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Mathematics is beautiful, but I am not good enough for it. Anyone else feel the same?
I found mathematics by accident, at the philosophy shelves of a bookstore near my house: I was flummoxed by the fact that 3 copies Bertrand Russell's *Principles of Mathematics* were right there next to Nietzsche's *Thus Spoke Zarathustra.* I was 16 then, and I did not know much of mathematics or philosophy, but I *was* conditioned to think of them as totally disjoint. My curiosity was piqued, I went ahead and bought both of those books.
It wouldn't be exaggerating to say that Russell's book changed my life. My only previous exposure to logic had been through the term-centric approach of Aristotle, and the fact that the algebra I was learning in my classes could be applied to study our own reasoning fascinated me. At the time I also enjoyed programming, and when I started to study Turing's tape model of computation and eventually the lambda calculus, I realized that mathematics was not solely about calculating things or modeling physical problems (though those are great ways to approach it) -- in some sense, it *is* the direct study of the concepts of structure, change, quantity, size, through the rigorous analysis of abstract objects or our mental intuitions (take your pick).
Mathematics appealed to my desire to keep my thoughts organized and elegant, and by the time I was 18 and starting university, my interests had shifted from computer science to mathematics. However, I did not pursue it at first -- I was scared I wouldn't be good enough. I went through a year of an economics degree, but when I enjoyed my linear algebra class more than anything else I took that year, I knew I had to pivot back to mathematics. That summer, I wrapped up the calculus sequence with a multivariate course, and switched my major back to math in the fall.
I took an "intro to proofs" class and a course on group theory (up to the Sylow theorems) at the same time. In retrospect, it may not have been the best idea to take the group theory course so early on -- but I don't regret it, despite not getting a perfect grade (it was hard to adjust to that much abstraction from calculus), I found it an extremely beautiful area (finding normal subgroups in particular reminded me of decomposing and rearranging Lego sets as a child). This semester, I am taking a topics course in algebra (we are covering basic representation theory, finite fields and type theory), and a course on rings, fields and Galois theory.
I am enjoying my college coursework like I never have before, truly. In fact, I would like, if possible, to pursue graduate studies in mathematics. But I also feel like something about me is intrinsically ill-suited for mathematics. My peers in my classes are able to fluidly discuss mathematical concepts in real-time, they are good at speedy recall of definitions (and example constructions). I am a bit of a slower thinker. Moreover, many have been in this pursuit for years, and are far more skilled and sophisticated than I am.
In some very bitter sense, I think I don't deserve to study mathematics as much as they do. Indeed, when my teacher put me and other supposedly "gifted" children in groups to study topics of interest back in elementary school, despite having my primary interest in the math & science group, I was "exiled" to the literature group. I am also pursuing a philosophy major, and I fear that might be the only path I can pursue. I am planning to take analysis & algebraic topology next semester (I have already self-studied the first 3 chapters of Pugh's book), but I fear even my fast pace won't make up for what I seem to (in my mind) intrinsically lack. I know it's fallacious, but I do wonder if I would have intrinsically gravitated towards mathematics if it was *truly* right for me.
But right now, I know I'm not happy doing anything else, so I'll keep at it.
#science
source
I found mathematics by accident, at the philosophy shelves of a bookstore near my house: I was flummoxed by the fact that 3 copies Bertrand Russell's *Principles of Mathematics* were right there next to Nietzsche's *Thus Spoke Zarathustra.* I was 16 then, and I did not know much of mathematics or philosophy, but I *was* conditioned to think of them as totally disjoint. My curiosity was piqued, I went ahead and bought both of those books.
It wouldn't be exaggerating to say that Russell's book changed my life. My only previous exposure to logic had been through the term-centric approach of Aristotle, and the fact that the algebra I was learning in my classes could be applied to study our own reasoning fascinated me. At the time I also enjoyed programming, and when I started to study Turing's tape model of computation and eventually the lambda calculus, I realized that mathematics was not solely about calculating things or modeling physical problems (though those are great ways to approach it) -- in some sense, it *is* the direct study of the concepts of structure, change, quantity, size, through the rigorous analysis of abstract objects or our mental intuitions (take your pick).
Mathematics appealed to my desire to keep my thoughts organized and elegant, and by the time I was 18 and starting university, my interests had shifted from computer science to mathematics. However, I did not pursue it at first -- I was scared I wouldn't be good enough. I went through a year of an economics degree, but when I enjoyed my linear algebra class more than anything else I took that year, I knew I had to pivot back to mathematics. That summer, I wrapped up the calculus sequence with a multivariate course, and switched my major back to math in the fall.
I took an "intro to proofs" class and a course on group theory (up to the Sylow theorems) at the same time. In retrospect, it may not have been the best idea to take the group theory course so early on -- but I don't regret it, despite not getting a perfect grade (it was hard to adjust to that much abstraction from calculus), I found it an extremely beautiful area (finding normal subgroups in particular reminded me of decomposing and rearranging Lego sets as a child). This semester, I am taking a topics course in algebra (we are covering basic representation theory, finite fields and type theory), and a course on rings, fields and Galois theory.
I am enjoying my college coursework like I never have before, truly. In fact, I would like, if possible, to pursue graduate studies in mathematics. But I also feel like something about me is intrinsically ill-suited for mathematics. My peers in my classes are able to fluidly discuss mathematical concepts in real-time, they are good at speedy recall of definitions (and example constructions). I am a bit of a slower thinker. Moreover, many have been in this pursuit for years, and are far more skilled and sophisticated than I am.
In some very bitter sense, I think I don't deserve to study mathematics as much as they do. Indeed, when my teacher put me and other supposedly "gifted" children in groups to study topics of interest back in elementary school, despite having my primary interest in the math & science group, I was "exiled" to the literature group. I am also pursuing a philosophy major, and I fear that might be the only path I can pursue. I am planning to take analysis & algebraic topology next semester (I have already self-studied the first 3 chapters of Pugh's book), but I fear even my fast pace won't make up for what I seem to (in my mind) intrinsically lack. I know it's fallacious, but I do wonder if I would have intrinsically gravitated towards mathematics if it was *truly* right for me.
But right now, I know I'm not happy doing anything else, so I'll keep at it.
#science
source
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