The Two Cultures of Mathematics (2000) [pdf]
dpmms.cam.ac.uk
The Two Cultures of Mathematics (2000) [pdf]
1–10 of 72 posts
Re: The Two Cultures of Mathematics (2000) [pdf]
#2I feel like I could sit down and rewrite this, in a couple of hours, to be about Computer Science, but the practical field and the educational as well.
I mean, I could feasibly include this sentence as a quote, depending on which aspect of CS I was talking about (academic CS and language design in particular): ‘It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the ones that appeal to problem-solvers.’
It is an interesting article and I will look forward to any discussion about it, especially the correlation to CS and development.
Re: The Two Cultures of Mathematics (2000) [pdf]
#3It 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 and for the US.
Math got taken very seriously due heavily to WWII and The Bomb. There The Bomb was seen as heavily from Einstein's E = mc^2. So, suddenly the US (especially Congress) concluded that for US national security the US had to lead in science and math. Over the years after WWII, various events, e.g., Sputnik, reinforced this conclusion.
One result was that the US NSF had funds for math research for culture (1) in the US research universities. The emphasis was on what was really new; that is, if there was to be another E = mc^2 result from math and science, then the US wanted to be the first to discover that result.
But the NSF was not much interested in funding math in culture (2).
Then there was some irony: For US national security, the NSF was funding math in culture (1) while also for US national security, especially the Cold War and the Space Race, the US DoD and NASA were heavily funding applications of math via culture (2). In those years, there were good culture (2) careers, especially near DC, for people with comparatively good backgrounds in math and computing.
But in the profit seeking, practical, commercial US, away from the motivation of the Cold War and the Space Race, math from either culture was ignored, laughed at, or in rare but overwhelming cases terribly feared.
The there was and is help for culture (2): The US research universities also commonly have schools of engineering, and there are journals eager to publish applications of math.
E.g., the usual criteria for publication are "new, correct, and significant", and an application of some math that is a new and correct solution for a significant practical problem can be seen to satisfy these criteria and qualify for publication.
So, net, currently, an application of math -- maybe all or nearly all old math -- that is powerful and valuable in practice -- i.e., some secret sauce -- can count on little or no competition.
Re: The Two Cultures of Mathematics (2000) [pdf]
#4I feel like I could sit down and rewrite this, in a couple of hours, to be about Computer Science, but the practical field and the educational as well. I mean, I could feasibly include this sentence as a quote, depending on which aspect of CS I was talking about (academic CS and language design in particular): ‘It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the o…
From my experience, among academic computer science professors, the attitude is that computer science is about the "fundamentals" of computing.
E.g., once I was talking with such a computer science professor and listing features I wanted in a better programming language, and immediately his reaction was that for a professor developing such a language would be "academic suicide".
Re: The Two Cultures of Mathematics (2000) [pdf]
#5previous submissions
https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
Re: The Two Cultures of Mathematics (2000) [pdf]
#6I feel like I could sit down and rewrite this, in a couple of hours, to be about Computer Science, but the practical field and the educational as well. I mean, I could feasibly include this sentence as a quote, depending on which aspect of CS I was talking about (academic CS and language design in particular): ‘It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the o…
From my experience, among academic computer science professors, the attitude is that computer science is about the "fundamentals" of computing. E.g., once I was talking with such a computer science professor and listing features I wanted in a better programming language, and immediately his reaction was that for a professor developing such a language would be "academic suicide".
That matches my experience as well. It also illustrates the divide in educational tracks, for lack of a better term, that I probably should have expanded on in my original post.
In addition to individual developers and development teams have the potential to be either the problem-solving or the theory building types, the path a person take to programming can go either of those directions. It is most apparent in the difference between a BS in CS from somewhere like Carnegie-Mellon (a bastion of high level theoretical CS education) and any code boot camp or online web-dev centric training course.
Re: The Two Cultures of Mathematics (2000) [pdf]
#7Just to also a couple existing comments here, a problem solver is not necessarily an applied person or an engineer. It's someone who looks for interesting unsolved questions, and invents what needs inventing to get a solution.
By contrast, an engineer uses well established techniques (with creativity!) to build bridges that they know can be built. Diving into unsolved mathematical problems - especially the ones that have picked up a reputation - is inherently a riskier endeavor.
As the text says: 'the interesting problems tend to be open precisely because the established techniques cannot easily be applied.'
Re: The Two Cultures of Mathematics (2000) [pdf]
#8It 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…
You seem to imply that the two cultures are pure vs applied but that’s not really right. Something like Sturm-Liouville theory is generally very applied and useful but falls into culture 1. The sort of mathematics that Erdős did was pure but fell more into culture 2.
Re: The Two Cultures of Mathematics (2000) [pdf]
#9In case it is not familiar, the title of this alludes to https://en.m.wikipedia.org/wiki/The_Two_Cultures
Re: The Two Cultures of Mathematics (2000) [pdf]
#10Unfortunately 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 the Michael Atiyah interview that this article sometimes feel like a direct reply to.