Some stuff I found interesting about number theory research

Re:Some stuff I found interesting about number theory research by mhh__ on Monday July 26, 2021 @09:25AM (#27959043)

I am kind of sceptical of these verified-mathematics projects in the sense that my litmus is whether I could easily verify my workings rather than the proofs I rely upon, but nonetheless I have enormous respect for those doing this work and really hope it comes to fruition.

I really hope this work trickles down to our programming - state machine problems are basically "solved" (for my needs at least), but more complex programs are really hard to prove.

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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).

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

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Re:Some stuff I found interesting about number theory research by mhh__ on Monday July 26, 2021 @04:25PM (#27964979)

I mostly hope you're right, good luck. Post your thesis here when the time comes.

I'm a bit of a philistine when it comes to cutting edge CS in this area so I'll leave you to it!

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Re:Some stuff I found interesting about number theory research by pramodbiligiri on Monday July 26, 2021 @10:44AM (#27959992)

When you say that state machine problems are basically solved, are you referring to any tools that you're using to reason about them?

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Re:Some stuff I found interesting about number theory research by mhh__ on Monday July 26, 2021 @04:24PM (#27964954)

By solved I really mean "in commercial use", there's probably a lot of research let to be done, but people are already verifying TLA+ specs all day everyday.

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