Other Should I Become a Mathematician?

[J77]

one thing that relieves math fatigue is contact with other mathemticians. i am now enjoying my birthday conference at uga and am extremely grateful to the visiting speakers and others who came to provide stimulus to those of us here. but guess what? at least one speaker said he himself was feeling the same lift from being here that we are feeling from having him here!

so try to get together with people who enjoy discussing together, and they will stimulate you and each other.

Yeah -- conferences certainly give you a lift. eg. I've just come back from a physics conference -- explaining your (mathematical) work to physicists really gives you new insight/avenues to explore.

 

[mathwonk]

what did you talk about?

 

[pivoxa15]

How common are mathematicians who scarifice their 'life' to do maths? i.e live alone without a partner or children and maintain minimum personal social interactions? How productive are they in the long term? I know Newton was one and the Russian who solved Poincare's problem but they have extroordinary abilities. How do people with lesser abilities do?

 

[mathwonk]

most mathematicians i know are pretty ordinary, and have families, friends, children, etc. those people you mentioned are very unusual, and not usually better mathematicians then the ordinary ones in my opinion.

 

[J77]

what did you talk about?

I pretty much fall under the category of nonlinear optics.

(ie. as opposed to GR/SR, HEP, Nano... etc.)

Response to above, also -- most mathematicians can usually be found occupying the local drinking spot at one time or the other. Communication and social skills are way up there if you want to succeed, imo.

 

[mathwonk]

feel like summarizing what you said about non linear optics? even if it way over my head, someone will enjoy it.

i will tell you for example what my friend asked me atmy conference.

he asked about generalizing riemanns proof of "jacobi inversion" for a single curve, to the analogous result for a pair of curves, one doubly covering the other.

in algebra its like generalizing a result about one field to the case of a quadratic extension of fields.

riemann showed that you could parametrize the jacobian of a genus g curve, which is a complex torus of dimension g, almost one to one, by a map from the product of g copies of the curve, via some "abelian integrals".

his argument can be given in two ways, one by using his theta function, (a fundamental solution for the heat equation), but there is another way, more geometric and almost tautological, using the dual torus called the picard variety of the curve.

of course this uses riemann's and abel's proof that the two tori are in fact isomorphic.

anyway my friend had done the analytic proof in the relative case and I then did the geometric proof the other night, between blogs here.

 

[mathwonk]

Now that my conference has ended and I am still exhilarated by the experience of meeting again so many mathematical friends and hearing so much interesting math that it has literally jump started my math research thinking again, I wanted to extend my earlier advice on becoming a mathematician to include strong advice to attend conferences.

Then I ran across edgardo's link to terence tao's advice, which contains everything i would have said and much more, but said more clearly and succinctly. Plus it has the stamp of approval of a Fields medalist. In fact I myself just reread Tao's advice for my own benefit.

Everyone here should read the advice of Terence Tao, and try to heed it. This is the best article i have seen on how to become a mathematician.

I am going to send it to our grad students at UGA for their benefit too.

For reference again, (and with thanks to edgardo):

http://www.math.ucla.edu/~tao/advice.html

 

[pivoxa15]

most mathematicians i know are pretty normal, and have families, friends, children, etc. those people you mentioned are very unusual, and not usually better mathematicians then the normal ones in my opinion.

But do you think had them or you not had a family etc would have enabled you to go further with your maths? In other words you would have had less distractions. Or do you think these things are necessary to make a good mathematician or at least keeping a balanced life is necessary to becoming a successful pure mathematian?

 

[pivoxa15]

Response to above, also -- most mathematicians can usually be found occupying the local drinking spot at one time or the other. Communication and social skills are way up there if you want to succeed, imo.

But what if it's pure maths?

 

[mathwonk]

well i find myself thinking sometimes that if I had no family obligations, then I could work more. There is a joke that a mathematician needs both a mistress and a wife because then when he is not with the mistress she thinks he is with the wife, and vice versa, so then he can skip out on both of them and go to the office and get some work done.

But in truth I never found it possible to complete my own grad studies and become a mathematician until i got married and had a normal family life. The birth of my children energized me also in my math.

Hironaka, the fields medalist once told me a joke about mathematicians who found they proved good theorems on getting married would sometimes get married several times to have this experience over again.

It is reminiscent of a remark made to me by an advisor at Harvard college on students who wanted get away from Cambridge and all its distractions to study more, but when they returned they found that the students who had stayed, somehow had accomplished more, even with all the distraction.

I personally cannot bear to stay longer than one week alone at a meeting or summer session. I love my work, but not exclusively, and I work better in a normal environment.

Life is not easy or simple. As my yoga teacher said, one has a spiritual self, a physical self, an intellectual self, an emotional self, etc...

The task is to keep them all functioning in harmony.

good wishes.

 

[Beeza]

Mathwonk,
At any point did you ever doubt your ability to succeed in advanced math courses? I just began self studying Apostol's Mathematical Analysis with a professor of mine (whom offered to continue working with me over the summer when the spring semester is over), and find even the beginning exercises very fun, but often time consuming and difficult. I sometimes worry I won't live up to my own expectations, or even my professors'.

 

[pivoxa15]

well i find myself thinking sometimes that if I had no family obligations, then I could work more. There is a joke that a mathematician needs both a mistress and a wife because then when he is not with the mistress she thinks he is with the wife, and vice versa, so then he can skip out on both of them and go to the office and get some work done.

But in truth I never found it possible to complete my own grad studies and become a mathematician until i got married and had a normal family life. The birth of my children energized me also in my math.

Hironaka, the fields medalist once told me a joke about mathematicians who found they proved good theorems on getting married would sometimes get married several times to have this experience over again.

It is reminiscent of a remark made to me by an advisor at Harvard college on students who wanted get away from Cambridge and all its distractions to study more, but when they returned they found that the students who had stayed, somehow had accomplished more, even with all the distraction.

I personally cannot bear to stay longer than one week alone at a meeting or summer session, because I enjoy being around my wife too much. I love my work, but not exclusively, and I work better in a normal environment.

Life is not easy or simple. As my yoga teacher said, one has a spiritual self, a physical self, an intellectual self, an emotional self, a sexual self, etc...

The task is to keep them all functioning in harmony.

good wishes.

What kind of distractions exist in Cambridge?

Your point about having balanced life is extremely important I think because we have evolved evolutionary and people who do a wide range of things are rewarded psychologically as a way of our body thinking us for what we have done to prolong its existence. Having children is one of those things I think. And when we don't do these things, our body punish us by making us feel depressed.

From your wide observations, what kind of wife is best suited to an academic mathematician? i.e another mathematician, school teacher, etc. OR is it too wide ranging to say?

 

[morphism]

pivoxa15, from all your posts I gather that you have some weird, disturbing idea about what a "pure mathematician" is. Mathematicians are humans, not machines that do mathematics...

 

[tehno]

Now that my conference has ended and I am still exhilarated by the experience of meeting again so many mathematical friends and hearing so much interesting math that it has literally jump started my math research thinking again, I wanted to extend my earlier advice on becoming a mathematician to include strong advice to attend conferences.

How many conferences,on average,you attend per year?Just being curious.

 

[symbolipoint]

Mathwonk, I just checked your initiating message on this topic and found what you said regarding foreign languages:

learn to struggle along in French and German, maybe Russian, if those are foreign to you, as not all papers are translated, but if English is your language you are lucky since many things are in English (Gauss), but oddly not Galois and only recently Riemann.

What more can you tell us about the usefulness of knowing Russian for the purposes of reading articles written in Russian about any Mathematics? How valuable? Do significant articles exist which have not yet been translated which Mathematical specialists might want to read and understand? In other words, is there still significant Mathematics work written in Russian which have not been translated? Would knowing Russian then be a special qualification for gaining admission to even an undergraduate Mathematics program (AS A STUDENT)? Were Russian Mathematicians known for any significant contributions to field of Mathematics (in other words, what were Russian Mathematicians famous for creating/discovering?)

symbolipoint

 

[JasonRox]

From your wide observations, what kind of wife is best suited to an academic mathematician? i.e another mathematician, school teacher, etc. OR is it too wide ranging to say?

Um... that's like asking the average guy the same question.

You want a wife that you'd love. If she's not suited for your career, don't marry her. A girl you love suits within your life in every way.

I'd want a nice good looking girl who loves playing in the bedroom. I need to clear my mind once in awhile.

 

[mathwonk]

well I admit the standard russian math journals are regularly translated into english so maybe it is not too crucial to know russian for math. but every now and then I find a russian preprint or paper that is not translated and it helps that i read russian. this does not happen too often though.

i do have several russian math friends though and i enjoy at least being able to say hello.

there are a lot of outstanding russian mathematicians and their contributions are legion: novikov, arnol'd, postnikov, shafarevich, tjurin, shokurov, alexeev,
nikulin, margoulis, dolgachev, moishezon, pontrjagin, tichonov, urysohn, sobolev, lobachevsky, malcev, kac, kazhdan, efimov, markov, givental, voronoy, delaunay, lefschetz, kurosh, gromov, iskovkikh,...

 

[mattmns]

Here is a silly question for you mathwonk How do you pronounce Spivak?

 

[pivoxa15]

I wonder why there are so many outstanding Russian mathematicians. It seems like the fields medalist list are dominated by them and Americans. However the Americans tend to come from many different ethinic backgrounds.

Is it because they are biologically more adapted to abstract things like maths and chess or is it because of their communist ruling for most of the recent past so there isn't many things to do or not many distractions.

 

[matt grime]

More strange opinions there, pivoxa. I would suggest you might consider that in Russia (in the past), eduaction was just more highly valued than elsewhere, and especially mathematics. Similar things have happened throughout the world in a variety of arenas.

The Aussies put a lot of emphasis on sports now, as they saw it an arena where they could compete with the rest of the world. Consequently in the 80s they spent a lot of cash on the infrastructure to create cricketing, rugby league and swimming teams that are te envy of the world. Another case, albeit an odd one, is scrabble. Some of the best scrabble players in the world (in English) are from Taiwan (or do I mean the Philippines) even though they can't speak English - it is taught in schools for some reason.

The Russians invested heavily in mathematics. Now they don't spend that much on it and consequently a lot of the best Russians are no longer in Russia.

 

[MathematicalPhysicist]

I'd want a nice good looking girl who loves playing in the bedroom. I need to clear my mind once in awhile.

exactly!
(-:

 

[mathwonk]

I pronounce Spivak as Spih - vak, i.e. not Spee - vak.And it is interesting that although the Soviets did invest heavily in math and science and valued it greatly, the communist government often tried to prevent their jewish citizens from benefiting from these math opportunites.

In spite of many obstacles in their path, nonetheless many Jewish soviets still became mathematicians and outstanding ones.

I do not know in general which of those I named are Jewish, but I know Moishezon was, since Boris was a friend of mine. Also Kazhdan, since I knew him slightly.

I also omitted to name perhaps the most famous recent Russian mathematician, Grigory Perelman.

 

[MathematicalPhysicist]

the better question is how spivak pronounce his last name?

 

[mathwonk]

well, i apologize for being vague, but since he is a friend of mine you may assume my pronunciation is one he has heard a few times without objecting, and that i have also heard many other people pronounce it as i do over the past 40 years.

i cannot recall hearing him pronounce his own name in a long time since he knows I know what it is.

 

[MathematicalPhysicist]

so it's spy-vak, i thought it was spee-vak.

 

[mathwonk]

spih not spy or spee, but i think it is allowed to say it other ways.

 

[Werg22]

Mathwonk, what do you suggest for self studiers? Learn one branch at a time or learn them all together?

 

[mathwonk]

if you are like me i can only learn one thing at a time, at best. and not one branch, one fact!

 

[Werg22]

Hummm, often I find myself amputated when it comes to some subjects in mathematics (for example, I know very little about linear algebra) because I've put all my energy into number theory and analysis. Wouldn't it be better, for example, to learn the foundations of several branches before pressing on the mastery of one?

 

[Data]

Hummm, often I find myself amputated when it comes to some subjects in mathematics (for example, I know very little about linear algebra) because I've put all my energy into number theory and analysis. Wouldn't it be better, for example, to learn the foundations of several branches before pressing on the mastery of one?

You're still in high school; study whatever catches your fancy! You will get a much more general background when you start a university program in math (or math-physics). For now, if you think you'd like to learn something about linear algebra, go ahead and pick up a textbook.

Personally, I'm taking advantage of the small gaps between my exams to start learning a few topics that I haven't had a chance to pick up yet. For example, I've just read all of the elementary material on measure theory that I can find online; Tomorrow, I have half a dozen books to pick up at the library!