Other Should I Become a Mathematician?

[pivoxa15]

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!

That's true but I have a feeling that having a phenomenal memory will help in some ways. Some of the best had exceptional memory like Euler, Fermi, Riemann, Gauss. At least one can save time such as bypassing time spent searhing through books or relearning old stuff. It is like doing computations. Actually relearning old stuff might be an issue for older people who has spent a lifetime researching. Even for undergrads some relearning is needed when he/she is in her final year.

People say being a good 'calculator' dosen't necessary make a good mathematician but I have a feeling that is because people think it is exceptionally boring and try to avoid it just as most try to avoid memorising. But some of the best were exceptional calculators as well. In fact all of the above. I don't know about Fermi though.

 

[pivoxa15]

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

I use to think self study in maths might be enough since it is a priori and there is no need to get a degree in it. I use to think that for science as well. But decided to do the degree anyway. I think it has been a very good decision as I cannot see myself self study these subjects. So if you are not a top student then try to do a formal degree.

 

[pivoxa15]

mathswonk, is it possible for a student to lift his mark in pure maths by 15 out of 100 when going from third year to fourth year? More specifically going from 60 average to 75 average?

Have you seen it done?

 

[mathwonk]

well yes. but if you want a different result, you must provide different behavior.

I myself went from a 1.2 gpa to a let's see, 3 or 4. i forget. the difference is i stopped skipping class and began attending every one.

And I started reading the materal assigned, and actually trying hard to write the assignments, and rewrite them, and so on.

i guarantee if you double the amount of time and effort you spend working your grades will go way up.

you know that guy you think is a twit, a wonk? try imitating him, going in the libs every day and maybe staying there until it closes. you are every bit as smart as he is, you just have a different list of priorities, you want to be cool, and have free time, and behave as you did in high school.

try putting that off for just a couple years and wonderful changes will occur. i did not learn this until grad school, but i was lucky to get in. then i became a "star" (4.0), just by doing all the work every day.

it is not at all easy, but you can do it. the difficulty is in terms of discipline, not smarts.

 

[J77]

That's true but I have a feeling that having a phenomenal memory will help in some ways. Some of the best had exceptional memory like Euler, Fermi, Riemann, Gauss. At least one can save time such as bypassing time spent searhing through books or relearning old stuff. It is like doing computations. Actually relearning old stuff might be an issue for older people who has spent a lifetime researching. Even for undergrads some relearning is needed when he/she is in her final year.

People say being a good 'calculator' dosen't necessary make a good mathematician but I have a feeling that is because people think it is exceptionally boring and try to avoid it just as most try to avoid memorising. But some of the best were exceptional calculators as well. In fact all of the above. I don't know about Fermi though.

I have no idea to what extent the memories of the people you mentioned are documented.

However, the key issue -- which I think I pointed out in my previous post, I can't remember -- is that when doing research, you don't recall everything which you have learned in the past. The way it works for me is to read recent papers, and if they use a technique I'm not familiar with, which will help towards my own work, then I will go to a library and take out some key works, plus going back over their (and subsequent) references.

Usually, the methods will have only been have remembered by myself -- or completely new to me -- you'll find it doesn't matter so much, ie. there is less pressure to "remember", when you are past any form of testing.

 

[JasonRox]

That's true but I have a feeling that having a phenomenal memory will help in some ways. Some of the best had exceptional memory like Euler, Fermi, Riemann, Gauss. At least one can save time such as bypassing time spent searhing through books or relearning old stuff. It is like doing computations. Actually relearning old stuff might be an issue for older people who has spent a lifetime researching. Even for undergrads some relearning is needed when he/she is in her final year.

People say being a good 'calculator' dosen't necessary make a good mathematician but I have a feeling that is because people think it is exceptionally boring and try to avoid it just as most try to avoid memorising. But some of the best were exceptional calculators as well. In fact all of the above. I don't know about Fermi though.

Really? Most bright people don't have the best memory at all. Most biographies I read said they were terrible at remembering things. Forgetting whether or not they ate, have an appointment somewhere, and so on and so on.

To say Mathematics is a subject of memory is like saying speaking English requires a lot of memory too. Speaking English does require memory and a lot of it too, but when you participate in it on a daily basis, it hardly comes across as something that requires memory. The same thing happens with Mathematics.

 

[threetheoreom]

To say Mathematics is a subject of memory is like saying speaking English requires a lot of memory too. Speaking English does require memory and a lot of it too, but when you participate in it on a daily basis, it hardly comes across as something that requires memory. The same thing happens with Mathematics.

This is the truth.

 

[mathwonk]

to get into grad school in math one must convince the admissions committee (that was me and 5 friends last year) that one has the potential to do strong independent work in math.

now what evidence are you going to offer for this if you do not take a certain number of hard math courses and do well in them?

self study will not do, since there is no test to adequately measure your preparation. the gre is pretty easy, and some admissions people do not even look at them.

i myself do look at them, because i think even though they actually test very little, still in my experience there is a good correlation between high scores on them (785-800) and success in the program.

but people are usually looking for success in a good hard course like abstract algebra, complex and real variables, topology, and a letter from the instructor testifying to the strength of the student.

self study means you have no one to write that letter. even if the letter is there it helps if we know the person writing it, and what they mean when they say "excellent chance to stand out" or "best in 10 years at this school".

there are other ways to make an impression but no substitute for that data. based just on posting experience here, i have said i would recommend hurkyl for our program for instance sight unseen, and there are others who have impressed me by their posts, but the committee would still want some supporting data.

let me mention one thing that can help, and that is exhibited sincere interest by the student. i.e. if we are making offers and stand to lose some of our best candidates to other schools, we want some hope of success. thus we appreciate a student who clearly prefers us to other schools, and that can weight our decision that way, even possibly above a stronger looking candidate on paper.

it is no guarantee, but something to think about. i.e. if you sincerely do prefer a certain program, be sure to let them know that. but do not say so if you do not mean it, as they will remember any deception when you are looking for a job.

 

[Darkiekurdo]

How does one know that one has the intelligence to become a mathematician? I doubt my own mathematical skills, but children of my age (14) do not know the things I know about mathematics, i.e., analyisis and algebra.

 

[JasonRox]

How does one know that one has the intelligence to become a mathematician? I doubt my own mathematical skills, but children of my age (14) do not know the things I know about mathematics, i.e., analyisis and algebra.

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

 

[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.