Math

There are lots of hysterical complains in the social media gutters, like /g/, about Leetcode and apparent uselessness of such math-based drills.. Nothing can be further from the truth. First of all, every remarkable programming achievements of the past, be it of NASA missions, or of Bell Labs, or of Ericsson, or some academic breakthroughs like ML or Scheme or Haskell – they all are due to the fact that the only way to have access to a computer used to be through mathematics, applied and even purely theoretical. The early Computer Science was basically considered, and especially taught at good schools, as applied math. It should remain this way(but, unfortunately, everything has been ruined). ...

This is a short follow-up to this post https://lawrencecpaulson.github.io/2023/11/01/Foundations.html To define the foundations of mathematics mere symbols are not enough. We have to consider the actual existence of what we call “reality” or “Universe” which has some observable properties. the “Mind (of an external observe)”, which actually builds and maintains a “map” (which is not a territory). the actual existence of a language-based shared human culture which stores the “previous results” invention of a symbolic notations and formal methodologies for creating “system” So, yes, intuitionists were right, and yes, the set theory is jsut another system, generalizing from what the Mind observes. ...