How does Much work Does it take to be a successful mathematician?

http://mathoverflow.net/questions/9799/how-much-work-does-it-take-to-be-a-successful-mathematician#

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Hi Everyone,

Famous anecdotes of G.H. Hardy Relay that he work habits consisted of working no more than four hours a day in the mornin G and then reserving the rest of the cricket and tennis. Apparently he ideas came to him, he wasn ' t ' doing work. " Poincare also said that he solved problems after working on them intensely, getting stuck and then letting his Subconsciou s digest the problem. This was communicated in another anecdote where right as he stepped on a bus he had a profound insight in hyperbolic geomet Ry.

i am less interested in hearing more of these anecdotes, but rather I am interested in W Hat people consider an appropriate amount of time to spend on doing mathematics in a given day if one has career ambitions Of eventually being a tenured mathematician at a university.

i Imagine everyone have different work habits, but I ' d like to hear them and Particula R I ' d like to hear how the number of hours per day spent doing mathematics changes during different times in a person ' s CA Reer:undergrad, grad school, post Doc and finally while climbing the faculty ladder. Meant to include working on problems, reading papers, math books, etcetera (I ' ll leave the question of whether O R not answering questions on MO counts as work to you). Also, since teaching is considered a integral part of the most mathematicians ' careers, it might was good to track, but I am I Nterested in primarily hours spent on learning the preliminaries for and directly doing.

I ask this question in part because I has many colleagues and friends in computer science and physics, where pulling late Nights or all-nighters is commonplace among grad students and even faculty. I wonder if the nature of mathematics is such, putting in such long hours are neither necessary nor sufficient for Bein G "Successful" or getting a post-doc/faculty job at a good university. In particular, does Malcom Gladwell ' s hour rule apply to mathematicians?

Happy holidays!

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I agree that hard work and stubbornness is very important (I think we should all take after Wiles and Perelman as much as We can). But it's also important how do you spend the many hours you dedicate to mathematics. For instance, choice of problems is quite important:it are important to make sure so when you work on something, you spe nd your time usefully, i.e. you do not have progress on this particular problem, but also learn something new about Math Ematics in general. It is also important not to get hyperfocused on a fruitless attempt to solve a problem; After some time and effort spent on it, it becomes addictive. In such a situation, it's sometimes better to stop and ask for help/read something or switch to another problem for a whi Le. Often, you'll wake up one morning a month or a year later and see that the insurmountable obstacle have magically disappear ed! Or maybe this "aha!" moment would come during a discussion with another mathematician, or when listening to a talk. For Many people it is also helpful to has many simultaneous projects, so if you get stuck on one, you can work on Ano Ther. To summarize, I think that isn't only the number of hours matters, but also how efficiently you spend them S of publishable results, but also in terms of your personal growth as a mathematician.

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Neglecting good sleep as a The doing mathematics is not a good idea. To does mathematics, you need to get enough rest. As to the number of hours per day, it's impossible to count this. When you think on a mathematical problem, you think about it all the time, including when you were asleep. It is true this mathematicians who work more does tend to achieve more, and those with the very top achievements does tend to Work really a lot. But no amount of hours spent per day sitting on the table guarantees anyone anything in mathematics. The key word is not a "long hours", but "dedication".

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Well, I can ' t consider my self a successful mathematician, but from observing a few ones I know, this is my 2 cents:

The hour rule (this is a course pseudo-science) certainly apply almost by Definition:most mathematician start tra Ining in college if not before. If you count up to postdoc, which are very typical, that's about the years, and an average of 3 hours/day give Lready.

Certainly work habits vary, but it does seem that quite a few successful mathematicians I had met know how to enjoy life. Have said that, I think a blessing/curse of our profession are that the lab are in our mind. So it looks like we don't work this hard, compared to some other fields, since some of my friends in Physics/biology has To stay at the labs at nights frequently because of experiments. On the other hand, math can follow you around even if you were playing tennis (I can confirm that from personal experienc e!).

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Grothendieck was known to work 10-12 hours a day + or less every day for the (something like) years of his Mathemati Cal Carrier. I think it ' s written in some memoirs of Cartier, this is one of the underlying reasons he decided to quit mathematics -he simply was too tired.

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Every excellent mathematician that I know works extremely hard and for very long hours; However there is many others who also work extremely hard who is just average or "journeyman" mathematicians.

In other words, hard work was necessary but not sufficient-the existence of prodigies such as the Terry Taos and Akshay V ENKATESHS (just to name II Aussies that I ' ve at least met) seems to me to being sufficient evidence that some natural talent /creativity/imagination/genius is necessary beyond mere hard work.

The working habits of mathematicians can also be endlessly amusing-we currently has a visitor who feels that he was full of creative energy immediately on waking, and so rather than getting out of the bed and wasting that energy showering and hav ing breakfast etc, he puts in an hour or both of maths and only starts the daily routine when he reaches his first dip in Energy.

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In order for your question to make sense, you need to define the terms "successful mathematician" and "Good university". An idealistic response might skirt the issue altogether and claim that it does isn't matter what other people think. On the other hand, you is constantly being evaluated throughout your schooling and well into your professional career. Maybe you can focus on what is it means to do good mathematics.

In the He essay "What's Good Mathematics" Terrence Tao explains why he thinks Szemeredi ' s theoremis good math. The theorem states that any subset of natural numbers with "positive upper density" contains arithmetic sequences of arbit Rary length. Although this is proven by Szemeredi in the 1970 ' s, it is proven by many other people using tools from all over Mathemat Ics:dynamical systems, Fourier analysis, hypergraph theory.

One of my favorite solutions is the proof of the Baik-deift-johansson conjecture on the longest increasing subsequence of A random permutation. Proofs of this theorem relate this statistic to eigenvalues of random hermitean matrices and to the lengths of random Youn G tableaux under Plancherel measure. Again The techniques use this come from different branches of math:e.g. The Riemann-hilbert correspondence, the represent ation Theory of the symmetric group, orthogonal polynomials, random matrices and quantum gravity. See longest increasing subsequences:from patience sorting to the Baik-deift-johansson theorem

Good mathematics takes a certain mixed of creativity and technical know-how to pose and solve. By solving thousands of problems, you can develop your own mathematical taste. Then you can judge for yourself what good mathematics are and what it isn ' t.

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How does Much work Does it take to be a successful mathematician?