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 to

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). A couple interesting recent works in this area: Categorical Complexity: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FB2CAC644C697FEF1092C285D784CAB4/S2050509420000262a.pdf/categorical-complexity.pdf https://www.cambridge.org/core/services/aop-cambridge-core/c... Dusko Pavlovic's Monoidal computer series: 1. https://arxiv.org/pdf/1208.5205 https://arxiv.org/pdf/1208.5205 2. https://arxiv.org/pdf/1402.5687 https://arxiv.org/pdf/1402.5687 3. https://arxiv.org/pdf/1704.04882 https://arxiv.org/pdf/1704.04882