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The Two Cultures of Mathematics (2000) [pdf]

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Re: The Two Cultures of Mathematics (2000) [pdf]

#51

Post by gryn »

29athrowaway wrote: post #13
josephg wrote: post #11

I wrote a blog post a few years ago[1] making a similar claim about computer science. I said there’s 3 main camps of programmers: - People who enjoy programming because it’s mathematically beautiful (eg Haskell programmers) - People who enjoy programming because they like reasoning about machines, and like mechanical sympathy (eg C programmers) - And people who like programming because it can solve real problems for…

And people that do not care about any of those things and just want a paycheck, or to be promoted so that they do not have to code anymore (95% of developers worldwide). Unfortunately the people that get excited building things is outnumbered by the people that is just in this for the money.

that feels like a false dichotomy, you can be both.

you were passionate, found a job that claimed to match your passion and later found out otherwise. rinse and repeat multiple times, and there you go.

soon you started to be paycheck only at your day job and passionate off hours in your free time.

Re: The Two Cultures of Mathematics (2000) [pdf]

#52

Post by 276 »

jorgenveisdal wrote: post #18

Sylvia Nasar's take on John Forbes Nash, Jr.'s type: "He was a mathematician who viewed mathematics not as a grand scheme, but as a collection of challenging problems. In the taxonomy of mathematicians, there are problem solvers and theoreticians, and, by temperament, Nash belonged to the first group. He was not a game theorist, analyst, algebraist, geometer, topologist, or mathematical physicist. But he zeroed in on…

let me try an example... ^^

'12 x 23 = 276'

Most often listed is the number '2'. The highest numbers together make '7' and if you defer 'the multiplication one position to the right', you have '2 x 3' -making '6'.

276 (-;

Re: The Two Cultures of Mathematics (2000) [pdf]

#53

Post by 29athrowaway »

gryn wrote: post #51
29athrowaway wrote: post #13

Earlier quoted context omitted.

And people that do not care about any of those things and just want a paycheck, or to be promoted so that they do not have to code anymore (95% of developers worldwide). Unfortunately the people that get excited building things is outnumbered by the people that is just in this for the money.

that feels like a false dichotomy, you can be both. you were passionate, found a job that claimed to match your passion and later found out otherwise. rinse and repeat multiple times, and there you go. soon you started to be paycheck only at your day job and passionate off hours in your free time.

Yes, you can make money pursuing your passion. But the point is that there are a majority of people that are not interested in programming and have no passion.

Their real passion is a having a band, or hiking, traveling, etc. And programming is just a way to fund those activities.

Others feel that programming is something that unimportant people do because they feel entitled to become managers. But why would a person like to work for a person they can't learn anything from? a person that looks down on their job? Noone wants a manager like that.

Re: The Two Cultures of Mathematics (2000) [pdf]

#54

Post by theflyinghorse »

ukj wrote: post #39

This paper makes a ton of brilliant points all of which strongly resonate with me: * The results that will last are the ones that can be organized coherently and explained economically to future generations (yes! effective compression!) * How effectively a result can be communicated to another mathematician (and perhaps even s/mathematician/person/) 90% of my time spend 'studying mathematics' is spent lexing the nota…

I remember in our intro to AI course our prof would sometime run out of English letters for symbols, then start introducing German ones, and eventually start using triangles and squares for stuff

Re: The Two Cultures of Mathematics (2000) [pdf]

#55

Post by yummypaint »

There is a similar kind of division of labor in physics between theorists and experimentalists. The cultural difference is closer to that between mathemeticians and engineers, but of course both groups are entirely dependent on each other and most successful collaborations have both. The days of solo publishing are mostly over.

Re: The Two Cultures of Mathematics (2000) [pdf]

#56

Post by dTal »

isolli wrote: post #34

Only tangentially related, but a friend of mine had to interrupt his doctoral thesis in mathematics because the set he was studying turned out to be empty. This gave a lot of ammunition to our Russian colleagues, who routinely make fun of French mathematicians for being far too ensconced in theory.

That still sounds like an interesting and publishable result, if unfortunate if you're trying to spin an entire PhD out of it.

Re: The Two Cultures of Mathematics (2000) [pdf]

#57

Post by 6gvONxR4sf7o »

eru wrote: post #31
6gvONxR4sf7o wrote: post #17

Earlier quoted context omitted.

> I'm not sure it makes sense to describe people who love programming and people who just do it for a paycheck as truly being in the same field. This is why I keep my mouth shut IRL about just wanting the paycheck. I'd imagine a lot more than a tiny minority of people are just there for the job where you've worked. We just keep our mouths shut because the passionate folks judge us paycheckers.

It's fine to optimize for the paycheck first and foremost. But while you are at your job anyway, might as well make it slightly less of a drudgery while you are at it. (Eg I quite like functional programming. Both because I like the style of thinking, but also because I don't trust myself nor anyone else with code; and eg a heavy emphasis on immutability means that I'm less likely to get woken up in the middle of the…

I have a ton of coworkers who try to make their job more interesting by trying the most interesting tools instead of the best tools for the job. They have less drudgery, but more stress from not hitting deadlines as reliably. Meanwhile I'll embrace the drudgery and do the boring thing, stay less stressed because get it done more quickly and reliably because I chose the right tool, and got promoted really high.

Taking a mercenary attitude towards work works just fine for me, and keeps me overall happier.

Per your example, I like FP and immutability for the same reasons (won't get paged as much), and I'm always reading to stay up on my game, but it's still just work. If you worked with me, you'd probably think I live and breath this stuff as a passion because I put so much time in to stay so much on top of the tools available. But I hate programming. Hell, you might even say my hate of it drives mastery in the same way your passion drives your mastery. To me, it's just a tool by which to automate things I do care about (and retire younger than I could in other roles).

Re: The Two Cultures of Mathematics (2000) [pdf]

#58

Post by bigbillheck »

graycat wrote: post #3

It appears that roughly the point of the OP (original post) is that in math there are two cultures (1) people who want to develop new fields of math with definitions, theorems, and proofs and (2) people who want to use math, all or nearly all old, to solve problems usually from outside math. Apparently the OP is from the UK (United Kingdom). Here I attempt to provide a view and explanation of those two cultures from…

> But the NSF was not much interested in funding math in culture (2).

I'm not sure that this is supported by the historical record.

For example, from NSF's own page: https://www.nsf.gov/about/history/overview-50.jsp > The first NSF grants are awarded to support computation centers and research in numerical analysis. Three years later, a separate budget is created for grants to enable academic institutions to acquire major computer equipment.

That seems like it's very firmly in your (2).

Going further, I found the distribution of NSF grants for 1952. Mathematics got one grant, to Lamberto Cesari, for work on "Asymtotic Behavior and Stability Problems". Cesari has a wiki page with links to some of his articles, for example : https://projecteuclid.org/journals/bulletin-of-the-american-... , and a bio at St Andrews: https://mathshistory.st-andrews.ac.uk/Biographies/Cesari/

Going by those, I don't see how that would not be (2)?

A little later we find UMN's "Institute for Mathematics and its Applications" (https://www.ima.umn.edu/about/history, sounds very (2)-ish) which was established with NSF funding in 1982. And a bit after that, in the 90s, I am fairly confident that some portion of my graduate work in applying mathematics to biological problems was NSF-supported.

Re: The Two Cultures of Mathematics (2000) [pdf]

#59

Post by paunstefan »

enriquto wrote: post #44
nicoburns wrote: post #42

Earlier quoted context omitted.

Perhaps you are a detail-oriented person? I've met quite a lot of people who - like you it seems (although perhaps you disagree) - find things that are low-level and procedural to be clearest. Such people often like languages like C and Go where this style is encouraged. On the other hand, I tend to think in terms of abstractions. And thus find things much clearer when they are based on high level abstractions (thing…

i think it may be that. When I see some code like this in C++: y = f(x); I'm extremely terrified to what is going on. It is like looking into an abyss. Is this code calling a function named "f" with argument "x"? If so, there may be several different functions "f" depending on the type of "x". Maybe none of them has the same type as "x", but there are some conversions that may happen and lead to that. Or maybe "f" is…

It sounds more like you have a problem with C++ and some of it's features, like function overloading and its move semantics, which I agree can be confusing and they always turned me away from C++, I just prefered C because it's straightforward. But then I tried Rust and I saw that it's not the abstractions that are confusing, it's C++.

Re: The Two Cultures of Mathematics (2000) [pdf]

#60

Post by dang »

alberto_ol wrote: post #33
dang wrote: post #15

Some past threads: The two cultures of mathematics and biology - https://news.ycombinator.com/item?id=8819811 - Dec 2014 (69 comments) The Two Cultures of Mathematics (2000) [pdf] - https://news.ycombinator.com/item?id=7970284 - July 2014 (28 comments) "Problem Solvers" vs "Theory Developers": The Two Cultures of Mathematics. [pdf] - https://news.ycombinator.com/item?id=682913 - July 2009 (5 comments)

the first thred "The two cultures of mathematics and biology" is not the same essay

Ah yes, sorry - I noticed that and meant to take it out but evidently just imagined that I did!
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