Other Should I Become a Mathematician?

[mathwonk]

no you ain't.

 

[Darkiekurdo]

Haha, I get the joke.

 

[DeadWolfe]

It's really a computer science joke.

 

[mathwonk]

seriously now (belive that?),smart or dumb is our ancestors' doing, achievement is our own.

not to malign my ancestors, who were very bright, but i used to call myself the "rocky" of algebraic geometry, dumb, but persistent.

 

[InbredDummy]

i always hear algebraic geometry being used in terms of string theory and quantum field theory, can you talk a bit about this mathwonk?

 

[mathwonk]

apparently the basic "particle" in string theory is essentially a riemann surface, which is an algebraic curve over the complex numbers, so algebraic geometers since the tim of riemann have been studying them, and the physicists seem to want to take crash courses in this topic for their own ends, which I know little about.

on the receiving end, algebraic geometers have been able to use Witten's formulas to calculate the expected number of maps from the curve of genus zero to various interesting manifolds such as quintic threefolds, but have not been able to prove the formulas calculate actual curves in all cases.

 

[pivoxa15]

Mathswonk, have you read the book 'Letters to a young mathematican" by Ian Stewart? From the opening pages it reads as if it is only the second book to be like the kind of Hardy's "A mathematician's apology". Although it's purpose is a bit different to Hardy's book.

https://www.amazon.com/dp/0465082319/?tag=pfamazon01-20

It seems these days, maths if a lot more social than in the past. Unlike the picture portrayed by Hardy. The ivory Tower image is gone and more and bigger collaborations. Team work seems to be important.

 

[mathwonk]

pivoxa, i have not read that book, and the first few pages indicate that stewart knows a lot more than i do about uses of math in diverse fields.

i was influenced more by hardy's views in the old days, that math was so interesting in itself that applications were irrelevant to my enjoyment of it. I regret somewhat taking hardys view now since it narrowed my experience. we never need a reason to ignore something, since evrything is potentially interesting.

but my own bent was in the direction of hardy's and i have always just tried to understand the internal structure of math itself, or whatever parts i found beautiful. indeed the more i have learned the more parts have become beautiful.

i like learning many proofs of the same result, and hopefully finding my own way to prove and understand things. I like guessing new facts and trying to prove them. I like finding simpler ways to understand things, and ideally getting the point where i can do what we were advised by some wise person, namely be able to explain everything to the man in the street.

I agree there are more interactions than perhaps before, but recall a highlight of hardy's career was a collaboration with ramanujam, or so he makes it sound in his book as i recall. and he has a famous collaborative book i guess with maybe wright?

so like me and some others, he may have fiound his greatest pleasure in at least discussing math with kindred souls. i love talking about math. I think i did some of my best work mostly so i would have something to tell my advisor.

after a while it began to seem like a fascinating exploration and search for exciting patterns and answers to mysteries. just as i never wanted to run my electric train after setting it up, i never careed about applying the theorems after proving them.

except in math, i did always take the approach that specific problems were more interesting than abstract theories, and i only discovered techniques and principles in order to apply them to the solution of specific problems, but they were purely math problems.

after discovering a method or technique to solve a problem, i would not develop it and sometimes others would work it out as a principle later, but if you read closely my work, the principle was already there in the solution of a specific problem.

so i like thinking and talking about and resolving specific interesting problems.

 

[threetheoreom]

but my own bent was in the direction of hardy's and i have always just tried to understand the internal structure of math itself, or whatever parts i found beautiful. indeed the more i have learned the more parts have become beautiful.

So If I understand correctly you were inspired by Hardy, more precisely his veiws of mathematics?

can you talk more about that.

thanks

 

[NathanExplosion]

Sounds like mathwonk was inpsired by mathematics itself, and Hardy's views on it just happened to ring true in his mind. Of course, I don't have any experience in psychoanalysis, so I'll shut up now.

 

[mathwonk]

i agree with nathan. but Hardy encouraged a narrow tendency i had which might have limited my early exposure to other areas of math.

 

[J77]

Mathswonk, have you read the book 'Letters to a young mathematican" by Ian Stewart? From the opening pages it reads as if it is only the second book to be like the kind of Hardy's "A mathematician's apology". Although it's purpose is a bit different to Hardy's book.

https://www.amazon.com/dp/0465082319/?tag=pfamazon01-20

It seems these days, maths if a lot more social than in the past. Unlike the picture portrayed by Hardy. The ivory Tower image is gone and more and bigger collaborations. Team work seems to be important.

Ian's an excellent writer -- most famous for his popular work "Does God play dice?".

Check out his personal page: http://members.aol.com/istewjoat/homepage.html containing his other popular works plus details of his more rigorous journeys into, for example, bifurcation theory and dynamical systems.

 

[pivoxa15]

Mathwonk, Can you shed some light to why Hardy said pure maths is a young man's game. Young being age 40 and under. Do you agree with him?

Also do you ever loss interest in maths or just not want to do maths at times? If so what do you do when that happens?

 

[mathwonk]

well, probably my best work was done when i was 35-40 or 45. It takes a lot of physical energy, long hours, and mental exertion is very strenuous.

So when you get older you have less energy. I guess people who do not do much of it do not realize that mental work takes physical energy, and that diminishes with age.

let me look at my vita and see...

Well i am most well known for that early work, but i am quite proud of some work done as late as 60 years of age, so maybe i am not so sure about that statement. it is just a general fact that we get older and less energetic i guess.

I also have still some hope of pushing on some ideas a bit further, and that would be fun. It does not really matter whether one is as good at 65 as at 25, what matters is to keep trying to achieve ones goals, and enjoy ones work.

I mean some people also say math is a genius's game, so then there would be no reason for us non geniuses to ever do anything. Well, too bad. I like doing math so I am going to keep on.

All that chatter is just part of the psychological detritus one has to ignore to succeed. If you give up everytime someone says you are not going to get aywhere, then you will have a harder time than you would anyway. I can definitely tell you I have seen some only modestly gifted persons, e.g. myself, who succeeded by perseverance on into their later age as researchers.

 

[mathwonk]

when you lose interest try something else for a while, take a break, a vacation, read novels, go to the beach, enjoy life, teach, read great writers and thinkers,... at length inspiration tends to rekindle.

i may be misunderstanding you here, but to me doing math is diferent from learning it, so when i lose interest in doing math i can also take a break by learning it, or by posting here, where i consider i am among friends.

sharing knowedge here is not "doing" math for me, i.e. not new math, but just talking about stuff I already know. Posting here is like an old man telling tales of his youth.

 

[pivoxa15]

well, probably my best work was done when i was 35-40 or 45. It takes a lot of physical energy, long hours, and mental exertion is very strenuous.

So when you get older you have less energy. I guess people who do not do much of it do not realize that mental work takes physical energy, and that diminishes with age.

well let me look at my vita and see...

Well i am most well known for that early work, but i am quite proud of some work done as late as 60 years of age, so maybe i am not so sure about that statement. it is just a general fact that we get older and less energetic i guess.

I also have still some hope of pushing on some ideas a bit further, and that would be fun. It does not really matter whether one is as good at 65 as at 25, what matters is to keep trying to achieve ones goals, and enjoy ones work.

I mean some people also say math is a genius's game, so then there would be no reason for us non geniuses to ever do anything. Well, ***** them. I like doing math so I am going to keep on.

All that chatter is just part of the psychological detritus one has to ignore to succeed. If you give up everytime some a** h*** says you are not going to get aywhere, then you wilol have a harder time than you would anyway. I can definitely tell you I have seen some only modestly gifted persons, perhaps myself, who succeeded by perserverance on into their later age as researchers.

So older people have less energy. Can you describe what it is like to have less energy compared to your youth? Or can one only feel it in order to know what it is like?

What about memory loss? Do older people forget easier and more often? Or is that an exception?

 

[JasonRox]

So older people have less energy. Can you describe what it is like to have less energy compared to your youth? Or can one only feel it in order to know what it is like?

What about memory loss? Do older people forget easier and more often? Or is that an exception?

mathwonk is full of ****. Less energy? If he's still doing mathematics now, he's full of energy. He comes on here to talk about mathematics and share his knowledge. He's amongst the most energetic and euthusiastic mathematicians out there. No energy? What a load of crock.



I know you don't count coming on here as math, and neither would I. But the idea to spread knowlegde and experience is there. That takes work. I'm sure lots of teachers and professors just go home and do their own thing. It takes special people to choose to share it.

 

[mathwonk]

less is relative. i used to work up to 30 or more hours at a stretch, and now i cannot do that. that's less energy than before. but it is true, even now my students say i am among their more energetic profs.

i used to commute to work and back home, 3 hours round trip, and sleep as lttle as one hour or less and go back and work a whole day, but i cannot do that any more, now i need 8 hours sleep like other people.

 

[JasonRox]

less is relative. i used to work up to 30 or more hours at a stretch, and now i cannot do that. that's less energy than before. but it is true, even now my students say i am among their more energetic profs.

i used to commute to work and back home, 3 hours round trip, and sleep as lttle as one hour or less and go back and work a whole day, but i cannot do that any more, now i need 8 hours like normal people.

But with what you passed on, you're now getting all these younger guys working! That's a lot of energy you passed on.

 

[mathwonk]

thank you so much! I hope i can psyche myself up for more theorems too! or maybe my proper role next year is to plan and organize some conference for the younger guys.

 

[quasar987]

My dear Mr. Wonk,

I have 6 credits left to do before completing my undergrad degree. Three of these I have to invest in a first algebra course, and three others I have already arranged to be invested in 'Measure & Integration', which is a graduate level course.

Now, I should be taking more classes because it would be a waste to only take 2. I am strongly inclined to take 'Logic' and am undecided btw 'Differetial Geometry' (another graduate level course!) or the undergrad 'Number Theory' course with Andrew Granville.

The dilemma is that

1) I don't know what graduate level courses are like. Are they much tougher than undergrad ones? Would it be too much to take 2 of them on top of the already hard 'Logic' and 'Algebra'? (N.B. My brain is of moderate proportion )

2) Number theory does not particularly appeal to me, but then again, I know next to nothing of the subject, and it is taught by Andrew Granville, which I remember you recommending me to take him in number theory class. And, I feel my math background would be lacking w/o at least an elementary introduction to number theory.

3) The 'Differential Geometry' class is taught by Octav Cornea, which I got last semester in 'Topology' and he was mighty fine. Plus, differential geometry is one of the two topics that appeal to me the most (with analysis) at the moment and I'm considering doing my masters in this topic (and hopefully with Mr. Cornea).


Got any advice? (And what's the answer to the question in dilema point #1) ?

 

[mathwonk]

talk to granville. he is a friend of mine so say hi. he will give you excellent advice and will teach a great course. my advice is to take his course because he is such a great teacher.

always try to choose teachers not topics.

let me know what transpires.

well now that i read your remarks, talk also to mr cornea since you liked his class and want to work with him. yes grad courses are a lot harder than undergrad onejs, and take more time. sounds like you have a wonderful group of faculty there. you can't go wrong.

ill say more if you want, but those two profs are the best experts to advise you on your exact situation there.

 

[quasar987]

k, I'll do that right now.

What else do you have to say? I'm all ears.

However, I can't imagine Granville's number theory course being less demanding than a grad course. When I had him in 'Applied analysis' (fourier stuff & sturm liouville stuff), he made us work like we had never worked before. lol, I had to lend the first homework set in two massive parts of 60 pages each that I jokingly labelled 'Vol. I' and 'Vol. II' It was great though... that guy understood and applied the principle that math is learned by doing it. Poor TA though.

 

[quasar987]

Hm, Andrew's email has an automatic response:

"I will be trying to avoid my email during the summer of 2007,
so please do not expect a response in the near future."

 

[mathwonk]

ok that means you have to persist. so keep in there. he is greatly in demand because he gets the most out of his students. and mention my name. i carry HUGE clout. harr harr.

or pm me your real name and i'll email him, but it may not matter. your good offices in trying to reach him count with me though. i think you have what it takes, namely good intentions and moxie.

 

[J77]

What about memory loss? Do older people forget easier and more often? Or is that an exception?

Mathematics isn't about remembering things!

This is a common trap -- thinking if you can remember every example in every textbook will make you a genius in your respective field.

Good results come from within, from using ideas from the past, but ultimately coming up with something of your own.

That's research!

 

[JasonRox]

I have a question about graduate school now.

I've been calling the two places that I'm interested in. Seeing how much it is and how it works, and etc...

Awhile ago I decided to do my Master's part-time, but the school I called said they don't offer night courses or anything like that. She said it's possible that they will make exceptions by offering night courses here and there, and we also discussed the possibility of having one class a week as opposed to 3 times a week. Therefore, I can just like book off every Wednesday morning to take a 3 hour class or something. I can do some courses independently while working with a professor here and there, and then write the exam for the credit. So, we talked about all these possibilities. I have to e-mail her back about what we discussed. She will look into it further. It's nice to see that they will consider it if I get in there or what not.

Anyways, my question is how hard would it be to handle one graduate course while working full-time? The industry I'm going in is mainly 9 to 5pm.

Note: I will also be attending part-time undergraduate to complete my business degree (which will be my second degree). I never found business courses hard to handle. It's just a matter of reading the chapter, thinking a little bit, and doing some work. It's not crazy hard, or it hasn't been yet anyways.

 

[mathwonk]

i think one is ok. it should be somewhat interesting and challenging compared to most regular work. but it will require time management. you might start preparing in advance by reading the book and doing exercises.

 

[mathwonk]

there are lots of different ways to make contributions to research. an older more knowledgeable person can often see connections between the work of a young oerson and some other older ideas and questions that are still out there and hence direct the thoughts of the younger person in a useful way. i.e. older persons can still provide valuable guidance even if the younger person provides more energy. In fact it is unfortunate when older persons decline to provide this because of a feeling it is not as exciting as doing the computations, or because they are discouraged by their superiors or funding agencies. Research is a community effort and very collaborative at its best and most productive.

 

[tronter]

does one need an undergrad math degree to go to grad school? Or can he major in something else (and self study the math)?