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Math writing is dull when it neglects the human dimension

golem.ph.utexas.edu

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Re: Math writing is dull when it neglects the human dimension

#171

Post by atoav »

latency-guy2 wrote: post #167
bedobi wrote: post #126

Earlier quoted context omitted.

This is exactly how my education went. Oh you're not engaged with my shitty teaching and forcing you to do endless abstract nonsensical formulae with zero contextualization or application? Then you're the problem - you have cognitive defects, you are plain dumb and stupid, you are disinterested, you don't care about your education etc etc so I cannot help you. Now let me spend my time on "teaching" the kids who mostl…

> This is exactly how my education went. No it didn't. I am very confident it did not. All students that make it past grade school go through nearly the exact same sequence and motivating examples beginning from geometry, high school algebra, and then some introduction to calculus if not calculus outright. And the motivating example has always been how to calculate area, and if advanced enough, volume, for all kinds…

Interesting form of confidence. I didn't write the comment you replied to, but I wrote the original comment.

The first fact I want to have written down is that there are bad math teachers. And sadly it is not uncommon for them to be bad, as I mentioned most of my collegues from other classes and schools had bad math teachers and some of them were people that liked math.

Now as an educator I am aware that students are quick to blame other people or the system for their own deficiencies, but I can tell you for a fact that our math teacher failed to explain us what an integral was actually for in an parsable way, even after multiple times of asking. She just knew how to do the formula stuff, she never used it herself on real applications. And when she did explain things, she always did it once, much too briefly in the beginning, so that by the point at which we started doing her always decidedly abstract examples nobody knew what the fuck this was for. As I said, our physics and mechanica teachers were better math teachers than her. As for the integral I had to go and look it up myself, the internet was still young and there weren't many grown ups who knew how to look such a thing up and when I saw the explainations I wondered why nobody ever told us..?

I understand btw. why it can be an advantage to understand math in purely abstract ways, but in her case she just didn't want to talk much and stick to the examples. And that is bad teaching. Ah and before we get into a discussion about specifics, like many on this site I grew up and live happily outside of the US, so educational plans etc. might differ.

Re: Math writing is dull when it neglects the human dimension

#172

Post by renonce »

mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

While I don't think it's practical to expect every paper author to write in the most consise and elegant style possible, one thing I do wonder is the lack of a "comment section" for papers: why isn't there a centralized place for academics to just leave comments or their understanding of the paper, like most of the web forums? I don't expect the author to respond or even be active in every comment section but there should certainly be such a place. Every other form of Internet-based discussion, including Reddit, any random Internet forum, mail lists, Discord, etc. are all interactive and everyone is expected to participate in a centralized and public discussion.

This way, even if the paper itself is hard to read, for the good ones I do expect someone else to leave a comment with a sketch of the most interesting parts of the paper that would get upvoted to the top, and the author could click a "promote" button or something to make it official. This way the author doesn't have to write very well as long as the paper is valuable enough for someone else to be interested.

Re: Math writing is dull when it neglects the human dimension

#173

Post by mycologos »

renonce wrote: post #172
mycologos wrote: post #10

As somebody who works in a mathy subarea of computer science, oh man, I agree. My heart always falls when I need a result and it turns out the original paper is some terse typewritten notice from the 70s whose first sentence is a definition with a bunch of proper nouns and whose main theorem is given at the most general possible level with no applications at all. I have talked with math people about why this is, and…

While I don't think it's practical to expect every paper author to write in the most consise and elegant style possible, one thing I do wonder is the lack of a "comment section" for papers: why isn't there a centralized place for academics to just leave comments or their understanding of the paper, like most of the web forums? I don't expect the author to respond or even be active in every comment section but there s…

Any comments section would require moderation, and internet moderation is a huge pain in the butt. It's not an unsolvable problem, as the examples you give demonstrate, but it does require a lot of effort, and I think you'd be pretty hard-pressed to find academics willing to expend that effort.

Re: Math writing is dull when it neglects the human dimension

#174

Post by Tainnor »

js8 wrote: post #28

IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution. We then "quantize" the algorithm to a state machine (e.g. convert reals to floats, algorithm steps to machine…

That's some of the most confidently written nonsense I've read in a while.

> all mathematics will be replaced with an automated process

FOL is undecidable, so we know this is impossible.

Re: Math writing is dull when it neglects the human dimension

#175

Post by Tainnor »

js8 wrote: post #97
constantcrying wrote: post #86

Earlier quoted context omitted.

Some facts to consider: - Polynomial problems can still require enormous computing power to the point they are unsolvable. Even if tomorrow there is an algorithm transforming every NP problem to a P problem, not all problems will be feasibly solvable. A O(n^100) Problem is still P. - P vs. NP is about algorithmic complexity, it has no implications about mathematics being an algorithm or not. - The most likely outcome…

I think what's more fundamental than just answering P vs NP, is what exactly makes boolean functions hard to (pseudo)inverse? And it's the latter where answering (unless the answer comes from an oracle) the former will help. And this question is crucial, because everything we can ask computers (or restated, math with real-world applications) can be rephrased in terms of finding a solution to a SAT instance. It can be…

> everything we can ask computers (or restated, math with real-world applications) can be rephrased in terms of finding a solution to a SAT instance

SAT is limited to propositional calculus which is far too weak for most mathematics.

Re: Math writing is dull when it neglects the human dimension

#176

Post by Tainnor »

constantcrying wrote: post #92
js8 wrote: post #90

Earlier quoted context omitted.

> Do you not realize that P vs. NP might have a negative outcome (extremely likely) The outcome will matter less than having an answer. And I do think it will be a negative outcome either way, because it will obsolete lot of beautiful math, and replace it with a more mechanical process. > In basically any field proving the existence of a solution is far, far harder than calculating the solution numerically. First of…

>The outcome will matter less than having an answer. And I do think it will be a negative outcome either way, because it will obsolete lot of beautiful math, and replace it with a more mechanical process. The negative outcome will have exactly zero implications about anything. Except "turns out we were right all along" polynomial problems are just fundamentally less hard than problems you can verify the solution of i…

> And if P neq NP, then SAT might not be P.

Small correction: If P != NP, then SAT definitely isn't in P. That's because SAT is NP-complete, so if it was in P, every other NP problem could be polynomially reduced to it and would hence also be in P.

Re: Math writing is dull when it neglects the human dimension

#177

Post by impendia »

samatman wrote: post #149
igorbark wrote: post #143

Earlier quoted context omitted.

culture war aside, there are many other more accurate ways to say "details omitted for brevity" than "obviously" and "it is easy to see that" this is also something that makes me want a more interactive publishing format, though i understand the good reasons to stick to the static quo. if it's easy to see, it shouldn't be too hard to write out in a collapsible sidebar for those interested

Like everything in mathematics, "obvious" is a term of art. Broadly speaking, it refers to a fact, proof, consequence, which is necessary for the proof to advance, but which is already established elsewhere, so it does not in itself aid in understanding the proof being presented. A proof is either providing a new result, or is proving an established result in a new way. Almost always, a proof will need other results,…

As a working mathematician, I would say "obvious" is most often used for omitted arguments whose analogues are widely established elsewhere.

As an elementary example, in an analytic number theory paper one might need to know that for some constant C we have

5x + x^3 + ln(x) for all positive x. (In practice, one would not need to determine such a C, just know that one exists.)

Such a claim would usually be described as "obvious" or else stated without any justification. I doubt you could find precisely this claim in the literature, but one can find plenty of very similar arguments in textbooks, and anyone doing research in analytic number theory would find this "obvious".

Re: Math writing is dull when it neglects the human dimension

#178

Post by atoav »

skhunted wrote: post #83
atoav wrote: post #12

Earlier quoted context omitted.

Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power. You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-l…

What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep. This is precisely what I was referring to about people who come back at a later time and relearn…

I am in education and what you claim here is in contradiction with both my experience and the direct feedback of the people I educated — most of which would say they dislike math or say they are bad at it. The argument that it is like it is for a reason can be made, but it has probably more to do with the historical role of school as an institution that is meant to produce obidient workers than with school as a place that is meant to produce people able to analyze nature and the world around them with the tools of mathematics. Ever student that got a bad grade because they solved the problem, but did so using the "wrong" way can testament to this.

Back when I was in school I had the luck to also have a lot of maths both physics and mechanics classes, so I had above average exposure to mathematical applications. This is what made me the most wanted maths-helper among my friends who went to other schools with a "purely theoretical"-maths approach: I could finally show them how the stuff they had a hard time with connects to the actual real world and nature around them — which contrary to your statement really their ability to grasp it.

If we think about how one would go about teaching any subject in a way that creates the maximum disinterest in the field it would be done dry theory only while keeping real world connections and story telling to a minimum. Sure, you could do that and there would always be a small number of students who would excell at that anyways because their brains are wired for abstract things — but that isn't a healthy approach to to take in general education.

Sometimes my feeling is that mathematicians, like many other nerds want to gatekeep and shroud their own field in an overly opaque mysticism, because they can derive a higher self value from that. So things get explained over complicated and they tell you, that you would never understand (because you are the wrong kind of person).

I like to instead believe that if explained right you can nearly explain everything to everyone — provided you manage to spark their interest, keep their interest and provide a good way into the matter. This is why Feynmanns lectures are so famous. He was really good at this.

Re: Math writing is dull when it neglects the human dimension

#179

Post by js8 »

Tainnor wrote: post #174
js8 wrote: post #28

IMHO it's even worse. Once we figure out P vs NP, we will understand what it means to invert boolean functions algorithmically, and all mathematics will be replaced with an automated process. Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution. We then "quantize" the algorithm to a state machine (e.g. convert reals to floats, algorithm steps to machine…

That's some of the most confidently written nonsense I've read in a while. > all mathematics will be replaced with an automated process FOL is undecidable, so we know this is impossible.

I think you miss the point. I am not disputing FOL being undecidable. What I am saying is that, once we know how to solve SAT well enough, most mathematics will become obsolete (especially for applications). It will be obsoleted the similar way that symbolic solving of equations got obsoleted with numerical solving, once computers (and numerical algorithms) became prevalent enough.

Practically minded people will simply skip logical proofs and model the world directly with SAT instances. Mathematics will remain an intellectual curiosity.

In a way, I agree with the article - what makes math interesting is the human perspective and creativity. But I believe it's "worse" - taken objectively, math is actually pretty boring and there is only little depth.

Re: Math writing is dull when it neglects the human dimension

#180

Post by Tainnor »

js8 wrote: post #179
Tainnor wrote: post #174

Earlier quoted context omitted.

That's some of the most confidently written nonsense I've read in a while. > all mathematics will be replaced with an automated process FOL is undecidable, so we know this is impossible.

I think you miss the point. I am not disputing FOL being undecidable. What I am saying is that, once we know how to solve SAT well enough, most mathematics will become obsolete (especially for applications). It will be obsoleted the similar way that symbolic solving of equations got obsoleted with numerical solving, once computers (and numerical algorithms) became prevalent enough. Practically minded people will simp…

> symbolic solving of equations got obsoleted with numerical solving

That never happened, symbolic and numerical mathematics coexist to this day. Cryptography, for example, relies on exact arithmetic.

On that note, good luck trying to solve problems in cryptography with "SAT instances".

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