“THEORETICAL MATHEMATICS”
Jun. 27th, 2008 11:33 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslArthur Jaffe and Frank Quinn (1993) - “THEORETICAL MATHEMATICS”: TOWARD A CULTURAL SYNTHESIS OF MATHEMATICS AND THEORETICAL PHYSICS
Is there a place for speculative mathematics? This paper does a better job than I could at expressing the analogy between formal proof and physical experiment.
From what I've read so far, their main message is: "Physics has a division of labor between theorists and experimentalists. Why shouldn't math work this way too?"
To whet your appetite, this is how the paper begins:
Being fond of speculation, intuitions and informal logic arguments, I personally feel like the "theoretical physicist" here. My interest in logic and formalization stems from trying to prevent/catch mistakes (and also partly from my desire to resolve disagreements).
Is there a place for speculative mathematics? This paper does a better job than I could at expressing the analogy between formal proof and physical experiment.
From what I've read so far, their main message is: "Physics has a division of labor between theorists and experimentalists. Why shouldn't math work this way too?"
To whet your appetite, this is how the paper begins:
<< Modern mathematics is nearly characterized by the use of rigorous proofs. This
practice, the result of literally thousands of years of refinement, has brought to
mathematics a clarity and reliability unmatched by any other science. But it also
makes mathematics slow and difficult; it is arguably the most disciplined of human
intellectual activities.
Groups and individuals within the mathematics community have from time to
time tried being less compulsive about details of arguments. The results have been
mixed, and they have occasionally been disastrous. Yet today in certain areas there
is again a trend toward basing mathematics on intuitive reasoning without proof. >>
Being fond of speculation, intuitions and informal logic arguments, I personally feel like the "theoretical physicist" here. My interest in logic and formalization stems from trying to prevent/catch mistakes (and also partly from my desire to resolve disagreements).