Should I Become a Mathematician?

[Darkiekurdo]

I'd say if you're intelligence is atleast above average your fine. If you're average but love mathematics, your fine too.

Note: 700th Thread Post

When is your intelligence above average? I have done several online IQ-tests and all of them indicate an IQ of around the 120 - 130, but then again those tests aren't very reliable.

Oh and mathwonk: congratulations with your 5000 posts!

 

[J77]

At 14, I wouldn't worry about it -- just keep going through classes at a consistently high standard and see if you still love maths when you hit 17/18 and are ready to think about college.

 

[Darkiekurdo]

Thank you for your advice.

 

[JasonRox]

When is your intelligence above average? I have done several online IQ-tests and all of them indicate an IQ of around the 120 - 130, but then again those tests aren't very reliable.

Oh and mathwonk: congratulations with your 5000 posts!

You just know. You're too young to know anyways.

 

[Werg22]

It's true that your too young to know. You will know when you'll compare yourself to people who share your academic interests. If you really are above average, you will find yourself able to play with ideas far more easily than your mates for inexplicable reasons.

 

[mathwonk]

there are people in the nfl or nba who are slower than others, and jump lower, but still succeed. this is analogous to being in professional math and slower or with worse memeory, but still a success.

 

[Darkiekurdo]

How old were you guys when you first began to study mathematics on your own, i.e., see how nice it is?

 

[mathwonk]

i read lincoln barnetts "the universe and dr einstein" on relativity when i was about 15, and began reading cantor's set theory at about 17.

i encountered courant's calculus at 18, and realized there was a whole new world of insight available in such excellent books.

 

[tronter]

is the material in both editions of courant the same (courant and courant and John)?

 

[Werg22]

No, Courant/John contains revised material and some additions I believe, the texts aren't exactly the same.

 

[mathwonk]

for the money, buy courant and john as it esentially just as good and much cheaper.

 

[mathwonk]

and thanks for the good wishes on my milestone of 5,000 posts! i did not want to have my 5001st be a lame thank you for some reason, so i waited until i forgot about it and just posted out of habit a few times. i guess I am superstitious. i like watching the odometer at numbers like 100,000, or 131313, or such.

 

[mathwonk]

and i just wrote another graduate algebra book, this one notes for a one semester course, 100 pages covering almost the same content as the 400 page book on my website, which were notes for a 3 quarter course. It isn't posted yet, but anyone who wants can receive pdf files by request.

 

[pivoxa15]

i read lincoln brnetts "the universe and dr einstein" on relativity when i was about 15, and began reading cantors set theory at about 17.

i encountered courants calculus at 18, and realized there was a whole new world of insight available in such excellent books.

Interesting. I started doing my own serious readings that contain equations when I was 14 and also on books on Einstein's relativity. I recall being really fascinated with this thought experiments.

Mathwonk, since your first book was on physics, were there times when you wanted to be a physicst? If so why did you choose to specialise in pure maths instead?

 

[mathwonk]

physics was more interesting. math was easier. i.e. i wasn't very good at physics but I could do math in my sleep.

a physicist has to be good at guessing what to assume. mathematicians get to be told.

 

[pivoxa15]

But wouldn't a pure mathematician need to produce conjectures of their own at some stage in their career? That takes some imgaination?

 

[mathwonk]

yes good conjectures need imagination, and knowledge of physics helps produce them.

as to conjectures, a colleague said his experience in applied math taught him that the simplest hypothesis that explains the data is best. in pure math we call it, whatever is "most natural".

 

[fopc]

and i just wrote another graduate algebra book, this one notes for a one semester course, 100 pages covering almost the same content as the 400 page book on my website, which were notes for a 3 quarter course. It isn't posted yet, but anyone who wants can receive pdf files by request.

400 page book? Are you referring to all parts of 3. and 4. collectively? I request your new 100 page version. Thanks.
Also, do you have any experience with Kaplansky's book, "Set Theory and Metric Spaces".

 

[cliowa]

It isn't posted yet, but anyone who wants can receive pdf files by request.

Sounds great. Could I have a copy? I pretty much liked the style of your linear algebra text, but haven't read the 400p algebra monograph yet. Thanks alot...Cliowa

 

[mathwonk]

the new 100 page book should be posted on my website today.

i think the 400 page book is the total page count for the notes from math 843-4-5. it started out as 300, and then i added some stuff on semi direct products and other things i guess.

i don't know kaplansky's book. metric spaces are important basic material, and there are lots of reasonable sources. one source that is very deep and a bit condensed is Dieudonne, foundations of modern analysis.

 

[mathwonk]

my posts are still not up, due to an error i made. i think i need your email address to send you a copy as pdf file. you could pm it to me if you wish, and i'll try to respond.

 

[mathwonk]

ok the new 100 page algebra book is up on my webpage. 6.a is the course outline or description,
6b is the theory of finitely generated abelian groups and pid's and a little on noetherian rings and modules.
6c is a second course in linear algebra, proving the existence and uniqueness of rational canonical form and its variation the jordan form. i also include a few words on spectral theorems abd duality since some people asked for them.
6d is a treatment of finite galois field extensions, including proofs of extensions theorems for homomorphisms, separability, normality, and existence and uniqueness of algebraic closures up to isomorphism. I did not give full proofs of galois' theorem on the necessary condition for solvability by radicals, but the statements are there, and all the big underlying technical results are actually there so its a good exercise. there is nothing on solutuions formulas for degree 3,4.
6.e is a set of homework problems and tests.

some stuff referred to is on either my webpage or the departmental page under grad student info, like old prelims.

If anybody looks at them i would appreciate any feedback. thanks.

the longer notes for 843-4-5 are better for a first time learner, but these are designed for a more advanced student, or someone willing to spend longer filling in details and making up or looking up illustrative examples. It is often useful to have a shorter version since you can actually get through all the pages of one section in a real life day or three. they were intended for grad students preparing for the algebra prelim, but are not guaranteed to be exhaustive for that purpose, even at UGA.

Interestingly, algebra was always my hardest and weakest subject, well until analysis I guess. I also wrote notes (twice) on complex analysis and riemann surfaces, but that was before personal computers and no magnetic copies exist. maybe someday. i also have several various algebraic geometry notes, plane curves (no magnetic copies), foundations, sheaves and cohomology, surfaces. sighhh... fortunately for you, better ones exist in print, but i still learn a lot by writing mine.

 

[mathwonk]

the book by kaplansky looks to be outstanding as an introduction to metric spaces, sets, and topology.

it was written by a famous algebraist and expositor, based on notes from a course given by the outstanding algebraic topologist edwin spanier.

moreover it is elementary in the sense that it begins the subject with the most natural version of topology, namely metric spaces, where euclidean intuition is most useful.

this is exactly the sort of book i would recommend to any young person. note i have not read it but i know very well the reputations of the author and the original lecturer. in fact i have met kaplansky, but not spanier. i have studied from spanier's great book on algebraic topology however, a very scholarly work indeed.

i had the good luck to audit a class on set theory and metric spaces that sounds much like this one, but mine was from the famous representation theorist george mackey at harvard.

oh yes, the kaplansky book is under $30! amazing in today's world of mediocre books for $150+.

 

[fopc]

the book by kaplansky looks to be outstanding as an introduction to metric spaces, sets, and topology.

it was written by a famous algebraist and expositor, based on notes from a course given by the outstanding algebraic topologist edwin spanier.

moreover it is elementary in the sense that it begins the subject with the most natural version of topology, namely metric spaces, where euclidean intuition is most useful.

this is exactly the sort of book i would recommend to any young person. note i have not read it but i know very well the reputations of the author and the original lecturer. in fact i have met kaplansky, but not spanier. i have studied from spanier's great book on algebraic topology however, a very scholarly work indeed.

i had the good luck to audit a class on set theory and metric spaces that sounds much like this one, but mine was from the famous representation theorist george mackey at harvard.

oh yes, the kaplansky book is under $30! amazing in today's world of mediocre books for $150+.

Thanks. I asked about Kaplansky's book because there was strong recommendation by Mendelson in his book on topology.
Mendelson's book is a beauty (a well written intro). So, I figure his references for concurrent or future reading are
worth a look. Yes, I noticed the $29 price tag. Not too bad.

Incidentely, I came across this Kaplansky quote.

"... spend some time every day learning something new that is disjoint from the problem on which you are currently working (remember that the disjointness may be temporary), and read the masters. "

Read the masters? That rings a bell.

Thanks for posting your new (100 page) algebra text. I'll try to give feedback.
But first I think I'll have to review your 843-845 .pdf's.

 

[mathwonk]

yes i like that quote. the first part too is meaningful to me, having seen so many times how someone using tools from another topic i had ignored, like classification theory, shed light on a problem of interest to me, like singularities of theta divisors.

 

[Werg22]

Question: How successful can someone outside of academia be successful in the filed of pure mathematics? Can one pursue the understanding of pure math with the same comfort than someone who works in academia?

 

[mathwonk]

well fermat was pretty successful while being a jurist. it all boils down to how much time you can spend at it.

 

[mathwonk]

here is a rambling, somewhat cynical, but in my opinion very truthful and representative account, of one mans life as a professor, for those wanting a realistic version of what one can encounter in academics.

he details the frustrations of trying to do a good job in the face of administrative indifference or hostility to good teaching, and frequent student indifference to useful learning. still he kept trying. like many of us he felt sympathetic to lack of ability, but not to lack of interest. that component of student interest is what attracts us to this forum.

http://www.math.hawaii.edu/~lee/education/kline.html there are a lot of free books on his webpage.

 

[Winzer]

wow, a good read mathwonk.
Thanks

 

[threetheoreom]

Yes a truly great read.

Thanks.

 

[J77]

mmm... The guy certainly has some issues.

At the same time, though, I have to realize that I'm simply wasting my life. Yes, a lot of the things I've done during my summers and otherwise have been personally very worthwhile for me. But for the most part, I'm not accomplishing anything. Nobody here at the University of Hawaii has any need of my talents.

I've got to get out of this place.

Other interesting articles of his include: http://www2.hawaii.edu/~lady/faq/why-stop.html

 

[mathwonk]

yes that last sentence surprized me. but i understand it.

if you have spent 30 years or so training yourself to do math and teach it to other like minded people, it is very stressful to be faced with 30 more years of trying to interest students, some of whom hate the topic and just want an A without doing any thinking.

thats why sabbaticals are a good idea. at schools without them, we depend on the rejuvenation of summer activities, conferences, colloquia, physics forum, etc...

another thing that seems to help is to learn not to judge people for their different attitudes towards a subject we love. to care about them and enjoy them as people, and then maybe if they begin to like you and your acceptance of them, they may ask themselves what it is about math that interests you.

this may seem almost somewhat saintly though, and recall he said somewhere "they don't pay me enough to be a saint". actually trying to adopt saintly patience is maybe impossible, but still helpful.

no matter where you are, eventually you may feel used, or underpaid, or unappreciated, or even disrespected. so it is crucial to do what you do for the love and enjoyment of it, not for prestige, nor money.

at Harvard the students are as good as anywhere, and the profesors are also, and they have relatively good pay, good conditions, and time for research, and collegial stimulation that is almost unrivalled.

still at 70, even the most respected professor is forced to retire there, regardless of activity level. if he has been dependent on that title of Harvard professor instead of joy in his work, this is very hard. he realizes he has been considered a commodity by his university, one which has exhausted its value.

but the intangible community of mathematics and mathematicians just continues discussing matters of interest.

maybe this is nonsense. I am just saying i understand Lee Lady's frustrations, have felt them, and have tried for decades to resist giving up the fun of doing math, and also to not give up the sense of community or being a teacher and member of a university myself.

at UGA we have several retired members who continue to come in and do research in the department, something i never saw at Harvard. this is a good sign. in fact Matt Grime is coming next week, currently from Princeton, to chat with some very active members of our group, some retired, some relatively young.

 

[mathwonk]

by the way, since you point out Lee Lady stopped doing research, that suggests to me one reason he may have become discouraged, because research is what "holds our molecules together" in the words of my closest colleague for several decades.

 

[threetheoreom]

The Future Mathematician should be a clever problem-solver but to be a clever problem-solver is not enough. In due time, he should have solved significant mathematical problems; and he should find out for which kind of problem his native gift is particularly suited.

For him, the most important part of his work is to look back at the completed solution. Surveying the course of his work and the final shape of the solution he may find an unending variety of things to observe. He may meditate on the difficulty of the problem and the decisive idea. He might try to see what hampered him and what helped him finally. He may look out for simple intuitive ideas: Can you see it at a glance?. He may compare and develop various methods: Can you derive the result differently? He may try to clarify his present problem by comparing it to problems formerly solved. He may invent new problems which he can solve on the basis of his just completed work: Can you use the result, or the method for some other problems? Digesting the problems he solved as completely as he can, he may acquire well ordered knowledge, ready to use.

The future mathematician learns as does everbody else by imitation and practice. He should look out for the right model to imitate. He should observe a stimulating teacher. He should compete with a capable friend. Then, what maybe more important he should read not only current textbooks but good authors till he finds one whose ways he is naturally inclined to imitate.
He should enjoy and seek what seems to him simple or instructive or beautiful. He should solve problems, choose the problems that are in his line, meditate on his solutions and invent new problems. By these means and by all other means he should endeavor to make his first important discovery: he should discover his likes and his dislikes, his taste, his own line.

taken from How to Solve It - A New Aspect of mathematical Method by G. Poyla.

Just wanted to share a piece of an interseting read from the classic.

I found of that passage this paragraph quite insightful:

The future mathematician learns as does everbody else by imitation and practice. He should look out for the right model to imitate. He should observe a stimulating teacher. He should compete with a capable friend. Then, what maybe more important he should read not only current textbooks but good authors till he finds one whose ways he is naturally inclined to imitate.

 

[mathwonk]

extremely good advice. thanks.