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Mathematics is hard for mathematicians to understand too

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Re: Mathematics is hard for mathematicians to understand too

#21

Post by mzl »

borracciaBlu wrote: post #3

I was writing a small article about [Set, Set Builder Notation, and Set Comprehension]( https://adropincalm.com/blog/set-set-builder-natatio-set-com... ) and while i was investigating it surprised me how many different ways are to describe the same thing. Eg: see all the notation of a Set or a Tuple. One last rant point is that you don't have "the manual" of math in the very same way you would go on your programming…

I wrote about overlapping intervals a while ago, and used what I thought was the standard math notation for closed and half-open intervals. From comments, I learned that half-open intervals are written differently in french mathematics: https://lobste.rs/s/cireck/how_check_for_overlapping_interva...

Re: Mathematics is hard for mathematicians to understand too

#22

Post by ekjhgkejhgk »

srean wrote: post #16
ekjhgkejhgk wrote: post #9

Earlier quoted context omitted.

von Neumann liked saying things that he knew would have an effect like "so deep" and "he's so smart". Like when asked how he knew the answer, claiming that he did the sum in his head when undoutedly he knew the closed-form expression.

I have tingling suspicion that you might have missed the joke. To date I have not met anyone who thought he summed the terms of the infinite series in geometric series term by term. That would take infinite time. Of course he used the expression for the sum of a geometric series. The joke is that he missed a clever solution that does not require setting up the series, recognising it's in geometric progression and the…

Ah. I was going by memory, and I had those two as separate stories. I didn't remember that he said "I did the sum" on the trains problem.

Re: Mathematics is hard for mathematicians to understand too

#23

Post by segfaultex »

MrDrDr wrote: post #19

I think this would be extremely valuable: “We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics—with consequently less energy on the most recent results.” I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood. A little off topic perhaps, but out of curiosity - how many of us here hav…

Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping.

I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply".

Statistics is a major culprit of this.

Re: Mathematics is hard for mathematicians to understand too

#24

Post by Someone »

MrDrDr wrote: post #19

I think this would be extremely valuable: “We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics—with consequently less energy on the most recent results.” I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood. A little off topic perhaps, but out of curiosity - how many of us here hav…

> I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood.

That assumes it’s the language that makes it hard to understand serious math problems. That’s partially true (and the reason why mathematicians keep inventing new language), but IMO the complexity of truly understanding large parts of mathematics is intrinsic, not dependent on terminology.

Yes, you can say “A monad is just a monoid in the category of endofunctors” in terms that more people know of, but it would take many pages, and that would make it hard to understand, too.

Re: Mathematics is hard for mathematicians to understand too

#25

Post by segfaultex »

BlackFingolfin wrote: post #8
borracciaBlu wrote: post #3

I was writing a small article about [Set, Set Builder Notation, and Set Comprehension]( https://adropincalm.com/blog/set-set-builder-natatio-set-com... ) and while i was investigating it surprised me how many different ways are to describe the same thing. Eg: see all the notation of a Set or a Tuple. One last rant point is that you don't have "the manual" of math in the very same way you would go on your programming…

I find it strange to compare "math" with one programming language. Mathematics is a huge and diverse field, with many subcommunities and hence also differing notation. Your rant would be akin to this if the sides are reversed: "It's surprising how many different ways there are to describe the same thing. Eg: see all the notations for dictionaries (hash tables? associative arrays? maps?) or lists (vectors? arrays?). Y…

Not the original commenter, but I 100% agree that it's weird we have so many ways to describe dictionaries/hash tables/maps/etc. and lists.

Re: Mathematics is hard for mathematicians to understand too

#26

Post by pfortuny »

mkl wrote: post #20
thaumasiotes wrote: post #18

Earlier quoted context omitted.

> As far as anybody can tell, mathematics is way older than literature. That depends what you mean by "literature". If you want it to be written down, then it's very recent because writing is very recent. But it would be normal to consider cultural products to be literature regardless of whether they're written down. Writing is a medium of transmission. You wouldn't study the epic of Gilgamesh because it's written do…

> That depends what you mean by "literature". If you want it to be written down That is what literature means: https://en.wiktionary.org/wiki/literature#Noun

Well, then poetry is not literature.

Re: Mathematics is hard for mathematicians to understand too

#28

Post by bell-cot »

segfaultex wrote: post #23
MrDrDr wrote: post #19

I think this would be extremely valuable: “We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics—with consequently less energy on the most recent results.” I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood. A little off topic perhaps, but out of curiosity - how many of us here hav…

Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping. I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". Statis…

Gatekeeping, or self-promotion? You don't get investors/patents/promotions/tenure by making your knowledge or results sound simple and understandable.

Re: Mathematics is hard for mathematicians to understand too

#29

Post by segfaultex »

bell-cot wrote: post #28
segfaultex wrote: post #23

Earlier quoted context omitted.

Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping. I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". Statis…

Gatekeeping, or self-promotion? You don't get investors/patents/promotions/tenure by making your knowledge or results sound simple and understandable.

Why not both? And that's a good point, there are a LOT of incentives to make things arbitrarily complex in a variety of fields.

Re: Mathematics is hard for mathematicians to understand too

#30

Post by thaumasiotes »

pfortuny wrote: post #26
mkl wrote: post #20

Earlier quoted context omitted.

> That depends what you mean by "literature". If you want it to be written down That is what literature means: https://en.wiktionary.org/wiki/literature#Noun

Well, then poetry is not literature.

No, the argument is even dumber than that. The person who writes a poem hasn't created any literature.

The person who hears that poem in circulation and records it in his notes has created literature; an anthology is literature but an original work isn't.

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