4 ms·

Ah, foundations of math, start with applied math for making money, descend to applied math that doesn't make money, descend to pure math, descend to foundations

Ah, foundations of math, start with applied math for making money, descend to applied math that doesn't make money, descend to pure math, descend to foundations, and, there, down in the dark basement try to make some sense. I've been there, done that, never made even 10 cents there! So, get to Zermelo-Fraenkel set theory, the axiom of choice, the work of Kurt Gödel and Paul Cohen (I still have the copy of Cohen's paper Max Zorn gave me!), etc. A friend worked in forcing arguments, Ramsey theory, etc. and never made even 10 cents there either. I climbed out of that dark basement and don't want to go back!

fizixer 9y ago
I'm on my way down but haven't seen the darkness yet :) Maybe because I didn't start out with money making in mind (not to say I don't want to make money. I do. I do.) Also how long did the whole process take for you? ... If you make up your mind in advance, as I have, that you're going to be in there for 10 years give or take, (in 8-hour days; so 20 calendar years if you spend 4 hours a day), and try to make a living on the side, does it still feel as dark?
- graycat 9y ago
  One way and another, starting in my senior year in college, I spent a year or so in that dark basement. The most intense time was in a course in axiomatic set theory in an NSF summer math program at Vanderbilt. The next fall, I was in a course in real analysis, and the prof started with foundations. After the first test he wanted to "see me". The exercises on the test were all trivial except one, and I got it only in the last minute or so so wrote quickly. I used little omega for the ordinal of the natural numbers without defining it. I told him that from the course I'd taken the previous summer I thought that that was standard notation. Apparently he didn't know that. After my explanation, he saw that my solution was correct and one step shorter than his. Then I asked him what he wanted to "see me" about, and he said "Now, nothing.". Gads. I got my Ph.D. later from a better program at another university. Occasionally later I touched on that material. That was all. No way did I spend or want to spend 10 years in that basement. And no way did I want to do original research with that material. Some of the pure math I studied I liked and still like a lot, and some of it is a crucial pillar of the crucial applied math core of my startup.
throwawayjava 9y ago
I used to say stuff like this, but honestly... don't. If you're mentoring a young impressionable mathematician, explain the trade-offs in pure vs applied work, and explain how to determine which pure math is likely to be helpful in their useful lifetime. Besides, "pure" and "applied" distinction is hilariously subjective and stupid. IME a lot of theoretical CS is more-or-less accurately characterized "pure math" and also far more financially remunerative than the bullshitty pointless PDE hacking lots of "applied math" folks do. Pure vs. applied is a stupid perspective these days because it almost exclusively defines a delineation among communities of mathematicians during the late 20th century; "useful in the next 3 years to ad tech folks" vs. "long-term/foundational importance in science and engineering" is a more useful and relevant distinction. But once people choose to focus on pure mathematics, don't shit on them for making that choice. They KNOW it's not a great financial commitment. It's like telling a committed humanist that "no one pays for poetry". Like, they get it already... (and besides, sometimes you're wrong and then you're that asshole that always doubted them.) Plus, plenty of pure mathematicians make high five/low six figures working 12 months with free trips all over the world. Or 9 months without the trips but with 3 months of freetime every year. And in both cases with near perfect job security. They don't have any social currency in the startup $$$$$$ obsessed world, but I bet they spend a fuckload more time with their kids and enjoy a lot more sunsets than any of startup founders. And probably make more money than the 90% of "failure cases" in the startup world too... This article is great case-in-point. All the profiled folks are sure to live very comfortable lives doing work they love patronized by lovers of the mathematical arts (or anyways live off of rich endowments one way or the other) without ever having to figure out how to nickle and dime customers. And none of this is to say that building businesses isn't valuable, since that's more-or-less taken for granted by the current venue. But it takes all types.
- graycat 9y ago
  I was not really running down pure math. Indeed, see my post below where I explained that some pure math is crucial to my startup. I was saying that I, personally, find foundations as in the OP down in the basement, dark and too far from applications in any sense. For making money as a full prof of math, first have to get there, and that usually takes over 10 years if make it at all. Yes, it's possible to play the academic game; heck one paper in math I published is pretty, surprising, etc. but I can't imagine that it will ever be useful directly or even indirectly even by several steps of indirection for the foreseeable future if ever. I've seen people publish such things and make some progress in an academic career; to me that's playing an academic game; I chose not to do that. When I was a prof (I didn't want to be but did it for a while trying to help my wife in her illness), it seemed to me that I was getting paid by students, pizza parlor owners and workers, auto dealership owners and workers, farmers, etc., and for them I wanted my work and teaching to be useful -- to me, personal curiosity, art, etc. didn't count. I really wanted the department to be clinical, professional, practical, like law and medicine, i.e., welcome people from outside academics with real problems and then seek to solve those problems. When can't solve a problem, then maybe that will be a good research direction; if make good progress, then already have one application! For applied math, determine that not by PDEs but by what can find that is useful. Early in my career around DC for mostly US national security, I found lots of such applied math. And my startup, while more focused, is basically some applied math. PDEs? I had very little to do with those; the one case was the Navier-Stokes equations, and they were so difficult to work with that the project wasn't making much progress and I was pleased to move on to other topics. It's not easy to see what pure math is the more useful. For the pure math I do respect, especially for utility, it appears that in some vague, large sense the results are fundamental, important broadly, and, eventually, inescapably relevant, but that is a difficult judgment call. Functional analysis? Sure. Algebraic geometry? Less sure. Foundations? Slim chance. I was not trying to give career advice to other people possibly interested in math but just commenting that I found the foundations as deep as in the OP just too far down in a dark basement. In math, that's an old remark about foundations -- "Drop what you are doing trying to be useful and come with me down into the dark basement and wrestle with really subtle issues down there." Standard, old remark in math. You read lots of stuff between the lines I wrote, stuff not really there.
omginternets 9y ago
Intellectual pursuits have value outside of money, you know. You speak like someone who knows the price of everything and the value of nothing.
- ambulancechaser 9y ago
  that's very uncharitable. This person has a PhD in mathematics and has done some studying in the field. This is their own personal opinion of the matter after a firsthand experience.
- graycat 9y ago
  You seriously misread my post. A lot of "pursuits have value outside of money"; e.g., for some years I pursued violin. But if a person is being paid to do research in mathematics, then usually in some sense commonly the people paying will want to know if the work is or will soon become useful. In fact, there was the David Report that severely criticized Federally funded math research that seemed to have no intended connection with applications. The theme of that criticism was if the math is being pursued just as art, then fund it like art. I was giving my personal opinion and not trying to change the opinion of anyone else. Read my other responses here.

fizixer 9y ago

I'm on my way down but haven't seen the darkness yet :) Maybe because I didn't start out with money making in mind (not to say I don't want to make money. I do. I do.) Also how long did the whole process take for you? ... If you make up your mind in advance, as I have, that you're going to be in there for 10 years give or take, (in 8-hour days; so 20 calendar years if you spend 4 hours a day), and try to make a living on the side, does it still feel as dark?

graycat 9y ago
One way and another, starting in my senior year in college, I spent a year or so in that dark basement. The most intense time was in a course in axiomatic set theory in an NSF summer math program at Vanderbilt. The next fall, I was in a course in real analysis, and the prof started with foundations. After the first test he wanted to "see me". The exercises on the test were all trivial except one, and I got it only in the last minute or so so wrote quickly. I used little omega for the ordinal of the natural numbers without defining it. I told him that from the course I'd taken the previous summer I thought that that was standard notation. Apparently he didn't know that. After my explanation, he saw that my solution was correct and one step shorter than his. Then I asked him what he wanted to "see me" about, and he said "Now, nothing.". Gads. I got my Ph.D. later from a better program at another university. Occasionally later I touched on that material. That was all. No way did I spend or want to spend 10 years in that basement. And no way did I want to do original research with that material. Some of the pure math I studied I liked and still like a lot, and some of it is a crucial pillar of the crucial applied math core of my startup.

throwawayjava 9y ago

I used to say stuff like this, but honestly... don't. If you're mentoring a young impressionable mathematician, explain the trade-offs in pure vs applied work, and explain how to determine which pure math is likely to be helpful in their useful lifetime. Besides, "pure" and "applied" distinction is hilariously subjective and stupid. IME a lot of theoretical CS is more-or-less accurately characterized "pure math" and also far more financially remunerative than the bullshitty pointless PDE hacking lots of "applied math" folks do. Pure vs. applied is a stupid perspective these days because it almost exclusively defines a delineation among communities of mathematicians during the late 20th century; "useful in the next 3 years to ad tech folks" vs. "long-term/foundational importance in science and engineering" is a more useful and relevant distinction. But once people choose to focus on pure mathematics, don't shit on them for making that choice. They KNOW it's not a great financial commitment. It's like telling a committed humanist that "no one pays for poetry". Like, they get it already... (and besides, sometimes you're wrong and then you're that asshole that always doubted them.) Plus, plenty of pure mathematicians make high five/low six figures working 12 months with free trips all over the world. Or 9 months without the trips but with 3 months of freetime every year. And in both cases with near perfect job security. They don't have any social currency in the startup $$$$$$ obsessed world, but I bet they spend a fuckload more time with their kids and enjoy a lot more sunsets than any of startup founders. And probably make more money than the 90% of "failure cases" in the startup world too... This article is great case-in-point. All the profiled folks are sure to live very comfortable lives doing work they love patronized by lovers of the mathematical arts (or anyways live off of rich endowments one way or the other) without ever having to figure out how to nickle and dime customers. And none of this is to say that building businesses isn't valuable, since that's more-or-less taken for granted by the current venue. But it takes all types.

graycat 9y ago
I was not really running down pure math. Indeed, see my post below where I explained that some pure math is crucial to my startup. I was saying that I, personally, find foundations as in the OP down in the basement, dark and too far from applications in any sense. For making money as a full prof of math, first have to get there, and that usually takes over 10 years if make it at all. Yes, it's possible to play the academic game; heck one paper in math I published is pretty, surprising, etc. but I can't imagine that it will ever be useful directly or even indirectly even by several steps of indirection for the foreseeable future if ever. I've seen people publish such things and make some progress in an academic career; to me that's playing an academic game; I chose not to do that. When I was a prof (I didn't want to be but did it for a while trying to help my wife in her illness), it seemed to me that I was getting paid by students, pizza parlor owners and workers, auto dealership owners and workers, farmers, etc., and for them I wanted my work and teaching to be useful -- to me, personal curiosity, art, etc. didn't count. I really wanted the department to be clinical, professional, practical, like law and medicine, i.e., welcome people from outside academics with real problems and then seek to solve those problems. When can't solve a problem, then maybe that will be a good research direction; if make good progress, then already have one application! For applied math, determine that not by PDEs but by what can find that is useful. Early in my career around DC for mostly US national security, I found lots of such applied math. And my startup, while more focused, is basically some applied math. PDEs? I had very little to do with those; the one case was the Navier-Stokes equations, and they were so difficult to work with that the project wasn't making much progress and I was pleased to move on to other topics. It's not easy to see what pure math is the more useful. For the pure math I do respect, especially for utility, it appears that in some vague, large sense the results are fundamental, important broadly, and, eventually, inescapably relevant, but that is a difficult judgment call. Functional analysis? Sure. Algebraic geometry? Less sure. Foundations? Slim chance. I was not trying to give career advice to other people possibly interested in math but just commenting that I found the foundations as deep as in the OP just too far down in a dark basement. In math, that's an old remark about foundations -- "Drop what you are doing trying to be useful and come with me down into the dark basement and wrestle with really subtle issues down there." Standard, old remark in math. You read lots of stuff between the lines I wrote, stuff not really there.

omginternets 9y ago

Intellectual pursuits have value outside of money, you know. You speak like someone who knows the price of everything and the value of nothing.

ambulancechaser 9y ago
that's very uncharitable. This person has a PhD in mathematics and has done some studying in the field. This is their own personal opinion of the matter after a firsthand experience.
graycat 9y ago
You seriously misread my post. A lot of "pursuits have value outside of money"; e.g., for some years I pursued violin. But if a person is being paid to do research in mathematics, then usually in some sense commonly the people paying will want to know if the work is or will soon become useful. In fact, there was the David Report that severely criticized Federally funded math research that seemed to have no intended connection with applications. The theme of that criticism was if the math is being pursued just as art, then fund it like art. I was giving my personal opinion and not trying to change the opinion of anyone else. Read my other responses here.