Mathematical Autodidact
2025 May 28
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Mathematical Autodidact
As I grow older, I find myself getting drawn towards things that I found interesting in the pre-university era. One such thing is mathematics. I had a blast preparing for IIT-JEE, and mathematics was my favorite subject.
Programming is about creativity and making something; mathematics is about truth and the search of aesthetics in that truth. Last year I picked up A Book of Abstract Algebra by Charles Pinter and it blew me away. I didn't manage to get to the end of it still, but the way it represented the history of algebra - in 1700s-1800s mathematicians challenged each other with some problem set. The winner got the coveted office position. The problems typically involved single-variable polynomial equations of increasing degrees, and they tried to find the general solution to degree-2,3,4...
Apparently, degree 5 and above polynomials don't have a general solution, and this is shown by abstract algebra! It was fascinating that something like that could be proved.
I've decided to self-study mathematics over the next couple of years. I'm interested in statistics, analysis, abstract algebra, type theory, complex numbers. Probably a long list. I'll pick and use a book, try to go through it and solve problems to cement understanding. I'll update bits here as I go...maybe just some exceptional things I read or general updates about how this is going.
Mathematical Autodidact
2025 May 28 See all postsAs I grow older, I find myself getting drawn towards things that I found interesting in the pre-university era. One such thing is mathematics. I had a blast preparing for IIT-JEE, and mathematics was my favorite subject.
Programming is about creativity and making something; mathematics is about truth and the search of aesthetics in that truth. Last year I picked up A Book of Abstract Algebra by Charles Pinter and it blew me away. I didn't manage to get to the end of it still, but the way it represented the history of algebra - in 1700s-1800s mathematicians challenged each other with some problem set. The winner got the coveted office position. The problems typically involved single-variable polynomial equations of increasing degrees, and they tried to find the general solution to degree-2,3,4...
Apparently, degree 5 and above polynomials don't have a general solution, and this is shown by abstract algebra! It was fascinating that something like that could be proved.
I've decided to self-study mathematics over the next couple of years. I'm interested in statistics, analysis, abstract algebra, type theory, complex numbers. Probably a long list. I'll pick and use a book, try to go through it and solve problems to cement understanding. I'll update bits here as I go...maybe just some exceptional things I read or general updates about how this is going.