What advise you could give, in general, to a math-related major(e.g. economics, physics) undergrad student who want to pursue math PhD in grad school? ]]>

If 40% of your intelligence were 76-80 points, then that’s a good sign :-) Keep in mind that neither your intelligence nor your ability to solve math problems are fixed. Both are presumably proportional to how many exercises you solve and how many ‘NEW steps of reasoning’ you understand when reading a textbook or anything. This proportionality actually becomes more apparent in chess, where I find myself making progress if and only if I solve lots of tactics puzzles.

I personally would strongly recommend you to study mathematics, but you should follow the advice in the articles which Prof. Tao offers above. Read all the articles; they are very well written. Ask yourself silly questions, and if you don’t comprehend something fully, ask yourself silly questions until you do.

And also consider the following: Our brain has something called ‘mirror neurons’. They make you feel an emotion if you see that somebody else feels that emotion. That might be one source of that fear. I can not be certain that it is, but it might be.

]]>There is a problem in my relationship with math and i need a little guidance. I like mathematics and i wanted to study it in university, and my problem is that i’m afraid. i’m afraid that i can’t pursue it, i afraid of this that what if i chose math and in the middle of the path i couldn’t do it.

and this fear made me like math lesser because it seems my brain resists toward things that make it feel bad.

actually now, i’m more of a math stupid than a math genius.(i don’t think just math geniuses can do math!).

anyone may think this fear is stupid and it indeed is. this fear roots from a big mental loss. due to some incidents i lost about 40% of my intelligence, and when i realized it was to late to do anything.(it dropped about 76-80 points!, i checked it.). before that loss i didn’t have any problem comprehending concepts in higher mathematics way beyond my age.(i’m not gonna start whining so i stop it)

so, what do you think i should do? should i stick to math or should i find another field like philosophy or literature or history or … ?

]]>You should learn a broad area of mathematics. One reason might be, that in research problems, in order to make progress one often has to apply a certain step of reasoning or a certain theorem to get another conclusion, and it is better to be able to choose from many theorems to apply.

]]>If by any chance you are reading this, I would like to hear your opinion concerning the following matter. I live in a country where mathematics research is not well funded and established due to the political turmoil. However, I managed for the past few years to study some advanced mathematics by myself. I have not yet graduated from college, and I fear that I will face a dead end upon graduation.

Also, the only type of research conducted at the local university is not what you would call “up to date”, and nearly no one works in the ‘big’ areas of math.

I would very much appreciate any suggestions.

Thanks,

A.A