I'm not the most qualified to ask this...or perhaps I am, since I'm no Terry Tao! I think what we bring to mathematics is the unique perspective afforded by our own individual experience. The more of us who are trying to do mathematics, the better, because this increases the diversity of perspectives in approaching the myriad problems we face. Also, as is popular to say, there is far more mathematics to do than any handful of powerful mathematicians can do. This is a "big tent".

Another thing that I've read someplace...someone was describing the difference between Kolmogorov and Israel Gelfand, and this person wrote/said the following: "when Kolmogorov went into a new mathematical landscape he immediately looked for the tallest mountain and climbed it, when Gelfand entered the same landscape, he immediately began building roads." (Someone please fill muad in on the proper location of this quote...I think it was the Notices...)

Others have said that most of what we do as mathematicians is organize and clean things up to clear the way for a future polymath, like a von Neumann, to really make some progress. And some road builders have built some unbelievable roads. (Didn't Serre say something like he spent most of his career rewriting other people's work?)

I don't know about you, but I'm fine with this! It's much better than having my name on the location of a transistor on some unknown circuitboard on the space shuttle...not that there's anything wrong with that!

Anyhow, don't worry about having things to do...there are plenty!

I'm not really qualified to answer this...or perhaps I am, since I'm no Terry Tao! I think what we bring to mathematics is the unique perspective afforded by our own individual experience. The more of us who are trying to do mathematics, the better, because this increases the diversity of perspectives in approaching the myriad problems we face. Also, as is popular to say, there is far more mathematics to do than any handful of powerful mathematicians can do. This is a "big tent".

Another thing that I've read someplace...someone was describing the difference between Kolmogorov and Israel Gelfand, and this person wrote/said the following: "when Kolmogorov went into a new mathematical landscape he immediately looked for the tallest mountain and climbed it, when Gelfand entered the same landscape, he immediately began building roads." (Someone please fill muad in on the proper location of this quote...I think it was the Notices...)

Others have said that most of what we do as mathematicians is organize and clean things up to clear the way for a future polymath, like a von Neumann, to really make some progress, and some road builders have built some unbelievable roads. (Didn't Serre say something like he spent most of his career rewriting other people's work?)

I don't know about you, but I'm fine with this! It's much better than having my name on the location of a transistor on some unknown circuitboard on the space shuttle...not that there's anything wrong with that!

Anyhow, don't worry about having things to do...there are plenty!