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I was giving my opinion for myself and not "deciding" for anyone else. > Who gets to decide what is and isn't useful? There is a recipe for rabbit stew that s

I was giving my opinion for myself and not "deciding" for anyone else. > Who gets to decide what is and isn't useful? There is a recipe for rabbit stew that starts out "First catch a rabbit". Well my own recipe for applied math starts out "First find an application." I don't define applied math as just mathematical physics or its connections with, say, mechanical or electrical engineering. For me, applied math is math that has been applied. Sure, you mention number theory and cryptography; so, now at least in part they are applied math. There is also finite fields and error correcting codes -- I took a whole grad course on coding theory. I had a good background in abstract algebra and was torqued that the prof was sloppy with the math. But coding theory is important, and for me that makes abstract algebra applied math. Just how R. Hamming saw to use finite field theory I don't know -- curious insight. My undergraduate honors paper was on group representation theory, and that is applied math at least for its connections with molecular spectroscopy. In fact, my work was stimulated by some people from the chemistry department that came to the math department for help with group representation theory. IIRC, the quantum mechanics part was in part from E. Wigner. > And lastly, even if a subfield provides no use to "common" humans, how should that matter? If the work is being paid for, then commonly it matters a LOT to some of the people paying for it. > People should be free to study what they want. Of course. For some years, I studied violin. I made some progress but set violin aside to have more time for my startup. Ah, but, no one paid me for studying violiin! People misread my post: First, the only math I was criticizing was foundations as deep as in the OP. Second, my criticism was only for my own personal values and opinion. Sure, maybe work in Ramsey theory will be as important in applications as the Riemann integral -- I doubt it, but maybe. I spent some months in that dark basement; others are welcome to do that if they wish; I wish I hadn't and wouldn't do it again.

Ar-Curunir 9y ago
Defining "applied math" as mathematics that has found applications is disingenous, IMO; what is and isn't applied can change rapidly in the course of a few years. A number theorist can go from pure to applied because someone else found an application of work done by other people in his field? Taking an example from TCS: Probabilistically checkable proofs. They allow you to encode a proof for a statement so that you checking the proof requires looking at in only a few locations. Back when they were conceived, in the early 90s, all constructions were efficient only asymptotically, with galactic constants. Only in the past 2 years have constructions of PCPs been realized that are sufficiently efficient for (some) applications to checking program executions. PCPs were for years what most theorists would consider a core theoretical object with not many hopes of finding application, and indeed 99% of research in the field focused on "negative" uses of PCPs for finding hardness of approximation results. > If the work is being paid for, then commonly it matters a LOT to some of the people paying for it. What makes an industry with a lot of money in it, like online advertising, worth more than study of something completely theoretical?
- graycat 9y ago
  > Defining "applied math" as mathematics that has found applications is disingenuous, IMO; what is and isn't applied can change rapidly in the course of a few years. Not "disingenuous" at all: I want to apply math, especially to making money. To make money is the main reason I studied math; I wanted math to help my career, to make money, to support a family. If not math, then maybe physics, some part of engineering, etc. > what is and isn't applied can change rapidly in the course of a few years. My experience is that that doesn't happen very often. But again, once again, over again, yet again, I am not, Not, NOT, N.O.T. -- clear enough -- running down pure math. NOT doing that. I just wrote that foundations as in the OP was too far from applications for me. I have been totally, overwhelmingly, crystal clear about this point in this thread, and there was nothing in my first post that ran down pure math. Again, yet again, ..., I was talking about my view for me of foundations such as in the OP. You misread my first post and didn't read my other posts. If someone found some applications for PCPs, then good for them, and that makes PCPs applied math. Better techniques for proofs of correctness obviously would be good work in computer science with plenty of valuable applications. > What makes an industry with a lot of money in it, like online advertising, worth more than study of something completely theoretical? Nothing, but most sources of financial investment want a financial return. That's much of how our economy works. To be blunt and frank, Congress votes money for math mostly for US national security and because of the role of math in WWII and off and on since then. If some people at the NIH tells Congress that they like math, too, then that will help. But the remark at the beginning of the movie on Nash is basically correct: "Mathematics won WWII". Congress can be slow on the uptake, but they tend to believe that math did win WWII and had a big role in GPS, Keyhole, stealth, design of the core of fission and fusion bombs, etc. Congress takes US national security quite seriously. The other biggie for Congress is the NIH -- if only because most people in Congress have gray hair and want research that will help them if they get sick. It remains, if you want a job in math, especially connected with computing, then those jobs are still where I started my career (and should have stayed there) within 100 miles of the Washington Monument.

Ar-Curunir 9y ago

Defining "applied math" as mathematics that has found applications is disingenous, IMO; what is and isn't applied can change rapidly in the course of a few years. A number theorist can go from pure to applied because someone else found an application of work done by other people in his field? Taking an example from TCS: Probabilistically checkable proofs. They allow you to encode a proof for a statement so that you checking the proof requires looking at in only a few locations. Back when they were conceived, in the early 90s, all constructions were efficient only asymptotically, with galactic constants. Only in the past 2 years have constructions of PCPs been realized that are sufficiently efficient for (some) applications to checking program executions. PCPs were for years what most theorists would consider a core theoretical object with not many hopes of finding application, and indeed 99% of research in the field focused on "negative" uses of PCPs for finding hardness of approximation results. > If the work is being paid for, then commonly it matters a LOT to some of the people paying for it. What makes an industry with a lot of money in it, like online advertising, worth more than study of something completely theoretical?

graycat 9y ago
> Defining "applied math" as mathematics that has found applications is disingenuous, IMO; what is and isn't applied can change rapidly in the course of a few years. Not "disingenuous" at all: I want to apply math, especially to making money. To make money is the main reason I studied math; I wanted math to help my career, to make money, to support a family. If not math, then maybe physics, some part of engineering, etc. > what is and isn't applied can change rapidly in the course of a few years. My experience is that that doesn't happen very often. But again, once again, over again, yet again, I am not, Not, NOT, N.O.T. -- clear enough -- running down pure math. NOT doing that. I just wrote that foundations as in the OP was too far from applications for me. I have been totally, overwhelmingly, crystal clear about this point in this thread, and there was nothing in my first post that ran down pure math. Again, yet again, ..., I was talking about my view for me of foundations such as in the OP. You misread my first post and didn't read my other posts. If someone found some applications for PCPs, then good for them, and that makes PCPs applied math. Better techniques for proofs of correctness obviously would be good work in computer science with plenty of valuable applications. > What makes an industry with a lot of money in it, like online advertising, worth more than study of something completely theoretical? Nothing, but most sources of financial investment want a financial return. That's much of how our economy works. To be blunt and frank, Congress votes money for math mostly for US national security and because of the role of math in WWII and off and on since then. If some people at the NIH tells Congress that they like math, too, then that will help. But the remark at the beginning of the movie on Nash is basically correct: "Mathematics won WWII". Congress can be slow on the uptake, but they tend to believe that math did win WWII and had a big role in GPS, Keyhole, stealth, design of the core of fission and fusion bombs, etc. Congress takes US national security quite seriously. The other biggie for Congress is the NIH -- if only because most people in Congress have gray hair and want research that will help them if they get sick. It remains, if you want a job in math, especially connected with computing, then those jobs are still where I started my career (and should have stayed there) within 100 miles of the Washington Monument.