The entirety of math is "human", there's no way for it to neglect that "dimension".
(the article's title is "Why Mathematics is Boring")
Math writing is dull when it neglects the human dimension
91–100 of 186 posts
Re: Math writing is dull when it neglects the human dimension
#92Earlier 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. Literal nonsense. Do you not realize that P vs. NP might have a negative outcome (extremely likely)? >Today, most of the math is figuring out how to solve an equation, i.e. to give an algorithm to calculate the solution. Plainl…
> 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 in polynomial time. This has ZERO implications on anyone, except the mathematicians who prove it, who will get a price and quite a bit of academic fame. That is literally it.
>But doing that is more complicated than, assuming there is a SAT solver, plug the SAT instance into it and see if there is a solution (and you can get, for a finite family of instances, a similar guarantee you would get from the existence proof).
Even is SAT is P that doesn't imply a solution can feasibly be found. And if P neq NP, then SAT might not be P.
Re: Math writing is dull when it neglects the human dimension
#93Earlier quoted context omitted.
While gatekeeping is definitely a thing, I really suspect it's not the major incentive here. In writing (both prose and code!) there is always a question of target audience, which inevitably excludes the not-target audience. Personally, for a field in which I'm an expert, it's really annoying to continually wade through introductory material and hand-holding just to get to some small nugget of substance. In that case…
The target audience point is fair. There are basic concepts that I don't bother defining in any paper I write, and I'm sure there are people who would make the same argument about them that I'm making here. But I'm not suggesting writing everything like "An Extremely Gentle And Slow Introduction to X, With Lots of Reassurances That You Can Do It". The question probably comes down to how accessible a paper should be.…
I’ve started to keep a collection of readable papers (mostly engineering/experimental science, but a little bit of more theoretical work as well) that cover what I consider to be pretty foundational concepts, because additional citations are ~free and it at least gives an entry point for readers that are on the edge of the target audience.
As a consequence, I’ve read papers that were written anywhere from the late 19th century to just a year or two ago. In my experience, the older papers tend to be more understandable at a conceptual level but more modern ones tend to be more precise with the details. There is likely some survivorship bias here, though, as there has been more time for the worst of the old papers to be forgotten.
The writing style has also changed a lot— The older papers present things in a much more narrative way, and it can be a challenge to bring the kind of motivational context that allows into a paper that would feel at home in a modern publication.
Re: Math writing is dull when it neglects the human dimension
#94Stephen Leacock answered this topic perfectly over a hundred years ago in Moonbeams from the Larger Lunacy, chapter six, Education Made Agreeable or the Diversions of a Professor.
https://www.gutenberg.org/files/4064/4064-h/4064-h.htm#link2...
Minor excerpts to whet your appetite (but seriously, read it, it’s excellent humour):
> In the first place I have compounded a blend of modern poetry and mathematics, which retains all the romance of the latter and loses none of the dry accuracy of the former. Here is an example:
The poem of
LORD ULLIN’S DAUGHTER
expressed as
A PROBLEM IN TRIGONOMETRY
—⁂—
> Here, for example, you have Euclid writing in a perfectly prosaic way all in small type such an item as the following:
> “A perpendicular is let fall on a line BC so as to bisect it at the point C etc., etc.,” just as if it were the most ordinary occurrence in the world. Every newspaper man will see at once that it ought to be set up thus:
AWFUL CATASTROPHE
PERPENDICULAR FALLS HEADLONG
ON A GIVEN POINT
The Line at C said to be completely bisected
President of the Line makes Statement
etc., etc., etc.Re: Math writing is dull when it neglects the human dimension
#95Earlier quoted context omitted.
imo this is largely because of the incentives around the game of school and testing. If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best. Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still hav…
For the vast majority of the students the curiosity, as you put it, isn’t really there. Understanding is very hard work and most people don’t want to put in the work to acquire understanding.
Perhaps, but it isn’t helped that spending effort to understand is often in direct conflict with the work required to get a good grade.
You’re not tested on understanding how stuff is derived or how it’s used, you’re tested on grinding problems, particularly ones that are easy for teachers to put on a test and easy to grade (if they even bother with that, my worst teachers didn’t create their own tests or grade them, machines did both). In English or humanities you’re tested on predicting whatever bullshit your teacher believes and then crafting an essay that leans into their cognitive bias.
I got very good at school and it was mostly by trying to model the minds of my mostly bad teachers and getting good at predicting what they want to hear and what they’d ask on the exam. With that down I could focus personal time on the stuff I was truly interested in (which ironically is what actually had market value).
At least in the US public school system this is further hurt by public school teachers often barely knowing the material themselves and that’s if they’re not also outwardly hostile/condescending to the kids (there are always great teachers, but they’re the exception to the rule).
The system isn’t selecting for the right things and those with enough money know this and work around it.
Re: Math writing is dull when it neglects the human dimension
#96I remember once reading an opinion piece that suggested that most papers should trim the "introduction" section greatly, instead referring to key review papers or textbook entries. Although I've never followed this advice -- I want papers to be accepted, after all -- I can see a lot of merit to it. The idea is to point readers to cohesive and well-cited treatments of the foundational material, rather than presenting…
If academic papers were published in HTML with living links on the web it would help. Hypertext solves this but are they not allowed to use modern (1990s+) technology?
Re: Math writing is dull when it neglects the human dimension
#97Earlier quoted context omitted.
Before there was AlphaGo, many top Go players believed that understanding Go is somehow special in helping us to understand the universe. The AlphaGo was a shock, because it turned Go into "just another game", which can be beaten by enough calculations on a powerful computer. I think the mathematics is the same. Lot of its beauty we cherish, because we don't properly understand it on the "raw" level of SAT (I would w…
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 a very large instance but if there is a practical way of approaching the problem, it shouldn't matter.
I think you're assuming that future computer scientists and mathematicians will continue to run (many different) algorithms, and I don't. I think there might be a single algorithm, a SAT solver, which will subsume all others.
Re: Math writing is dull when it neglects the human dimension
#98As 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?
Re: Math writing is dull when it neglects the human dimension
#99[flagged]
Re: Math writing is dull when it neglects the human dimension
#100Earlier 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…
> Even is SAT is P that doesn't imply a solution can feasibly be found.
It does, because in this case you also assumed that running numerical algorithm was feasible. So if your SAT solver fails to find the answer, it is either suboptimal method (because numerical method exists), or (if the instance is UNSAT) the numerical method gives you a flawed result.