Becoming a mathematician - I am so depressed ..

Kevin_Axion

Are you aware of how mathematical learning works? It generally starts on primary principles i.e arithmetical operations. Following that, one finds proofs for simple mathematical ideas and learns algebra. The process is continuous and builds upon the principles of the previous steps. There is no apex but a perpetual climb upwards like Penrose's stairs. You cannot leap ahead of these steps because missing them would be a flaw in structure and knowledge. If you're dissatisfied with your proofs the rigour and beauty can only get greater and before you know it, you may be deriving a proof of the Riemann Hypothesis. At this point, it isn't reasonable. Taylor series proofs are impressive and are among the first steps to becoming a mathematician.

mathwonk

have you had any professional psychological help? or have you had some scary stuff happen in your life? it makes no sense to most of us who worry about our actual failings that you, who are having mostly success, are so worried.


Would you rather have a measured IQ of 185 and still not be able to prove anything, or have a measured IQ of 92 and be solving problems independently. Apparently you prefer the former, and we don't get it.

depression is a sickness caused i think by a chemical imbalance, it does not have logical reasons. most of us wind up taking pills for ours. and it helps frequently. you might get checked out though.

Functor97

I agree with Mathwonk and micromass, it sounds like you have depression, which is quite common amongst teenagers and high achievers, i suggest you look into getting that sorted before you worry more about a Phd.

Why do you want a mathematics Phd? Is it to make you feel intelligent? To vindicate a belief in yourself? Or is it because you can't imagine doing anything else? Could you see yourself as a Physicist, Engineer or Economist? If you can't enjoy pure mathematics maybe you should look into some of those careers? If not, and you simply love mathematical beauty, then i am having trouble seeing the problem!

Diracula

There's actually a very rational way to look at this even if we assume you need the magical 145+ IQ to be a math professor (which you don't, but anyway...).

Everyone's mind develops at different rates. The 12 year old genius probably plateaus a lot earlier than the average person. You may peak later. This is actually a good thing if true because you have the emotional maturity (assuming you deal with the low self-esteem and obsessive-compulsive thing) to complement the math ability. You'll probably be able to produce more math over your career. And you can produce a lot of math over your career if your teacher is right.

Also, what do you think happens when you do math? You learn new concepts, which actually causes your brain to rewire itself and form new connections. You become smarter and better at math the more you do. This may even increase your IQ if you care about such things (which you shouldn't). You can train for IQ tests. I wouldn't recommend doing that though because it's not exactly a useful skill to have.

So yeah. Even if you aren't smart enough now to produce new math you can get to that point the more you work at it.

Levis2

Well - you guys might actually be right. I don't know if i am actually depressed, but i certainly do have problems with self-esteem. I think too much about stuff - and i set my aims too high. I have an underlying psychological law, that dictates me to have success in what i do. I must be good at what i do - i think its hardwired into me. On top of that, i am a complete pessimist and i posses a great amount of skepticism.

This is where my problem lies - i love math. No doubt whatsoever. I want to work with math for the rest of my life, for now that is certain. But then the "specs" of my mind and body, notifies my brain that there might be a problem regarding performance in math - i may not be smart enough, due to the fact that I'm not a prodigy and so on ... this doesn't work along with the fact that i need to be good at what i do, so I'm stuck in some kind of conflict: On one side, i want to study math. On the other side, i need to be great at what i do, no matter what. Now that i doubt i will be able to make a good mathematician, my brain is telling me that i shouldn't be a mathematician, and i can't become a college professor.

The reason i want a math phd, is because this is a requirement for at least being considered for a teaching/research position in higher math education.

I don't want to become anything else than a mathematician, because math is what i like. I can't stand economy, engineering etc. I could definitely see myself as a physicist, since i do really like that subject aswell - but again, my brain tells me I'm not smart enough to become a physicist.

Lol - when i lay it out like that, i really sound like a person who needs professional help ^^

Diracula:

I really hope that is true - but again, my family has no records of academic success/talent, and people do say intelligence is inherited? Or am i wrong? It just seems like all the scientist who are really quick to begin college, end up being the greatest. I don't think I've even read about a famous mathematician/physicist who did not start college early. Oh wait einstein didn't - but he was somewhat of a prodigy aswell i guess

micromass

Why?? Isn't it enough to enjoy what you do?? Why do you need to be "great" or "the best"??

Kevin_Axion

You're smart from what I can tell. If I showed you your post to someone my age and identified where you stated you can solve differential equations and prove power series their response would be: "What is a differential equation" or more commonly "Math? Forget it." You have the intelligence and clearly have the interest and if you impede any progress beyond that point you will never be a mathematician which is in itself more dissatisfying than the prospect of becoming a mathematician but not a great one.

Functor97

From what i recall Grothendieck never believed he was a "prodigy", he certainly did not see himself as a student who would do well in Mathematical olympiads. However he was most certainly one of the greatest mathematicians of the 20th century and his creativity was astounding. If you love the subject, that is all you need.

As for the post about the prodigy about to disprove relativity. Spare us. That is utter rubbish, if the boy thinks that he can "disprove relativity" then he isn't as intelligent or as well read in the physics literature as the journalists seem to claim.

ahsanxr

I think you're highly mistaken that all or even most math professors were prodigies and are extremely smart with 150+ IQs. Sure, you need to have a certain amount of natural ability to do well in math, but you certainly seem to possess that if your high school teacher says that you're one of the best he's had and if you're doing differential equations at a young age. Being a prodigy certainly isn't a requirement for going into math. Stop depressing over how you may not be good enough and why not just give it a try?

BruceW

Levis2 - If you want to do maths, then do it. Don't be put off by thinking you won't be the best. You should decide what you want from life, then go for it. Everyone has doubts about themselves. Also, if you're too worried about it being perfect, then you might miss out on doing something really fulfilling.

TheCool

I'll echo what a few other posters have said, that you may want to seek psychiatric help. If you really need professional help, none of the comments here are going to permanently change your outlook on life and career.

The emboldened sentence is not entirely true. I recall stories of child prodigies here in the U.S. who started college early but never became great scientists. I think it's reasonable to assume that such people are, on average, less likely to make huge discoveries in science. Some prodigies fold under the pressure of being "great" at what they do. Some simply give up the moment they encounter something that they actually have to work at. And still others become wildly successful. But who's to say how frequent that is?

I can tell you, for certain, that math prodigies are extremely rare. More rare than music prodigies, painting prodigies etc.

In fact, most famous mathematicians were not prodigies. Indeed, the vast majority of mathematicians, famous or not, are not even exposed to "real" mathematics until they're well into their 20s. The good thing about math though, is that it's never "complete". As long as there are humans, there will be unsolved problems in math (maybe). So don't view it as a race. That will not sufficiently motivate you to put up with all of the grunt work that preceeds the glamour. Just find an area that highly interests you, and try to become an expert of sorts. Pose your own problems, try to find solutions.

Robert1986

Uh-Huh, and if you saw Beautiful Mind would you think you would need to have Schizophrenia to be successful? I don't think so. You have read stories about really genius math guys. Why? Because these are the ones people write about. There are probably 25 or so math profs at my school. You probably haven't read a single thing about them. Does this make them stupid? No. They are ordinary people whose job just happens to be doing math.


Here's an idea: read the book I Want To Be A Mathematician: An Automathography. It is by mathematician Paul Halmos. Now, there aren't too many people who would disagree that Halmos was a good mathematician. However, he got into the math Ph.D. because he failed in the philosophy Ph.D. He was unfunded. And, to top it all off, he made a B in Calculus. I'd be willing to bet that the average mathematician is much closer to Halmos than to Gauss.


So, to put a fine point on it: quit whining!

Cuauhtemoc

IQ is ********, it's just something created by psychologists to measure people. Ok, bs maybe a strong term, it is ok to see if someone is intelligent or dumb, if you have 80 IQ, well it's pretty bad, but if you have 120, 140 or 180, it doesn't really make a difference, except that you're really good at these iq tests.
Also most mathematicians iq's you read about are estimations, nobody really knows what gauss iq was, but since he accomplished so much they think he probably had 180 iq.

cobalt124

Apologies if this seems rushed or disjointed or long, repeats what other posters have said (needs re-emphasising anyway), and for possibly sounding like I want to slap some sense into you (I do), but you need a serious (and very well intended) butt-kicking:

Seems like a reasonable well thought out dream on the face of it.

IQ is irrelevant. There must be loads of threads in PF that will convince you of that, even one about famous scientists having low IQ's (Feynman?). Ah, I see you know that. You seem to be beating yourself up over nothing.

You are seeing this in the wrong perspective. Stop beating yourself up. It would be more productive to be inspired by the likes of Feynman than try to be like them, you cannot make the comparison because at the end of the day you are you.

Crap. Just to emphasise this.

Listening is usually more productive than being annoyed. And listening is different to agreeing. And anyway it sounds like a compliment. From what I am reading you have all the qualities required to complete a maths Phd. That statement has to be qualified by the fact that I am no maths expert and I do not have a Phd.

I suspect your internet reading is skewed/"spun" towards "geniuses". Where are the articles about the "real" mathematicians and what thay have done/do?

Don't rule out seeking counselling. Far easier to do this proactively than wait for a potential situation to get a lot worse, which may result in a "Shouldbe" maths Phd not becoming one at all.

Ask the right questions instead of the wrong ones.

Aaaaargh, the fount of all knowledge...NOT!

I'd say it's right to aim high with ambitions, but it's wrong to aim high with expectations.

The fact that you even posted this speaks volumes. I'm glad you did. A teacher has twenty years solid of poor students or you are a potential maths Phd!!!!! I no know most of your ideas on this are in your head and nowhere else and you need to test your claims in reality. I believe you will be pleasantly surprised.

Your posts hint at you having low self esteem. Counselling.

My impression is not "the quickest of minds", but "the hardest of work". Bet my impressions are better than yours.

It tells me I didn't watch enough SpongeBob.

I strongly suspect you are saying: "I can do this stuff, therefore it is easy", and "I can't do this other stuff, therefore I'm rubbish at maths". If so, you have set yourself up to fail.

Wrong, and another "setup to fail".

Do a PF search on neuroplasticity. Things may not be as hardwired as you imagine. Knowing this helped me.

Only one way to find out.

Nature vs Nurture is not a black and white issue. At the end of the day you can do nothing about the Nature, but lots about the Nurture.

kings7

Not to put too fine a point on it, since you have received some great responses already, but there are many types of intelligence.

In any case... sometimes you can never tell what 'aspect' of intelligence it will take to come up with a great discovery. Most of it stems from creativity, perseverance, hard-work, and passion for the subject. My guess is you have all of that, even if you can't see your own creativity right now (which is a life-long process anyway).

Most of the greatest discoveries weren't thought up by even the most "superior" scientists of our species (Darwin, Einstein, Goedel, Curie, etc...) until mid or late into their lives when they have had copious exposure to their respective subjects. You need not worry about things like this now.

Do what you love because you love it. Your life will then be fulfilled and happy. Life is not about money or fame or success... it is about passion.

Here's the advice I would give you:

I'm 24 and have pursued two separate paths in life so far (music and maths). I've finally discovered that my true passion is in music and that is what I'll be going to grad school for. For years I was afraid of this because I thought it wouldn't "prove" enough that I had a high intellect. It's a hard phase to get over, especially if you're self-conscious like myself (and most likely you too), but you MUST get over it. It helped me to realize that it takes just as much dedication, intelligence, creativity, hard-work, and PASSION to do music as it does to do mathematics. This is true for most (but not all) subjects, as long as it is your true passion.

The only way you'll make a difference in this world is by pursuing your passion. You're already a step ahead of a lot of people just by knowing what your passion is.

The only other piece of advice would be to stay modest and humble. It sounds like you have a lot of talent, and as you progress, it becomes more and more difficult to be humble. But it is something that will certainly help you in many areas of life, for reasons that are beyond the scope of this topic.

Hope that helps. Good luck.

epenguin

Looks like your problem is not you and maths.
Your problem is you and concerning yourself with nothing else but maths.

For instance 145 is an object with indubitable meanings in maths, for instance it's 29X5 - though I won't have a depression if I got that wrong.
Whereas an IQ of 145 does not have that quality at all, it is a number that means no more than the methods used to obtain it, and above all justify and interpret it as meaning anything. Still controversial and considered ideologically driven by some. The facts you can solve those eqs. and help other students say much more about you in my opinion (and others' we have seen).

Numbers in real life are a convenience but a curse.

For instance a mathematical physicist may miss tricks if he just takes the numbers that experimentalists give him and doesn't understand how they were obtained. Read e.g. Feynman's 'The 7% solution'.

I am thinking of my experience in (grant) administration. Once a number had been put on something, it became thereby Scientific. Sacred. Unchallengeable. People really ended up believing a project that had got 78 points in evaluations was about 1% better than one that had got 77 points! Even if one was in Physics and the other in Biology! The recriminations I remember when an element of qualitative, policy or relevance judgement was allowed! - This 78-point Project Has Not Been Supported When This Less Good 77-point One Has!!! In the end justifying and explaining was given up and we just let numbers rule mechanically. But, starting as a convenient help to sieving, people finished believing these numbers (like you do). And it wasn't just contemptibles like politicians, lawyers, economists who were number worshippers either - I can remember theoretical physicists and statisticians who were the worst!

You see now the curse of numbers? They are used to relieve people of responsibility, of judging. (And so once we could say 'your project was not financed because it got one less point than the cutoff' we found ourselves in an unattackable fortress).

Well this has led to something wider than your question but I think this is of general interest to scientists and the assumptions in your question do lead to this.

But my message just to you is forget the foolish figures and also do something additional besides mathematics.

Levis2

I must say, you guys have really helped me to get a better view on all this. You have encouraged me to at least attempt a shot at my dream. I will do everything to get the education i need - if i even make it to my masters that is.

And you might also be right about the iq thing - i sat down in order to think rationally for a moment about the whole iq setup. Why is it, that i let one number, obtained from some stupid internet mensa test, control my life. Why is it that number to decide whether i am capable or not? Screw the iq - i just hope its a coincidence, that *almost* all mathematicians have a very high iq.

You have really helped me get over my iq obsession - it might seem like nothing to you guys, but the feeling of your future being decided by one single number is horrible. I will not let that number rule my life. I will put no more significance into iq, and i will forget my stupid test result.

The only doubt that i have left, is whether i will be able to complete a phd - my doubt roots in the fact that, if I've got it correctly, when you pursue a phd, you have to come up with something NEW. If the most brilliant of minds struggle with coming up with something new, then how am i suppose to do just that, when i am no match for them?

And about the Paul halmos being close to the "ordinary" mathematician - paul halos obtained his bachelor of mathematics when he was 19 - when i am 19, i will have just finished high school. If the ordinary mathematician is like paul halmos, then I'm screwed.

I seriously consider getting some professional help with the self-esteem complications - as stated before, it has come to a point where it inhibits other aspects of my life aswell.