Is the Pressure to Produce Groundbreaking Mathematics Holding Scientists Back?

[elfboy]

regarding the huge quantitiy of mathematics to learn? There are so many concepts and so little time it seems. The volumes of mathematics even from specific fields is staggering, and you have to become accustomed to the previous works of that field before you can even pursue research. What makes matters worse is that the peak age of producing quality mathematics is around thirty so you don't even have much time.

Also it seems everything is already done, but better than you could do.

 

[SticksandStones]

If it makes you feel any better, there is no such thing a peak age. :)

 

[MrJB]

I agree there is no peak age. A physics professor once told me that even though he was older he was still doing research as fast as when he was younger. He said his mind wasn't as quick, but because of his years of experience, he would investigate in the right direction more often and not waste as much time trying things that didn't work. I assume this carries over to math.

And yes, there is a lot of math to learn, too much for one person. That's why you specialize. It is a lot of work. And I wouldn't worry about producing groundbreaking results. There's enough math out there where you can find a little area that interests you, and produce some results. Eventually you may stumble across something bigger. Also, talk with others about math, someone else may have a piece of the puzzle you're working on. Don't worry, work hard, have fun.

 

[handsomecat]

regarding the huge quantitiy of mathematics to learn? There are so many concepts and so little time it seems. The volumes of mathematics even from specific fields is staggering, and you have to become accustomed to the previous works of that field before you can even pursue research. What makes matters worse is that the peak age of producing quality mathematics is around thirty so you don't even have much time.

Also it seems everything is already done, but better than you could do.

Yes, it is hard, even harder if your supervisor is equally clueless. However, after groping around for a while, it usually is possible to find some direction.

Personally, I struggled for about 3 years before i found my direction in a moment of serendipity. The supercomputing centre had just bought a new software and it was something that I could use!

 

[mhazelm]

I feel that way sometimes, but then again, if you're doing what you're passionate about, don't worry so much about making some huge new theorem for the next hundred years or whatever. I think it's way too easy to get caught up in this mindset of "I've got to do something big". Everyone wants to be Einstein. But really, I think we should just do what we love, and the rest should fall out of that. So just do math! The volumes of it will come with time.

 

[Mathemaniac]

I think it's way too easy to get caught up in this mindset of "I've got to do something big". Everyone wants to be Einstein. But really, I think we should just do what we love, and the rest should fall out of that. So just do math! The volumes of it will come with time.

I disagree. I think someone on these boards said that if you shoot for the moon and miss, you'll still be among the stars.

There's nothing wrong with having lofty aspirations, just as long as you don't beat yourself up if you don't fulfill them. In fact, in my opinion, people these days aren't thinking lofty enough.