The Great Math Mystery (2015) [CC][HD] " Is math a human invention or the discovery of the language of the universe? "

I must confess I didnt watch the video, cause Ive had this discussion many many times before and I dont know if theres really anything new that can be said in a video of this kind. Having said that I am very much inclined to believe that math is fundamental at least in some way.

Many results in math come directly from pathologies given by the basic axioms most mathematicians use ( ZFC ), many weird things happen due to axiom of choice, or we get results depending on our possition accepting this or that axiom. Many things are results of our skewed perception or our not so precise models of reality. But there are some other results, some other amazing coincidences I really cannot justify as, well, a coincidence, or a product of the way we define things.

About 70 years ago mathematicians developed category theory as a language to ease our understanding of another area ( algebraic topology ) but it turned out to be the most amazing thing. Category theory is a language for mathematics and a math branch itself, the point is that it helps us relate so many concepts and areas of mathematics in ways we couldnt or in ways that would have been incredibily complicated before. It is due to category theory that we could stablish many relationships between algebra and geometry, in fact a basic result of algebraic geometry says that 'to study algebra' is the same as 'studying geometry' ( Im being very lax with my terminology ), and this is a very common phenomenom, we can have relationships between probablility and algebra, logic and geometry, algebra and geometry, etc.

And this to me is enough proof, we managed to develop all these areas of mathematics almost independently from each other, somebody worked in topology, somebody else was doing complex analysis and somebody else was doing algebra and it turns out we can mix all of this things and find relationships between them all and use this relationships to find relationships between all these different areas. We didnt decide on putting them all together like this, by formally developing our simple mathematics we got something that I certainly wasnt expecting. I dont think we could have put all of this together so nicely even if we would've wanted to.

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