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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

#31

Post by worthless-trash »

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…

> You don't have "the manual" of programming languages. "

Well, we kinda do when you can say "this python program" the problem with a lot of math is that you can't even tell which manual to look up.

Re: Mathematics is hard for mathematicians to understand too

#32

Post by bell-cot »

johngossman wrote: post #5

Mathematics is such an old field, older than anything except arguably philosophy, that it's too broad and deep for anyone to really understand everything. Even in graduate school I often took classes in things discovered by Gauss or Euler centuries before. A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. So, you end up having to spe…

I'll argue for astronomy being the oldest. Minimal knowledge would help pre-humans navigate and keep track of the seasons. Birds are known to navigate by the stars.

Re: Mathematics is hard for mathematicians to understand too

#33

Post by bncndn0956 »

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…

3blue1brown proves your point.

The saying, "What one fool can do, another can," is a motto from Silvanus P. Thompson's book Calculus Made Easy. It suggests that a task someone without great intelligence can accomplish must be relatively simple, implying that anyone can learn to do it if they put in the effort. The phrase is often used to encourage someone, demystify a complex subject, and downplay the difficulty of a task.

Re: Mathematics is hard for mathematicians to understand too

#34

Post by dr_dshiv »

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…

See Brett Victor’s: Kill Math https://worrydream.com/KillMath/

He separates conceptual understanding from notational understanding— pointing out that the interface of using math has a major impact on utility and understanding. For instance, Roman numerals inhibit understanding and utilization of multiplication.

Better notational systems can be designed, he claims.

Re: Mathematics is hard for mathematicians to understand too

#36

Post by master-lincoln »

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.

Is that really the case or are you just assuming so? Seems counter-intuitive to me.

Re: Mathematics is hard for mathematicians to understand too

#37

Post by aleph_minus_one »

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…

> 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".

OK, challenge accepted: find a way to write one of the following papers much more simply:

Fabian Hebestreit, Peter Scholze; A note on higher almost ring theory

https://arxiv.org/abs/2409.01940

Peter Scholze; Berkovich Motives

https://arxiv.org/abs/2412.03382

---

What I want to tell you with these examples (these are, of course, papers which are far above my mathematical level) is: often what you read in math papers is insanely complicated; simplifying even one of such papers is often a huge academic achievement.

Re: Mathematics is hard for mathematicians to understand too

#38

Post by gjulianm »

bncndn0956 wrote: post #33
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…

3blue1brown proves your point. The saying, "What one fool can do, another can," is a motto from Silvanus P. Thompson's book Calculus Made Easy. It suggests that a task someone without great intelligence can accomplish must be relatively simple, implying that anyone can learn to do it if they put in the effort. The phrase is often used to encourage someone, demystify a complex subject, and downplay the difficulty of a…

3blue1brown, while they create great content, they do not go as deep into the mathematics, they avoid some of the harder to understand complexities and abstractions. Don't take me wrong, it's not a criticism of their content, it's just a different thing than what you'd study in a mathematics class.

Also, an additional thing is that videos are great are making people think they understand something when they actually don't.

Re: Mathematics is hard for mathematicians to understand too

#39

Post by gjulianm »

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…

> I suspect they do so as a means of gatekeeping

I'm surprised at how could you get at this conclusion. Formalisms, esoteric language and syntax are hard for everyone. Why would people invest in them if their only usefulness was gatekeeping? Specially when it's the same people who will publish their articles in the open for everyone to read.

A more reasonable interpretation is that those fields use those things you don't like because they're actually useful to them and to their main audience, and that if you want to actually understand those concepts they talk about, that syntax will end up being useful to you too. And that a lack of syntax would not make things easier to understand, just less precise.

Re: Mathematics is hard for mathematicians to understand too

#40

Post by threatofrain »

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.

Sure in the context that you mean it’s an oral tradition.
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