How indicative is olympiad mathematics on a person's mathematical strength?

[huey910]

I have always loved math and have done independent theorem-proving and research. However, I have had absolutely no olympiad training but it seems that the math olympiad is quite important in applying to universities. I have started to do some of the questions myself and find that I progress unexpectedly slowly. Does this mean I should choose another subject altogether in university or is this irrelevant? Please advise.

 

[micromass]

Olympiads are useless in terms of a persons mathematical capability.

Sure, if you do good in olympiads, then you will be a good mathematician, but the converse is not true.

Many mathematicians I know are very good researchers, but would suck in terms of a competition. The reason is that they like to think things through. They like to prove everything and be sure of their statements. This is totally contrary to what an olympiad wants you to do where you have to come up with a solution fast.

Do not waste your time on olympiads, it's totally useless. Read a good math book instead, it's much more indicative: if you enjoy it and get through it easily, then you're ready for math.

 

[Stephen Tashi]

I have always loved math and have done independent theorem-proving and research.

should choose another subject altogether in university or is this irrelevant? Please advise.

You should consider the following questions: Is the math you did independently representative of the math you will encounter in the university? Or have you specialized in one particular type of problem (for example, combinatorial problems)? Are the proofs you wrote up to the standard that is required in a university and in mainstream mathematics?

There are some people who do independent study and only form their own eccentric opinions and flawed techniques for doing things. There are other people who understand material in the standard way and, if they innovate, they invent methods that the world would ackknowledge to be valid and useful.

If you are "off in left field" mathematically, you should consider a different major in the university.

 

[homeomorphic]

You should consider the following questions: Is the math you did independently representative of the math you will encounter in the university? Or have you specialized in one particular type of problem (for example, combinatorial problems)? Are the proofs you wrote up to the standard that is required in a university and in mainstream mathematics?

There are some people who do independent study and only form their own eccentric opinions and flawed techniques for doing things. There are other people who understand material in the standard way and, if they innovate, they invent methods that the world would ackknowledge to be valid and useful.

If you are "off in left field" mathematically, you should consider a different major in the university.

Sounds a little too "in-goup/out-groupish" to me.

On the one hand, there are those people out there claiming to be able to trisect an angle using a ruler and compass and prove everyone wrong. That is just silly. We certainly don't want any of that non-sense. But perhaps even those people could recover and become mathematicians with more training and mental discipline.

But I think people who think differently from the mainstream can often have useful ideas and perspectives.

Sure, it should be up to "meainstream standards" of proof, but as long as its correct there shouldn't be an issue. Of course, you can always judge the significance of things, too, beyond their correctness, but only with great caution. I find it astounding how mathematicians in the past have opposed good ideas on their own conservative philosophical grounds. Some mathematicians fought against Cantor's set theory, some people objected to Mandelbrot's fractal geometry.

Rejecting important contributions because they are too new and different is just as silly as taking those angle trisection claims seriously.

Finally, if someone is intellectually honest enough to admit that their math was flawed, then what's the problem? The problem would be if they are unable to detect the problems with it.

No, no, no. If you want to study math, you should study math, if you have thought about where you can go with it career-wise ,and if it's what you really want. If you don't do well, you don't do well. That's it. You'll find out.

 

[Stephen Tashi]

Sounds a little too "in-goup/out-groupish" to me.

That's the way universities are. The original poster seems to have a flexible attitude and is willing to consider alternative majors. He doesn't sound like he's looking for a fight.

 

[I like Serena]

I started with math olympiads very early - just for fun.
That's what I feel math should be: fun!

If you feel that it's no fun at all, it seems unlikely to me that you'll get good at math olympiads, and then I suspect it is a waste of effort.

 

[homeomorphic]

That's the way universities are. The original poster seems to have a flexible attitude and is willing to consider alternative majors. He doesn't sound like he's looking for a fight.

To an extent, maybe, but they will just grade your papers. They don't care if you think you can trisect an angle with a ruler and compass, as long as your work is correct. If you did make that claim, then they would just mark it wrong and that would be that. They don't make you go around wearing a dunce cap. They just mark it wrong. Perhaps, it wouldn't help when it came time for recommendation letters, I guess.

If he want to think about other majors, he can do that. I'm just saying if math is what he really wants to do, he should do it.

 

[Functor97]

I have always loved math and have done independent theorem-proving and research. However, I have had absolutely no olympiad training but it seems that the math olympiad is quite important in applying to universities. I have started to do some of the questions myself and find that I progress unexpectedly slowly. Does this mean I should choose another subject altogether in university or is this irrelevant? Please advise.

They are good indicators to some degree of mathematical talent.

However, no one is going to stop you majoring in math if you have no olympiad training. The vast majority of math majors have never seen high level olympiad problems, let alone represented their country at the IMO.

 

[disregardthat]

Many mathematicians I know are very good researchers, but would suck in terms of a competition. The reason is that they like to think things through. They like to prove everything and be sure of their statements. This is totally contrary to what an olympiad wants you to do where you have to come up with a solution fast.

Do not waste your time on olympiads, it's totally useless. Read a good math book instead, it's much more indicative: if you enjoy it and get through it easily, then you're ready for math.

I don't think you have seen the problems for e.g. the IMO. Every problem is asking for a full proof of the solution, just as rigorous as one would expect in any course of mathematics. The difference in an olympiad setting is that you have to think things through fast. I think it's an excellent way to become a better mathematician, it's not useless at all. Everyone I know who have practiced for olympiads will agree with me on this. Not only because it requires you to spend so much time thinking about how to prove things, but that you have to come up with your own theorems/conjectures and methods to solve a problem. Personally I believe it improves your awareness of details.

So I would recommend you to look into it, but Serena says you will have to have fun with it, and prepare to spend a lot of time with it. A great book to help you with this is Paul Zeit's "The art and craft of problem solving". It doesn't require more than high school knowledge of mathematics.

 

[Acid92]

It is a good indicator of a persons natural aptitude in my opinion since they test your Mathematical intuition and problem solving ability as opposed to your content knowledge (which school Math is mostly all about) and obviously for that reason are a better measure of aptitude.

But I also think that people greatly underestimate them, people have the misconception that those who make it to IMO teams just happen to be able to do these sort of problems from the beginning without a lot of experience. In reality, Olympiad problems are very very very hard unless you happen to be someone like Terence Tao. There are two documentaries on the IMO, one on a US team and one on a UK team, if you watch these you will notice that first timers who make it to the teams usually begin at a level where they struggle with national Math Olympiads let alone the IMO and these people begin competition Math at very young ages too. So my point is that you should expect slow progress on competition Math.

Also I wouldn't recommend Paul Zeitzs masterpiece which, although along with Engels "Problem solving strategies" is pretty much the Bible of Math Olympiads, is much too hard for the beginner, if you can do most problems on Zeitzs book then youre pretty much going to be capable of getting a Gold medal at the IMO as about nearly half the problems in his book are IMO and even Putnam problems. Engels book is even more advanced.

Instead you should start out with these books before trying Zeitz (Ive been sporadically working on Zeitzs book for several months now but found these very good as a preliminary to his especially the last one)
https://www.amazon.com/dp/4871878309/?tag=pfamazon01-20
https://www.amazon.com/dp/0273728911/?tag=pfamazon01-20
https://www.amazon.com/dp/019953988X/?tag=pfamazon01-20