Posted by: Alexandre Borovik | October 18, 2008

Why there is only one way of doing mathematics?

Peter McBurney kindly send a link to a paper in Science on Japanese mathematics in 17th century. A quote:

Seki worked on determinants simultaneously with Leibniz, another mathematician whose work went unrecognized for decades because he never published it. “There were striking similarities in mathematical thinking” between the two men, says Eberhard Knobloch, a Leibniz scholar at the Berlin University of Technology. If the Eastern and Western mathematical sages had been in contact, Knobloch says, it probably would have advanced mathematics worldwide.

Why there was (and there is) only one way of doing mathematics?

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Responses

  1. I wouldn’t say there is only one way of doing mathematics, but different methods work better than others in different circumstances. The more methods you are familiar with, and the more exchange of ideas occurs, the more chance you have of discovering a way to solve the problem you’re working on.

  2. Mathematical ideas replicate across individuals and across cultures because the ideas come from our biological origins. Even though each of us has a different mind, our minds are constructed very similarly: same lipids, same protein, same DNA.

    Mathematics as the supreme act of introspection leads to external truth. Were you and I engage seriously in a mathematical discussion, one or the other would say one thing, the other or one would thing something else entirely, and between us we would come to an agreement about the general and specific nature of the subject at hand.

    When I read what you write (generic you), I don’t read the words and symbols so much as I think about the meaning of the words and symbols, and come to my own conclusion which —once the misunderstandings of the subtle terminology vanish — agrees with your conclusion.

    So the same idea is found at different places in different minds because the underlying social structure has lead precisely to that level of evolution.

    Or at least that’s how I view it ;-)

  3. Who says there is only one way? It’s a very harmful myth. There are many different ways to solve almost any problem.

  4. It’s a descriptive, not a normative statement. The simple fact is that widely separated people independently came to very similar mathematics. The question is why that happens, over and over and over. Alexandre’s mistake was in trying to take some poetic license in asking it.

  5. This thread reminds me a little bit of an article written twenty years ago by David Ruelle, “Is our mathematics natural? The case of equilibrium statistical mechanics”. Final sentence of abstract: “In view of this the author argues that our mathematics may be much more arbitrary than we usually like to think.”

  6. (On my computer screen, it is difficult to tell that the word “article” in my previous comment is actually colored green and links to the article in question.)


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