Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Math writing is dull when it neglects the human dimension

golem.ph.utexas.edu

Post reply on HN
Print view View original

121–130 of 186 posts

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

#121

Post by constantcrying »

js8 wrote: post #119
constantcrying wrote: post #107

Earlier quoted context omitted.

Do you not realize that SAT might just be O(2^n) at best? Even if by a gigantic miracle SAT is in P, unless there is another incredibly great miracle and it is something like O(n^3), which would almost certainly be the greatest discovery of CS, it would not replace almost any other algorithms? Simply because many of the most important ones are O(n^2) or even less. >I think there might be a single algorithm, a SAT sol…

> Do you not realize that SAT might just be O(2^n) at best? Yes, but that's the worst case on all possible instances. Even with this worst case performance, there might be an algorithm that works on par with other algorithms that specialize only on certain instances. E.g. there can be an O(2^n) algorithm for general SAT which performs in O(n^(3/2)) on XORSAT. We simply don't understand the problem well enough to tell…

The average case is also O(n^2).

You have a completely utopian idea about what might be computationally feasible. I don't even know what you are arguing. Certainly it is thinkable that SAT is somehow ridiculously simple to calculate, just in the same way that achieving simple and near free fusion energy is thinkable. It just isn't going to happen and speculating on it is pure science fiction.

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

#122

Post by js8 »

curtainsforus wrote: post #105
yau8edq12i wrote: post #31

Earlier quoted context omitted.

> 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. I'm sorry, but that's just naive techno-solutionism. Maybe the computer will be able to solve your syntax problems, i.e., write proofs. It will never know anything about the semantics. Said differently. Maybe the computer will…

Strange, for you to say this in the age of transformers. They are obviously not there yet, but it seems inevitable to me that e.g. gpt 'understands' things better than a markov chain, and that future systems will understand more.

I know you're responding to someone else, but funny you say that. I suspect modern NN's are just iteratively solving some really large instances of SAT (similar to WalkSAT), to find a representation of a circuit that best matches a function defined on training examples (which are the constraints). So they're, unwittingly, kinda the SotA SAT solvers.

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

#123

Post by keybored »

protomolecule wrote: post #77
saithound wrote: post #24

Earlier quoted context omitted.

In my experience, (c) is a very large part of it. At one point in my career, I decided to try writing good, accessible articles, which properly motivated definitions and well-explained arguments with plenty of hand-holding. When I did that, a version of the derogatory sentence "The proofs are easy / non-technical." would appear in the reviews. Every. Single. Time. Of course, I have some independent confirmation that…

Yeah, when the result is easy to understand people think it was easy to arrive at. What surprises me that smart people don't correct for that bias.

This is the HN IQ bias: assuming that smart people are somehow less susceptible to cognitive biases etc. that the mere mortals have.[1]

Smart people can be incredibly biased and ideological. Some careers for smart people are even all about reasoning backwards from a given conclusion.

[1] redacted footnote

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

#124

Post by twelfthnight »

lapinot wrote: post #63

> Of the people who see your math paper, 90% will only read the title. Of those who read on, 90% will only read the abstract. Of those who go still further, 90% will read only the introduction, and then quit. My personal experience is usually quite different. Perhaps i'm very weird but i like to think i'm nothing special. I mostly read papers when searching for something specific (referral by someone in a discussion,…

So, marketing is inevitable and necessary, but I have a hypothesis that the current Internet is making it worse. For example, creators (I'm lumping in researchers with songwriters, actors, etc) used to focus on passing the hurdle of getting an "elite" power (record company, publisher, University) to support them. Once over that hurdle, they specialized in creating and left marketing to the elite.

The elites would pressure the creators to do things they thought were marketable, but it didn't always work because creators had some leverage in negotiation and a small number of elites actually cared about making good stuff.

Now, there are fewer gatekeepers, but instead there is an all powerful algorithm. Creators all have to do their own marketing in addition to creating, and the algorithm can't be negotiated with.

So what we wind up with is insipid YouTube thumbnails and myriad academic papers with breathless "state of the art" claims.

There are tradeoffs, but I do think it's worth noticing how effectively we've started to reward creators for marketing rather than creating.

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

#125

Post by lupire »

humansareok1 wrote: post #98
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…

>whose main theorem is given at the most general possible level with no applications at all. Outside of Applied Math why would this be an expectation at all?

Because it's an expository paper, not a reference manual. Applications help communicate and create understanding.

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

#126

Post by bedobi »

atoav wrote: post #14
latency-guy2 wrote: post #7

Earlier quoted context omitted.

Establish why its "crappy teacher" and not "crappy student". I've seen far more of the latter than the former. I don't think its hard to find something interesting about math either, and it is immediately applicable, even with what I think is extremely stupid in the form of common core as presented in the USA, you are literally being presented story problems about common every day occurrences and activities.

As someone who routinely teaches (Non-STEM) university students practical applications of math I can assure you that none of the students that told me "I am bad at maths" went out of my class without an understanding of the topics we talked about. Yet I routinely hear a: "Wow, if they told it to me this way during school I might have cared!" or "It really made my head smoke, but it felt good." Step 1 is believing tha…

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 mostly already know what I'm "teaching".

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

#127

Post by lupire »

Dalewyn wrote: post #52
saithound wrote: post #30

Earlier quoted context omitted.

This is good advice, but for a very different problem. 1. The problem in math is not that the way the "orthodoxy" insists on presenting things in a suboptimal way, but that if the reviewers find a good explanation of your result, they'll recommend that you publish in a lower-ranked venue than your result would ordinarily merit (at least unless you solved a famous problem). So researchers are incentivized to make the…

I've always found math is taught in the most daft, bland, vapid, worthless ways imaginable and I've thought it had to do with those who do the teaching: The teachers and textbooks. But reading this comment chain, am I correct to understand that this problem stems from the very essence of math itself? The people who live and breathe math just fucking hate sharing their passion with others? What the hell.

Academics (not just mathematicians) are famously bitter and political, because they do things tht the world values so little, but they care about so much, and they are fighting for scraps of recognition and funding.

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

#128

Post by gbacon »

Thank you. This is beautiful.

Related gems from Simon Peyton Jones are below. In the first, he also advocates telling a story.

https://www.microsoft.com/en-us/research/uploads/prod/2016/0...

https://www.microsoft.com/en-us/research/uploads/prod/2016/0...

https://simon.peytonjones.org/assets/pdfs/writing-a-proposal...

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

#129

Post by woopwoop »

I think mathematics is in a good place with regards to tolerance of self-promotion. I do not think that we should put up with excessive hype in the name of "humanizing" papers. I do think that a lot of mathematicians do not provide enough detail or motivation for their arguments. Not necessarily motivation in the sense of "why is this important", but motivation in the sense of "we are beginning a three page proof. Let me give you a paragraph to give you the outline so that you can fill in the details yourself, rather than having to read all of the details just to reconstruct the outline."

I do have a pet peeve about mathematical exposition. At some point, phrases like "obviously" and "it is easy to see" became verboten, or at the very least frowned upon. The problem is that it didn't become verboten to skip details (this would be impossible in general), and those phrases actually do contain information. Namely they contain the information that there actually is some detail remaining to fill in here. Often in papers there will be some missing detail which is not so hard to verify, but whose presence is so ghostly in the exposition that I think I've missed somewhere where it was stated explicitly, and have to go back. I feel like this is the case of someone excising an instance of "it is easy to see that" and replacing it with... nothing.

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

#130

Post by kouru225 »

A_D_E_P_T wrote: post #59

The best math book I've ever read -- which I think can completely transform somebody's appreciation of math -- was William Dunham's "Journey Through Genius - The Great Theorems of Mathematics." What this book did was place mathematics in human and historical context. It starts with Hippocrates' Quadrature of the Lune, then moves on to Euclid's proof of the Pythagorean theorem, and moves along through history all the…

Putting it on my list
Post reply on HN