What makes putnam-style problems 'different' from other problems?

[DrWillVKN]

I have only begun to study mathematics, and the competitions look pretty exciting. I heard the math competition style problems follow a certain style and follow specific heuristics of solving, compared to non competition problems.

So what is this 'difference'? Besides the fact that they were written using known results and are meant to be solved within 6 hours, is there really a difference?

Is it possible for someone to just do loads of putnam-style problems and do well on it? I know it is very, very useful to get into that problem solving sort of mindset when researching mathematics, but is it necessary for someone to be able to solve putnam-style problems in order to do well in mathematical research?

So if you aren't good at doing putnam problems, does that mean you aren't a good mathematician in general?

 

[micromass]

I don't know what putnam is, but most of the time these mathematical competitions have nothing to do with research.

Being good in a mathematical competition means that you know a lot of theory (like the AM-GM inequality and others), that you have solved a lot of problems and that you have a quick mind.

However, research is (in my limited experience about something else). Of course you'll need to know a lot of theory to be able to do research. However, research doesn't mean that you can solve any problem in 6 hours. In fact, some problems will take you weeks to solve. It also requires a lot of creativity. Competitions want you to be creative too, but not so much.

I have met a lot of professors who claimed that they were really "slow" thinkers. That means that they had to do a lot of effort to understand a problem in all it's complications. That means that they would be very, very bad in competitions. Nonetheless, they were really smart and good in their research.

So, I would say: no, if you aren't good at competitions, then you can still be good in research.

 

[doodle_sack]

While I agree to most of what micromass said, I don't agree to this: but most of the time these mathematical competitions have nothing to do with research. Being good in a mathematical competition means that you know a lot of theory.

This can be true, but not always. You can be a good researcher although if you are not good at competitions, but, mathematical competitions has everything to do with math research. Normally, Olympiad type questions are open-ended, just like actual research.

I won't stick to the fact that one should be good at mathematical "theory" to be good at competition, I'm one counter example.

To answer your question: No, it is neither necessary nor sufficient to be able to solve putnam-style problems to be a good math researcher. But remember, if you can be good at it, not by simply using the tactics, but by understanding thoroughly from where it came, then you can shine in areas other than math, like Theoretical Computer Science, Physics, Engineering, etc,.

 

[deluks917]

There are 12 Questions on the test and you have a seemingly reasonable 6 hours. If the Putnam was graded like a normal test (65% to pass in this case at least 79 points) then only 30 undergraduates in the whole country were going to pass. Almost nobody is actually "good" at these questions because the test is extremely difficult. Don't beat yourself up if you can't do them consistently.