Comment by quus
2 days ago
I’m actually interested in the “can benefit from” claim in this title. I don’t particularly doubt that most people could become reasonably good at math, but I wonder how much of the juice is worth the squeeze, and how juicy it is on the scale from basic arithmetic up to the point where you’re reading papers by June Huh or Terry Tao.
As anti-intellectual as it sounds, you could imagine someone asking, is it worth devoting years of your life to study this subject which becomes increasingly esoteric and not obviously of specific benefit the further you go, at least prima facie? Many people wind up advocating for mathematics via aesthetics, saying: well it’s very beautiful out there in the weeds, you just have to spend dozens of years studying to see the view. That marketing pitch has never been the most persuasive for me.
Pure math is probably not worth the squeeze. I think more important to everyday life is systems thinking and a bit of probability/stats, mainly bayesian updates. "Superforecasting" was an eye-opening book to me, I could see how most people would benefit massively by it.
Similar to systems thinking, just the ability to play out scenarios in your head given a set of rules is a very useful skill, one which programmers tend to either be good at because of genetics or because we do it every day (i.e. simulate code in our head). You can tell when someone lacks this ability when discussing something like evolutionary psychology. Someone with a systems thinking mindset and an ability to simulate evolution tend to understand it as obvious how evolutionary pressures tend to, and really must, create certain behavior patterns (on average), while people without this skill tend to think humans are a blank slate because it's easier to think about, and also is congruent with modern sensibilities.
This skill applies in everyday life, especially when you need to understand economics (even basic things like supply and demand seems elusive to many), politics etc.
Abstract Algebra, Combinatorics, and Discrete Mathematics are all definitely worth the squeeze; and incidentally something that could easily be taught to middle- and high-schoolers with the right examples.
Is it worth it to be able to think better, have a growth mindset and learn how to learn? Yes. Everyone can benefit from that. Pushing on into higher math? No, very few people can benefit from that.
Math doesn’t seem to me the only source of thinking clearly, or learning how to learn, etc. And if I’m searching for an aesthetic high, there are definitely better places to look — and ones that don’t require such a long runway.
It doesn't need to be for me to be right. These are false constraints you're trying to put on it. Mathematics in moderation can benefit everyone. This claim stands.
I'll second guerrilla - you can absolutely benefit from mathematical thinking without pushing into territory higher than undergaduate studies.
You can even benefit from the thinking taught in good high school coursework (or studying online).
At an arithmetic, bookkeeping level you can better appreciate handling finances and the seductive pitfalls surrounding wagers (gambling, betting, risk taking).
My claim isn’t really that there’s no benefit or utility to math — that’s obviously false — but that maybe its benefits to regular people are more modest than the cheerleaders want to admit.
What are the costs (in your estimation at least) to "regular people" (regular by your metric) of not engaging in easy bake low level "mathematical thinking".
* How many have a lower return on { X } through not understanding compound interest, tax brackets, leveraging assets, etc.
* How many have steady net losses through "magical thinking" wrt gambling, betting, hot stock tips.
2 replies →
i’ve always found that mathematical thinkers do better, no matter the role. it’s difficult to express how, it’s kind of intangible, but it’s just a mental process that helps break down tasks and come up with unique solutions.
that being said, my marketing pitch for math was always, nothing else is even close to as intellectually stimulating as math.