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My professor keeps saying that he's too old to discover anything important and that it's up to us to solve tomorrow's physics problems while we are young. I realize that all the great scientists did their major life works in their twenties but do you really have to discover something while you are so young????? I feel I wont come up with anything major in my 20s and likely I will do more prevailing work in my 30s or 40s or maybe I'll be a late bloomer and reach my peak in the 50s or 60s. Do you think my professor, being circa 42 has missed his deadline? Do you believe this crap?

The "Mathematicians do their best work before 30" thing is a relic at this point. Mathematics has become so large that you need something like 15 years of formal schooling to even be at the point where you can make new discoveries. The age of prodigy mathematicians has largely ended, in my opinion.
Unfortunately, mathematical discovery also depends a lot on openmindedness, and as people grow older, they tend to become more set in their thinking. Your professor should still be all right at 42, though.
I really hope my first paragraph is correct because I have no idea where mathematics actually is at this point. The only famous math problems are the Millenium problems and a couple others, and the Millenium problem that most interested me has just been eaten by Perelman.

I find it fascinating how first it was "the last man to understand all of science" and then Hilbert as "the last man to understand all of mathematics", and then someday it's going to be "the last person to understand all of algebra" and so on.
Eventually human knowledge, should we retain these limited human bodies and these limited human mindsets, will expand so far beyond the human capacity that we'll end up being the equivalent of idiot savants: very good but only at a very tiny slice of a field.
It's kinda depressing.

I think there is a 3-fold reason why many mathematicians report that they have doen their best work when young
1) To be a good mathematician many mental structures must be internalized-- this process seems similar to language aquisition and works best when young. I think the window of opportunity is different than language but still-- the earlier you start the easier it is. This is NOT the same as learning math-- this is internalizing the sorts of structures that you need to learn the math. This can be accomplished without formal training or even exposure to mathematics (though that's rare). However if the meta-structures aren't already in place when young then you are unlikely to become a GREAT mathematician.
2)The acquisition of structure is supported by positive and negative reinforcement so those who pick up some structure EARLY tend to be moved in directions where they gain more-- they are much, much, much more likely to end up in math. Those who do not gain these structures early are moved in directions where they pick up different structures and are move away from math acquisition.
3) The random swirl of personality, insight, and experience that makes a one mathematician's sub-matrix distinct from another mathematican's are based on certain key components-- when these components are new/unique then they lead to rapid insight and breakthroughs and new mathematics, but when these insights and breakthroughs are sourced in a finite number of differences. Under the influence of these differences all the NEW breakthroughs-- the ones most closely related to these underlying assumptions--take place first. This is the BEST work of which most great research mathematicians speak. It's NOT that they become less creative when they're older, or less open-minded-- it's that they've already applied their unique blend of creativity to the problems at hand.

I beg to differ. The large research teams at Georgia tech are failing miserably at modeling fatigue and are being trumped by a single person. Most theorists I know work more or less alone as well. Experimental teams can't really work alone due simply to the nature of their profession, but theory is entirely different.