Becoming a mathematician - I am so depressed ..

StatOnTheSide

Mathematicians have proved incredibly great theorems. Godel has shown that no set of axioms are consistent as in there will always be a paradox no matter which set of axioms you start with. I am sure that is the case with other sciences too. There are great scientists just as there are great mathematicians.

For that reason, I wonder as to what scientists have to say about IQ. When I browse google about IQ, I do find that many scientists believe that IQ has a strong correlation to success in academic career even though that may not be the only factor.

Even though I will not stop doing math under any circumstances and my advice will still be that do what you feel like doing, I am curious to know what the truth is. It would be ironic to shy away from the truth for me as one of the qualities of a mathematician or a scientist is to consider all the possibilities with no bias and try to discover the truth. If the question is regarding the importance of IQ in being able to do math, then a scientific approach would be to figure out the truth without bias.

It might be true. It might be a bad news for all of us who do not have a good IQ. As I have said again and again, I will not stop doing math under any circumstance; however, I am really really curious to know THE answer to this question. What is IQ? Why is it important OR not important?

Whether or not IQ matters, I do not want to be unscientific about this matter and I will accept whatever is the truth. But knowing that Einstein had a very high IQ and so do many geniuses in math, there is a very strong likelihood that IQ does matter to a great extent.

H2Bro

High IQ score is more likely to be something associated with mathematical ability rather than determinative or a necessary condition. It's quite clearly not a sufficient condition if you read the above post reviewing a book by the lady who currently holds the highest IQ score on record.

I'm betting its unlikely to find mathematicians with a very low IQ. And I bet a lot of successful one's have a high IQ. However, finding even a few successful mathematicians with only slightly-above average IQ is enough to demonstrate that a high IQ is not at all necessary for success in mathematics. This is simply something demanded by the scientific method.

One of the most influential effects of education is not just knowledge and networking, but actually instilling confidence in oneself and one's abilities. I have a feeling IQ scores can operate in a similar manner where those who find themselves with lower scores self-select out of the process, while those with higher scores assume they have fair to reasonable odds. When you go and do the measurement, it would appear only high IQ holders go on to maths success.

StatOnTheSide

It sounds very much similar to the case where some of the Olympiads go on to become great mathematicians and win the Field's medal. They usually have like 5 gold medals in Olympiads. It makes sense because for kids who do not get through Olympiads, there is no boost in confidence at that time. Success very much depends on how hard one works along with intelligence.
Hard work comes with motivation. The entire problem is with motivation.

Contests are good for people who make it through to the top but for the others, it leaves them with a very strong sense of diffidence. It is the same everywhere. A "successful" incumbent president almost surely wins the election while a president who was not able to "lift the economy" will almost surely fail with some exceptions. The economy may not even depend on the president but the candidate's success depends on the state of the economy. The analogy is loose and may be not directly applicable here but the the point is that if someone succeeds in a difficult endeavour, there is a h___uge ego boost which pushes them greatly in their career while it has the EXACT opposite effect for the ones who fail early on.

Animals have the same problem. A dominant male lion cub will show early signs of being a successful leader and that perception alone helps him become one after he grows up as the motivation is present in him which is the result of an early ego boost. Now the question is that for someone without that ego boost early on in life, what are the chances that he or she will succeed later? Failure, in whatever form it maybe, is like a thorn that keeps pricking in your mind every time you try to come out of that notion and try to do mathematics. On one hand, you cannot succeed in solving problems in the text. On the other hand, you will always have it in the back of your mind this thought that is working against you saying "I failed at Olympiad and I am not intelligent" or "I have a low IQ and I am not good enough for math". Under these circumstances, what is the likelihood of someone succeeding when all the factors "seem" to work against you?

It is about psychology. It is about emotions. Even though math is highly logical, or rather it is about formalizing the logic in a given setup, the factor that drives someone to the successful end is an emotional or a psychological one. Remember that you have to work for years and work hard to succeed and if you have these notions like failing in contests or low IQ etc, it is like trying to run a marathon thinking that the leg is broken or that it is not strong enough.

The irony is that for someone who wishes to know the truth about IQ, if he says things like "I have low IQ so I will fail", without even considering the validity of that statement, just the fact that a person thinks that way is very unscientific and may not qualify to become a mathematician. It is the question about his outlook and thinking. Math on the other hand needs you to be an EXTREMELY scientific person. You have to dispassionately try to figure out the truth. Talk to really wise people. Read books. Think and think and think. Before you even go onto becoming a math major, take this as your very first problem and demonstrate to yourself the ability to think logically.

I believe that as long as you have legs which are strong enough to carry your body for 26 miles, you are fine. It may take longer for you than the others but you will reach the target. Worse comes to worst you can walk if not run and cover the distance unless there is a rule stating that walking is not allowed. In real life, nobody cares if you are walking.

I think the reason why a lot of people do not succeed in math is that it is very intimidating, and yes, it requires intelligence. For most people, it requires a strong character too. I believe that a strong character is equally hard to find.

H2Bro

I agree that the motivation and confidence are huge factors. They are actually well-documented in the animal kingdom as well.

Ivan D. Chase is a professor at Stony Brook university who does research on the formation of transitive hierarchies of dominance in animal groups. It's fascinating stuff, if your interested I suggest checking it out.

The short and sweet of it is, winners go on to win more because they learn aggressiveness pays off, while losers learn deference because previous attempts resulted in failure. This is actually noticeable in the academic and job world as well - get a couple bang on papers early in your career, and you get more positions, offers, experience, which begets better offers, and so on.

StatOnTheSide

I will check it out. Thanks for pointing it out H2Bro.

Even though it is true for animals, I am sure humans are not the same as animals. We are different. There may be common factors but there are a lot of factors not common to animals. That is why we call ourselves as being different from animals!

As teenagers, a lot of it is like in animals. But as you grow up, you will enter the adult world. The reason why there are exceptions in mathematics is that there are people who have pursued math without worrying too much about any of the above.

If a pin pricks you when you are looking at it, you will feel the pain.When it pricks you when you are not looking at it, it just goes un-noticed!

Long story short, you just do math if you like it and like the idea of thinking about formalizing the logic hidden in the mathematical structure. If you enjoy it, it means that you understand it and love to do more of it. It has a positive slope and will lead you to success some day. As long as you enjoy it, why do you care right?

mathwonk

this thread is based almost entirely on one of the biggest difficulties facing those who aspire to do well in mathematics. namely the confidence problem. we all know the extreme unlikelihood that we will ever do anything comparable to the work of abel, gauss, galois, riemann, dedekind, etc, etc.... indeed it is discouraging even to begin to list the names that will almost certainly always be bigger than our own.

but the same problem faces people who want to become athletes, or artists, or newspapermen, or politicians, or salesmen. so if we still love our career path and want to pursue it, we have to summon up the courage to embark on a very difficult venture in which we have every chance of falling far short of our hopes and dreams. we have to maintain optimism and objectivity, to take satisfaction in small successes, and we need to learn not to let our mental health depend completely on every little sign of success or failure.

one thing that helps some of us, especially oldsters, is trying to teach and help other younger people. this helps us realize the long spectrum of learning that exists, and that we are not at the bottom of it, even if we are also not near the top.

ultimately we learn to work "for the glory of god", i.e. for enjoyment, not for personal aggrandizement. also it helps if we have a plan B, i.e. if not all our eggs are in the same basket. even david hilbert took a teaching certificate in case research did not work out for him. one good thing that can come from competition, or comparing our work with other stronger workers, is that it can teach us how to improve, and inspire us at least to do our own best.

i hope the OP has had some chance to grow and flourish, but i was frustrated that his high school was so short sighted as not to allow him to attend the university class that suited him better than high school. i would have appealed this with help from the university professor. perhaps he has since suffered some more setbacks and again faced the ongoing challenge of finding his place. i wish him well. he certainly has youth and intelligence on his side.

H2Bro

+1 for mathwonk. I think you definitely hit the nail on the head.

Physics and math might more than other subjects make us uncertain or doubt ourselves because the ability is so quantifiable, i.e. physicist X or Y mastered calculus by age 13, or independently thought up a proof or theorem at age 10. There's a lot of these anecdotes floating around, especially the one about Gauss as a child, which make us think "gee, I never did that!"

Something that helps me is to know that I simply have a different kind of learning curve than a lot of people. My intellectual side didn't fully blossom until my 20's, but now its full steam ahead and I'm starting to notice the difference between me and the younger people around me in terms of drive and motivation. I think acknowledging that different people have different styles of learning, and that sometimes its not clear cut if one is definitively 'better', helps to calm down the voice saying 'you wont make it because you're not a prodigy, or 99th IQ percentile, etc'.

Humans are animals, actually. The most important factor in the 'winners keep on winning' pattern of behavior among animals is the observance of winners by bystanders. Observing another win increases your perception of their capacity and potential, and reduces your self-confidence when it comes times to challenge them.

There is an interesting line of research on this, focusing on people in discussion groups which over time produce transitive hierarchies of interaction participants. If you like PM me and I can link you to some more sources that explore it a bit more fully.

StatOnTheSide

I do not challenge anybody regarding this. In this matter, I would much rather trust my experience than the research out there. Please do not be offended by that statement. I am quite sure that the researcher has done good research and has sound conclusions but that increases his conviction but not mine.

I have a friend who is a PhD from U of Chicago and is into Representation theory. He is one of the few from India to have a gold medal at the IMO. You may or may not know it but there is no training in India for IMO and he for sure did not receive any help. He had just one book that his uncle gave him who is in the US and he made it to IMO just by solving the problems in that book. On top of that, he did receive help as soon as he cleared the regional round.

I have actually observed him and his friends and the dynamics in the group. I do agree with you that as long as you are a subordinate to people like him and tell him "you are a genius and I won't equal you ever", you will not bring out the full potential in yourself. There is no doubt about that. If a researcher has come to the same conclusion, I am not at all surprised as I knew that for a long time. But amongst his friends, there is another guy who made it well into mathematics and is still doing well. He is not a PhD from U of Chicago or anything but he nevertheless got a PhD in mathematics and is a faculty member somewhere. They may not be "equal" but it is not like one has made it way better than the other. He is happy with his teaching job and gets to do mathematics which is all that matters.

As Mathwonk has pointed, there are some people who are way beyond others and I just acknowledge that. Many are actually dead. The main problem arises with the peers. There is always a huge ego clash between the so called friends who are in the same field atleast till they establish themselves. Sometimes it continues well into their old age.

When I say that we are different from animals, I do believe that it is possible for some humans to not get bogged down by the immense success of their so called friends. They keep going at their own pace and maybe in secrecy because they do not want to confront their friends. It might take time but then one day, they come up with something substantial and then their friends are indeed surprised at that time. They go "he is after all not that bad". I have known such instances.

I still think that doing what we love without getting bogged down by the success of a so called "friend" is the key to success in anything in life. In this aspect, I am pretty sure that we humans are different from animals as I haven't heard of animals succeeding once the trend has been set during childhood. I am not saying this to be optimistic and show sympathy to the OP. If it was the other way round, I would much rather tell the OP about the truth rather than lie in order to be encouraging. I do not think that approach works. I truly believe it. I have seen it and experienced it in my life based on my observation of the members of my group. I hope that OP takes the approach of just doing what he loves without worrying about IQ and all the other factors.

Mdhiggenz

Dude you are 17 relax. Oh and your iq tends to increase as you progress uni. I suggest you take the summer of maybe meet some girls and party a bit before you start uni.

hurdler1

I am also trying to be a mathematician. But I have realized something. It is a love, not a state of being. Unless you are very intelligent, which I think most mathematicians are not (necessary), doing math research as a job is more of a habit than a state of being.

i second the sentence that success is not the right mindset to have. I had an iq of 150 as a second grader. I don't know what my iq is right now. But i have failed at learning math because I was focused on trying to do things fast like many people at mit. However, I am not a fast thinking. I like to think slowly and deeply and work on a problem for many hours if I can. However, this is hard to do at MIT. I don't think you have any iq to get a phd in math. I think you have to work hard, and have a non-proud mindset constantly. There are tons of smart mathematicians out there. However, if you know what you are doing when you solve differential equations, then that is sufficient. As long as you want to study mathematics and work at it for the love of it, then it doesn't matter if you aren't smart. Many of the professors at MIT are bad at computation, but good at what they do.

ALso, I think many mathematicians have some idea of what other people are doing, but I think overly stressing about how other people are doing is also not helpful, and actually harmful.

modnarandom

I guess this relates to the balance between doing something you love and being realistic. Like everyone else already said, you shouldn't study something unless you enjoy it a lot. However, especially with math, I found that it was like a lot of people who didn't have a lot of background in math from high school were left behind in college in comparison to those in other majors. I'm not sure why this is the case, but this really is something to consider. As for being realistic, math isn't the most "practical" or applicable to other fields and this is something to consider especially if you aren't all that interested in applied math. So, this is something the OP (and anyone else considering the major) needs to think about carefully.

I don't really understand why this should be a problem. At first, it was intimidating to be surrounded by these people, but I'm constantly amazed by the people around me and it is exciting to learn from them.

StatOnTheSide

I am not commenting on any particular case. I have been told that each person is different and it may not be the same for everybody. I have certain beliefs based on my experience and it is very strong. It is nothing more than a mammalian trait. If you are a person who has a set of friends and if you are not at the top of the ladder in that group, then it affects your performance. It is like a bunch of lion cubs. The most aggressive of the bunch will eventually be the leader. You can tell by looking at the bunch in their early childhood developmental phase. Same with humans. A kid who is way better than his peers in math will remain there. The only difference is that some of them drop out of the group not liking the hierarchy that exists in that group. Why? It helps immensely if you are in a group where you get the ego boost that you are the best in that group. Or else it does not make sense to be in that group. Why be an ego booster for someone else?

The fact of the matter is that it is all about competition. The confidence that you develop is cumulative and will results in a strong conviction that you are the best. Next time there is a competition, you start out with that mindset. Others look at you believing the same thing. This fact works against them in the competition. Nature, this way, accomplishes selection of the best. When you are running a race and see that others are taking over, just that fact works against you. So even if you have the potential to run faster, you will be looking at others thinking that they will remain ahead and there is not point running the race anymore which feeds on itself and eventually you will lose.

I do not intent to contend anyone here. modnarandom might be in a place where the only thing that people care for is learning and very little to no emphasis on competition. All the places that I have studied, it was all about competition. That being the case, it works against you if you are not running as fast as others. Even though a career in math or engineering is more like a marathon, it still is a competition. I was talking more in the context of undergrad in math/engineering or like later part of high school where you write math olympiad and other contests. Those are 100m races. It is all about psychology. Typically the one who gets the initial lead wins.

I have to admit that in a marathon, the case is different. Most winners do not have a lead initially but win it eventually.

42Physics

You are obviously capable of achieving in the field of mathematics. I wouldn't let petty occurrences discourage you from an ever-rewarding field. We are very close in age and seem to share our talent. I myself wish to be a Physicist; perhaps one day we will work together.

StatOnTheSide

Thanks for your kind words 42Physics. Please do not take my theory about ego boost etc too seriously. I do believe that it is different for older people. To be a grown up has its advantages and this is probably one of them. I was talking about my experience during my undergrad/highschool days and it might be different for you. Not that those people have changed but just that now there is lot more freedom to choose only the nice people, like yourself, to be a friend.

BTW I am 32 years old :)

42Physics

I appreciate your time greatly. I'm just trying to help birth the people who make the tomorrow of science and math come. I am 14 years old btw

Jimmy84

Levis, In my own opinion one of the most important factors in excelling in a given subject is first the motivation, that you obviously have, and second, having time. You obviously have both.

The more time you invest learning, the more you will be able to learn deeply and intimately a subject.

One of the biggest advantages that young people have now is the huge amount of information on the internet.
The best mathematicians like Hilbert, Grothendieck, Gauss etc They never had access or an easy way to find 200 graduate math books online, or online lectures, wikipedia or websites that could orient you.
If you can exploit that to teach yourself additional subjects, if you have some orientation and if you administer your time. You would be able to learn many mathematical related subjects in a deep way.

JimmBean

Apologies for bumping a somewhat old thread, but I really couldn't let this go. That "child prodigy" you refer to in your post, Jacob Barnett, is basically a fake. He has a good memory no doubt (possibly autistic?) and so is able to memorize a great deal of intelligent sounding phrases - even though he knows almost nothing about what he is talking about. In fact his Wikipedia page has been deleted as a result. Watch this:

http://www.liveleak.com/view?i=91e_1301861454

EDIT: Here is some additional material. Watch from 8:31 onward... http://www.youtube.com/watch?v=Uq-FOOQ1TpE

This more candid video (filmed by his Mom) is disturbingly stupid, with he only reciting patently obvious facts and hinting towards his new theory which "he cannot talk about on video". He obviously understands very little about the math/physics he is reciting. I get the feeling that this kid is vaguely intelligent with a good memory and has been unfortunately taken advantage of by his parents in a pathetic attempt for their 15 minutes of fame. I actually feel sorry for the kid.

Moral of the story Levis2: don't believe everything you read in the media - most of it is sensationalized to the extreme. Do what you enjoy and don't let others (e.g. the media) tell you what you can and can't do. And get some professional help if you are feeling really depressed - that won't help anything.