Mathematicians

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• The imprint of the world in our minds is not photographic; all the brain knows of the outside world is a chaotic sequence of electric impulses and out of these it creates a structural entity: our perception of what we see and hear. Most of the time, an adult's brain talks to itself and creates more and more refined structures within itself. The word "structure" means a mathematical structure, something which becomes more and more abstract and better and better logically organized in the course of this self-conversation. The mathematical ability of each person's brain by far exceeds those of the greatest geniuses of all time. Nobody, given the input the brain starts with, could be able to arrive at such a level of abstraction, for instance, as the five-fold symmetry (for example, a starfish... (查看原文)

  alreadydone 1赞 2014-01-12 11:29:07

• I have always preferred working in unpopular areas of mathematics. I recognize the benefits of working in popular areas—a community of experts to discuss problems with, a group of friends you see regularly at conferences, a reference group to compare yourself to, a crowd to instantly appreciate your newest results—but it's not for me. However, even if you're working in an unpopular area, when you find some fertile ideas, people will notice and pile into your area. My solution is to get out and move to another area that is less crowded. I am a geometer at heart. When I discover a mathematical idea, it comes as a geometric mental picture that completely convinces me. It is always a real struggle to translate my mental picture into words so that I can communicate it. Once I have put it into... (查看原文)

  alreadydone 1赞 2014-01-13 09:27:06

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