.org/core/services/aop-cambridge-core/c...
Dusko Pavlovic's Monoidal computer series: 1. https://arxiv.org/pdf/1208.5205 2. https://arxiv.org/pdf/1402.5687 3. https://arxiv.org/pdf/1704.04882