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When I told John Tate I was thinking of switching out of mathematics, his response was in effect "Good heavens! If there's anything else you can imagine doing,

When I told John Tate I was thinking of switching out of mathematics, his response was in effect "Good heavens! If there's anything else you can imagine doing, don't stay in math!" I later read that Wittgenstein had famously said something similar about philosophy. (Context: I was 19 years old and finishing up my PhD in math at Harvard. In that small department, Tate was not one of the professors I knew well.) In fact, I often feel pangs about not staying in academia. On the other hand, I've been able to carve out a life with a big dose of public intellectual -- for want of a better or less pretentious term -- so that's cool too. E.g., I'm repeatedly told that my blog is "required reading" for grad students in the relevant areas of computer science ...

yodsanklai 12y ago
> "Good heavens! If there's anything else you can imagine doing, don't stay in math" I heard similar advice from people in many different lines of work including laws, finance, medicine, academia... usually they add it's not as interesting as it used to be. It's a matter of compromise. I wish I could have the salary of banker, the freedom of a tenured professor and the prestige of a doctor.
- impendia 12y ago
  > the freedom of a tenured professor Well, one disadvantage of academia is that you don't really get to choose where to live, even if your CV is quite good. Indeed, there are a number of academic couples that make crazy long-distance commuter marriages work because they weren't able to get jobs at the same institution (or in the same city).
  - michaelochurch 12y ago
    It didn't used to be that way. The academic job market melted down in the 1980s and now commuter marriages are the norm. These days, there are too many PhDs and few full-time faculty positions. It's horrible, but academia doesn't have to be that way, and wasn't always.
graycat 12y ago
At least at one time and maybe still, there was a decently good living in applied math within 100 miles of the Washington Monument in DC. There early in my career, once I sent some resumes and in two weeks went on seven interviews and got five offers. Big topics were scientific engineering programming, numerical analysis, especially numerical linear algebra, standard applied statistics -- hypothesis testing, linear statistics, analysis of variance, curve fitting, etc. -- the fast Fourier transform, digital filtering, power spectral estimation, deterministic optimal control theory, linear and non-linear programming, discrete and continuous time stochastic processes, Monte-Carlo, numerical solutions of ordinary and partial differential equations, etc. Some of these topics are part of mathematical EE. At one time I my annual salary was six times what a new, high end Camaro cost. My wife got to pursue her Ph.D. in essentially mathematical sociology as part of her desire to save the world while we had big times at Thanksgiving and Christmas, shopped in Georgetown for high end French wine and cheese, were regulars with good tables at high end restaurants, went to lots of concerts and plays, got a good piano for her and a good violin for me, got boxes of fancy French pastries and sweet, sparkling dessert wines and on Saturday nights pigged out watching old movies, went to Shenandoah for vacations, had plenty of time for trips to families in Tennessee and Indiana, did some fancy cooking at home, etc. Of course the money was coming almost entirely through the US Federal Government, mostly for US national security, e.g., via the US Navy, DARPA, etc. But, still, there was money via the DoE, NIST, and more. I went ahead and got an applied math Ph.D. at Johns Hopkins, research on stochastic optimal control. My startup has at its core some applied math I derived based on some advanced prerequisites I got mostly at Hopkins. The math is an advantage. If the startup works, then the math will have been the key -- except for the math and the basic business idea, it's all routine, that is, the math is the only thing really special. Math can be used to say how to take data that is available and manipulate it to get data that is valuable. Now there is a lot of data and means to communicate, store, process, and display it, infrastructure software to make the rest much easier, ads to run to get revenue, etc. Except possibly for coding theory and cryptography, I don't know if there are valuable applications of algebraic topology, algebraic geometry, algebraic number theory, commutative algebra, etc., but for the topics I mentioned it would seem that there is some practical value. For some of what can be done with applications, there is a long dessert buffet from the Hahn-Banach theorem and more in D. Luenberger, Optimization by Vector Space Methods. One heck of a toolkit. Make just one good application and retire, make a donation to a university, and get your name on a building. Here's another possibility: Attack integer linear programming problems in business. Focus on the problems that can attack with min cost flows on networks with integer arc capacities. Why? Because it is just linear programming; the simplex algorithm becomes really simple in that case; in practice the simplex algorithm is fast beyond belief on problems large beyond belief; and get integer programming for no extra effort -- if start with an integer basic feasible solution, then the simplex algorithm will maintain an integer solution and, if there is an optimal solution then will get an integer optimal solution. Can use this in various resource allocation problems. For more, use it as a linear approximation in nonlinear problems and for still more enhance it with some Lagrangian relaxation. Show that P = NP? Nope. Make money? Maybe.

yodsanklai 12y ago

> "Good heavens! If there's anything else you can imagine doing, don't stay in math" I heard similar advice from people in many different lines of work including laws, finance, medicine, academia... usually they add it's not as interesting as it used to be. It's a matter of compromise. I wish I could have the salary of banker, the freedom of a tenured professor and the prestige of a doctor.

impendia 12y ago
> the freedom of a tenured professor Well, one disadvantage of academia is that you don't really get to choose where to live, even if your CV is quite good. Indeed, there are a number of academic couples that make crazy long-distance commuter marriages work because they weren't able to get jobs at the same institution (or in the same city).
- michaelochurch 12y ago
  It didn't used to be that way. The academic job market melted down in the 1980s and now commuter marriages are the norm. These days, there are too many PhDs and few full-time faculty positions. It's horrible, but academia doesn't have to be that way, and wasn't always.

graycat 12y ago

At least at one time and maybe still, there was a decently good living in applied math within 100 miles of the Washington Monument in DC. There early in my career, once I sent some resumes and in two weeks went on seven interviews and got five offers. Big topics were scientific engineering programming, numerical analysis, especially numerical linear algebra, standard applied statistics -- hypothesis testing, linear statistics, analysis of variance, curve fitting, etc. -- the fast Fourier transform, digital filtering, power spectral estimation, deterministic optimal control theory, linear and non-linear programming, discrete and continuous time stochastic processes, Monte-Carlo, numerical solutions of ordinary and partial differential equations, etc. Some of these topics are part of mathematical EE. At one time I my annual salary was six times what a new, high end Camaro cost. My wife got to pursue her Ph.D. in essentially mathematical sociology as part of her desire to save the world while we had big times at Thanksgiving and Christmas, shopped in Georgetown for high end French wine and cheese, were regulars with good tables at high end restaurants, went to lots of concerts and plays, got a good piano for her and a good violin for me, got boxes of fancy French pastries and sweet, sparkling dessert wines and on Saturday nights pigged out watching old movies, went to Shenandoah for vacations, had plenty of time for trips to families in Tennessee and Indiana, did some fancy cooking at home, etc. Of course the money was coming almost entirely through the US Federal Government, mostly for US national security, e.g., via the US Navy, DARPA, etc. But, still, there was money via the DoE, NIST, and more. I went ahead and got an applied math Ph.D. at Johns Hopkins, research on stochastic optimal control. My startup has at its core some applied math I derived based on some advanced prerequisites I got mostly at Hopkins. The math is an advantage. If the startup works, then the math will have been the key -- except for the math and the basic business idea, it's all routine, that is, the math is the only thing really special. Math can be used to say how to take data that is available and manipulate it to get data that is valuable. Now there is a lot of data and means to communicate, store, process, and display it, infrastructure software to make the rest much easier, ads to run to get revenue, etc. Except possibly for coding theory and cryptography, I don't know if there are valuable applications of algebraic topology, algebraic geometry, algebraic number theory, commutative algebra, etc., but for the topics I mentioned it would seem that there is some practical value. For some of what can be done with applications, there is a long dessert buffet from the Hahn-Banach theorem and more in D. Luenberger, Optimization by Vector Space Methods. One heck of a toolkit. Make just one good application and retire, make a donation to a university, and get your name on a building. Here's another possibility: Attack integer linear programming problems in business. Focus on the problems that can attack with min cost flows on networks with integer arc capacities. Why? Because it is just linear programming; the simplex algorithm becomes really simple in that case; in practice the simplex algorithm is fast beyond belief on problems large beyond belief; and get integer programming for no extra effort -- if start with an integer basic feasible solution, then the simplex algorithm will maintain an integer solution and, if there is an optimal solution then will get an integer optimal solution. Can use this in various resource allocation problems. For more, use it as a linear approximation in nonlinear problems and for still more enhance it with some Lagrangian relaxation. Show that P = NP? Nope. Make money? Maybe.