I asked this question on Mathematics Stackexchange, but one of the users suggested that I ask this question at MathOverflow.
I've just come across a Twitter thread by Laurent Fargues explaining a work by Dustin Clausen & Peter Scholze under the name condensed mathematics and how condensed mathematics can algebrize topology and analysis. I find it somewhat surprising (or hard to believe) that you can do such a thing. So my question is can condensed mathematics completely algebrize topology and analysis, or can it only algebrize some analytic object close to algebraic geometry? Can we reprove theorem and inequalities in analysis such as mean value theorem, Hölder's inequality, dominated convergence theorem, and so on using condensed mathematics?