"Applied pure mathematics is any application of any mathematics to anything outside of the closed world of mathematics itself. You never know which weird corner of the vast libraries of “apparently useless” mathematics will help you make sense of reality."
May be the classical pure vs applied is the wrong taxonomy. Hardy defended, dare I say even fetishized the search of truth regardless of whether it has an application as if that were pure. The math that is untainted by whether or not it has applications - but this changes over time. Is number theory less pure once it has application in cryptography? Is category theory less abstract now if parts of it underlies the basis of type theory (CS)?
This is why Tim Gower’s Theory Building vs Problem Solving distinction (he doesn’t take sides as he explained recently) is useful. Because this defines taste of what style appeals to you.
The natural complement to Tim Gower’s two cultures axis is the source of what drives you to build theory. Here, I see as you as unapologetically grounded in real life, much in the culture of Shannon. He founded an entire theory around a problem he was trying to solve. So, may be you are an application-inspired theory builder? And for this you need a little bit of both - persistence as in problem solving and an aesthetic sense when you are not merely satisfied when you got the trophy.
Agreed, have always thought that practicing mathematical-problem-solving or theorem-proving would never go out of vogue since it trains the brain in a different type of thinking. Working out did not go out of vogue after most professions became sedentary. Except working out has a visible benefit on your muscles. We should make sure our mathematical thinking muscles do not atrophy.
“That is, a lot of mathematics is training people to benchmaxx”
I would go further and say a lot of education is training people to benchmaxx and this is another ill-intended effect of quantifauxcation. Liberal arts education was traded with the benchmaxx education and we have found out that machines can benchmaxx better than us.
As I see it, if you are in pure "pure mathematics" the practical successes from applied pure mathematics are not going to cut it anymore once you have to argue for your existence (Tao already tried exactly that with the compressed sensing story a year ago). That of course is a problem of pure "pure mathematics" and it will be interesting to see if the field is going to fission.
As for the second point that probably requires a bit of elaboration. But in short I think, if you are in it for l'art pour l'art then the consequentialist route of justification is blocked for you. Of course it might happen, that some of your creations by chance find some application. But this is not why you did it to begin with and there are others who do exactly that. And more efficiently. Why not be honest then and join the other products of culture that are created without practical intent?
Hi professor, it's surprised to know that you view compressing sensing as some type of gold rush. Thank you for introducing the term of applied pure math and this golden post
To pile on the Wigner references, the last paragraph from "Are We Machines", 1969
> Returning to the question in the title of this section, we must conclude that, if the preceding discussion is valid, life does share with machines the property that it can be created artificially. None of this should obscure the fact, self-evident to this writer, that having emotions and desires does profoundly distinguish us from machine.
I'm sure the words to replace "emotions and desires" are in people's minds
I like this a lot and cackled at "What are millennium problems other than humanity’s final math exam?" and sobered up at "This unfortunately makes a lot of sense with the benefit of hindsight!"
"This is why I like (and have been using throughout) Jordan Ellenberg’s term applied pure mathematics."
STOP TRYING TO MAKE FETCH HAPPEN
Never! I will Stiglers Law this into existence.
"Applied pure mathematics is any application of any mathematics to anything outside of the closed world of mathematics itself. You never know which weird corner of the vast libraries of “apparently useless” mathematics will help you make sense of reality."
MAH GAWD THAT'S OPERATIONAL RESEARCH'S MUSIC!!
May be the classical pure vs applied is the wrong taxonomy. Hardy defended, dare I say even fetishized the search of truth regardless of whether it has an application as if that were pure. The math that is untainted by whether or not it has applications - but this changes over time. Is number theory less pure once it has application in cryptography? Is category theory less abstract now if parts of it underlies the basis of type theory (CS)?
This is why Tim Gower’s Theory Building vs Problem Solving distinction (he doesn’t take sides as he explained recently) is useful. Because this defines taste of what style appeals to you.
The natural complement to Tim Gower’s two cultures axis is the source of what drives you to build theory. Here, I see as you as unapologetically grounded in real life, much in the culture of Shannon. He founded an entire theory around a problem he was trying to solve. So, may be you are an application-inspired theory builder? And for this you need a little bit of both - persistence as in problem solving and an aesthetic sense when you are not merely satisfied when you got the trophy.
Agreed, have always thought that practicing mathematical-problem-solving or theorem-proving would never go out of vogue since it trains the brain in a different type of thinking. Working out did not go out of vogue after most professions became sedentary. Except working out has a visible benefit on your muscles. We should make sure our mathematical thinking muscles do not atrophy.
I really enjoyed this and overall agree. You say
“That is, a lot of mathematics is training people to benchmaxx”
I would go further and say a lot of education is training people to benchmaxx and this is another ill-intended effect of quantifauxcation. Liberal arts education was traded with the benchmaxx education and we have found out that machines can benchmaxx better than us.
As I see it, if you are in pure "pure mathematics" the practical successes from applied pure mathematics are not going to cut it anymore once you have to argue for your existence (Tao already tried exactly that with the compressed sensing story a year ago). That of course is a problem of pure "pure mathematics" and it will be interesting to see if the field is going to fission.
Can you point me to Tao's compressed sensing reflection?
And could you say a bit more about why building potential intellectual scaffolding won't cut it for the pure mathematicians?
Sure, it is a series of posts (I guess they are called toots) on his mastodon beginning with https://mathstodon.xyz/@tao/114967650999562435
As for the second point that probably requires a bit of elaboration. But in short I think, if you are in it for l'art pour l'art then the consequentialist route of justification is blocked for you. Of course it might happen, that some of your creations by chance find some application. But this is not why you did it to begin with and there are others who do exactly that. And more efficiently. Why not be honest then and join the other products of culture that are created without practical intent?
Hi professor, it's surprised to know that you view compressing sensing as some type of gold rush. Thank you for introducing the term of applied pure math and this golden post
To pile on the Wigner references, the last paragraph from "Are We Machines", 1969
> Returning to the question in the title of this section, we must conclude that, if the preceding discussion is valid, life does share with machines the property that it can be created artificially. None of this should obscure the fact, self-evident to this writer, that having emotions and desires does profoundly distinguish us from machine.
I'm sure the words to replace "emotions and desires" are in people's minds
I like this a lot and cackled at "What are millennium problems other than humanity’s final math exam?" and sobered up at "This unfortunately makes a lot of sense with the benefit of hindsight!"
I did not however care for the recent Fields Medal Winner's statement (the authors could benefit from reading this post) because I found it mostly to be preaching to the choir. https://computingandsociety.substack.com/p/the-debate-about-ai-companies-proving.
At least, something that doesn't feel me with despair.
*fill