The Two Cultures of Mathematics (2000) [pdf] • Hacker News Board

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

#11

Post by josephg » Mon, Apr 26, 2021, 7:18 AM UTC

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 their users.

I got pushback here and elsewhere that lots of people fit into multiple camps - which makes sense. Maybe they’re better described as an ecology of values. But I also think there’s something real here. I worked in a consulting shop a few years ago and my boss came back from some front end development conference gushing about a talk he’d seen that I had to watch. The talk was a layman’s description of FP’s immutability approach applied to react. My boss had never heard of immutability before because it had never come up in front end web development circles. There’s lots of opportunities for our software to improve by cross contaminating all our best ideas.

[1] https://josephg.com/blog/3-tribes/

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

#12

Post by QuesnayJr » Mon, Apr 26, 2021, 7:23 AM UTC

thomasahle wrote: post #10

Unfortunately the article quickly descends into a long defence of the merits of Combinatorics, rather than a description of the two cultures. Since combinatorics are so ubiquitious today in computer science, algorithms in particular, it would be more interesting for me to better understand the "algebraic number theory and differential geometry" world thst the author continously refers to. I guess I should just read t…

It's a real phenomenon that you see at elite departments. I got into an argument here in the comment section with a mathematician on whether graph theory was a "core" area of mathematics. I don't even like graph theory or combinatorics.

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

#13

Post by 29athrowaway » Mon, Apr 26, 2021, 7:28 AM UTC

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.

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

#14

Post by throwaway17_17 » Mon, Apr 26, 2021, 7:36 AM UTC

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…

I remember reading one of threads on your post here. The level of depth that the commenters went into regarding every possible permutation and exception to the broad classification were astounding.

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

#15

Post by dang » Mon, Apr 26, 2021, 7:38 AM UTC

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)

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

#16

Post by josephg » Mon, Apr 26, 2021, 7:45 AM UTC

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.

I'd love to see actual numbers on this. Its not 95% - but all of our intuitions will be a bit wrong because people cluster in workplaces based on personal values. So no matter what you're like, you'll end up working with people similar to yourself.

I wouldn't be surprised if people who just program for a paycheck are the majority of employees in many offices. I know they're a tiny minority in a lot of the places I've worked at. That's not a boast or a coincidence - humans cluster in tribes based on shared values. I don't consider myself part of the same community as people who show up to work to close jira tickets and collect a paycheck.

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

#17

Post by 6gvONxR4sf7o » Mon, Apr 26, 2021, 7:53 AM UTC

josephg wrote: post #16

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.

I'd love to see actual numbers on this. Its not 95% - but all of our intuitions will be a bit wrong because people cluster in workplaces based on personal values. So no matter what you're like, you'll end up working with people similar to yourself. I wouldn't be surprised if people who just program for a paycheck are the majority of employees in many offices. I know they're a tiny minority in a lot of the places I've…

> 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.

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

#18

Post by jorgenveisdal » Mon, Apr 26, 2021, 8:00 AM UTC

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 areas in these fields where essentially nobody had achieved anything. The thing was to find an interesting question that he could say something about."

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

#19

Post by Double_Cast » Mon, Apr 26, 2021, 8:03 AM UTC

To me, the distinction maps onto the Effectual vs Causal distinction. For some path "A to B", some people prefer to consider their present tools/resources (point A) and work forward opportunistically. While others prefer to consider the end-goal (point B) and work backwards recursively. If the analogy is unclear: a theory is a tool; a specific problem is an end-goal.

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

#20

Post by tarsinge » Mon, Apr 26, 2021, 8:14 AM UTC

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…

Interesting. I am definitely of the third kind since I'm a kid. But with the years I've come to appreciate mathematics (maybe FP was a gateway), and machines through wanting more real world connection, learning electronics and building physical things. Totally agree with your conclusion, no matter the path, all these aspects are important.