- #36
homeomorphic
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- 130
However inapplicable pure maths may be, it will never change.
If it's really inapplicable, then what's the point of not changing? Its worth is zero and since it can't change, its worth will always be zero. I actually don't completely dismiss the value of math for math's sake, but I think that applies more to simple things than the kind of baroque, ultra-complicated stuff I see mathematicians working on today. On the one hand, you could look at something like a proof by pictures of the Pythagorean theorem that doesn't require a ton of background to appreciate. I once explained it to a graduate student in music, and I could tell he was really excited. Ignoring the immense practicality of the Pythagorean theorem, that kind of mathematical beauty comes quite cheaply, and I would say it's worthwhile, just purely for the fun of it! But as you get deeper and deeper, the price of admission gets bigger and bigger. You could take a theorem like the spectral theorem of functional analysis that's pretty deep and not really accessible to laymen, but you don't exactly need to devote your life to understanding it. If you go much further than that, it gets to some unknown territory for me. Maybe I'd see more value in more math if I understood more of it, but I do have the distinct impression of having diminishing returns, as far as I did get. I don't think it's worth all the intense competition and all the insanely hard work. Not even by a long shot. Not for me, anyway. Unless it can make a difference in people's lives.
I think you're not seeing the forest through the trees when it comes to programming. Programming is very logical. The particular details of syntax are not that important. The concept of a for loop makes sense, independent of the details of how it has been implemented in various languages. It's DRY. Don't repeat yourself. If you didn't have loops, you'd have to type the same code over and over, possibly hundreds of times. The necessity of iteration can therefore be viewed almost as if it were a timeless mathematical truth. When you are stuck looking at the trees, you don't see this forest. Don't worry about the fact that it has to be
for(int i = 0; i<100; i++)
{
// do stuff
}
Who cares about that? If you learn it in C++, it's the same concept in Python, even if the exact way that you write it out is slightly different.
It's a form of engineering. Do you think if someone designs a car that they had to make every piece exactly the way they did or was there some wiggle room? Obviously, there was some wiggle room--just look at all the different kinds of cars out there. And math is that way to some degree, too. A proof doesn't have to be done exactly the way they did it. There may be 50 different ways to prove the same thing. Which way do you choose? As it turns out, the choice in the way the same piece of mathematics is proven can evolve over time.
Plus, a PhD in maths would allow you to enter academia, where you would age like wine as an employee (tenure = unfirable). Programmers age like fruit - at 40+, your value as an employee drops like a rock.
I have a PhD in math and to put it in Biblical terms, it would be easier for a camel to pass through the eye of a needle than for me to enter academia. Except as an adjunct, but I'm not sure that's any better than flipping burgers, prestige aside--there's definitely no aging like wine there.
I'm not sure it's really true that programmers age like fruit. Especially someone like me because if I break into programming, my math expertise will open a lot more doors when combined with being able to say I worked professionally using Java or C++ for X years.