I'm reading the biography of Erdös (I actually have an Erdös number, though shamefully high), and I figured now's as good a time as any to write these thoughts down, before they too are lost to the vast gray mist of my forgotten experiences.
Before my suicide attempt, during the height of my illness, I was still looking for some meaning in life. In practice, this meant searching for a major to do my master's on. In Finland, at least when I was a wee undergrad, you were fairly free to shop around within your faculty (in my case, science), take whatever courses you wanted, I had long ago done the vast majority of the compulsory stuff. So I sat in courses ranging from MHD to celestial mechanics. Among these excursions into the cornucopia of science were a couple of courses on number theory. For the less scientifically minded in the audience, number theory is precisely what it says on the tin, the study of numbers and their properties. For example, a result known since antiquity is that every integer you care to think of has what is called a prime factorization; namely, every integer can be expressed as a multiplication of primes in a way that is unique for each number. 20 is equal to 2 times five times two again, and so forth. (A prime number is a number that is only divisible by itself and 1.)
I have always found mathematics to be beautiful. This is a sentiment common amongst the scientifically oriented, yet I've not really seen a good explanation towards the lay person to explain what it exactly means. I do not imagine I could do any better, but for the sake of the memory, let's give it a go. In my experience, when I see a handsome woman smile, her unclothed thighs, shapely buttocks, or the well trained abs of a young man, these are things that I associate with the concept of 'beauty'. Simply viewing them delights the mind, with invitation for further proceedings, naturally, but delights all the same.
Similarly, the process of 'doing math', and I do not mean the rote arithmetic taught in elementary school but the genuine deal, provides an aesthetic and uplifting experience. As someone who wound up doing experimental science, it is a banal truism that I am always looking at approximations of the world, I can never say things 'as they are' but only how they appear to my limited apparatus. Mathematics, on the other hand, is far more comprehensive, definite. What is, is.
Setting aside for the moment Gödel's seminal work (which, roughly speaking, says that no system can prove all its axioms, a devastating result in its own right), mathematics is very much a procedural thing; one starts out with some knowns, and progresses forward with set rules. Nothing could be simpler!
Physics (and biology, and economics for that matter) mostly deal with variables changing as a function of time. This leads to the path of differential equations, integrals, and all sorts of things that become ugly real fast. Ugly in the same sense as mathematics can be beautiful; the equations that are examined are difficult, laborious, do not have nicely converging solutions, all sorts of frustrations. Like the handsome woman who smiled at you, but denied your offer of a shared drink, some equations simply do not play the way one wants. In many ways, physics is the art of doing horrible violence to offensive equations.
Elementary number theory is nothing of the sort. The logic is sound yet simple, the results profound and satisfying. Satisfying as that woman smiling at your joke, with that glimmer in her eye. Naturally I am contrasting a very glandular joy with a most cerebral one, but surely you get the gist!
Now. In my greatest dissatisfaction, greatest desire to die, in my most profound self-loathing, I sat in a couple of courses of number theory. My university doesn't do much active research in the field; the lecturer was an old, tall man, who would retire a few years after the lectures took place.
I probably cannot do justice to him, but here's my impression: He was a very tall, old man. A head taller than I, for sure. Bald, spectacled, thin as a scarecrow. He had a good voice, one that carried easily through the room. His English wasn't bad, but I always lamented the times he had to resort to it, I find it's a thing of their generation, they simply lecture better in Finnish.
The courses were simple, there was no homework and one only had to submit a paper at the end to get course credit. I went through a couple of Ramanujan and Hardy proofs, I'm not a good mathematician by anyone's standards but I had a good time examining their work and trying to comprehend their logic.
The reason I remember these courses, my number theory days, is simple and humanely mundane. In my bleakest hour, as I was busying myself in my past-time explaining the futility of existence, I was able to spend a few hours each week listening to lectures on number theory. I took extensive notes of the lectures, and this way was always 'on track' with what was going on, I could see the proofs as they progressed. And I listened to this old lecturer wander between the topic at hand and anecdotes about his own life, the lives of old great mathematicians, in what seemed a perfect mix of science and humanity. A figure larger than life, easily, as he portrayed not only the way the prime numbers work but his own adventures through Europe and mathematics. It is rare indeed for a mathematician to even emulate humanity, but for one to clearly demonstrate it? All the while making both accessible and enjoyable the topic at hand!
I believe those lectures were the only times I were ever truly happy during that period. Seeing the theory of numbers unfold before me, understanding it, it was the only life-affirming experience I had in a time where I rejected life. A blithe observation could be made that I only found happiness in a place totally devoid of human influence, the realm of numbers, but I do not think that is so. Always was there an element of those who created the theory present in the lectures, the way the lecturer presented things always kept an element of absurd along with the pure logic.
The beauty of numbers is undeniable to me. If I weren't a third-rate mathematician, I like to believe I'd have gone into number theory myself. As things are, number theory remains, for me, the only bright and happy memory of a time otherwise devoid of enjoyment.
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