Peng Zhou

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quotes:thurston-says [2023/07/24 05:47] – pzhouquotes:thurston-says [2023/07/24 05:53] (current) – pzhou
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 In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining --- they depend very heavily on the community of mathematicians. In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining --- they depend very heavily on the community of mathematicians.
  
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 +===== and Joe Silverman says =====
 +It's 12:40am New Year's Day, so maybe not the best time to be writing MO responses, but I loved reading everyone's encouraging answers to this question. (BTW: @Lubin: Taking algebra, with a dollop of algebraic number theory, from you was inspiring.) Anyway, my answer to the OP would be to learn lots and to work hard on problems that interest you. Don't worry so much about whether you're proving breakthrough theorems, just try as hard as you can to understand the parts of mathematics that interest you the most. (By "understand", of course, I mean get into the guts, figure out what's really going on, and prove as much as you can.) Also don't worry that you won't solve every problem (or even a majority of the problems) on which you work, and don't worry that you won't ever feel you fully understand everything about a problem; that's why there's always more to investigate. Then, after a decade or two, feel free to look back, and I think you'll find that you have made a contribution to humanity's knowledge of mathematics.
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 +And even when you're doing research, it's hard (at least, I've found it hard) to decide on the significance of what you've done. I think the difficulty is that after working hard on a problem for a year or two and making enough progress to write a paper, one understands the problem so well that everything that one can prove seems trivial, while everything that's left undone seems hopeless. So maybe my saying "wait a decade or two" is a bit excessive, but it's definitely worth waiting a couple years before you decide on the quality of the work you've done.
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 +Happy New Year to one and all at MO.
  
  
quotes/thurston-says.1690177665.txt.gz · Last modified: 2023/07/24 05:47 by pzhou