“THEORETICAL MATHEMATICS”

[gusl]

Arthur 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:

<< 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).

Comments

[rdore.livejournal.com]

"Yet today in certain areas there is again a trend toward basing mathematics on intuitive reasoning without proof."

This sounds like a pretty extraordinary claim. How do they back it up?

[psifenix.livejournal.com]

Probably by listening to those people who send out proofs of the Poincaré conjecture that are "so simple a child could understand it."

[gustavolacerda.livejournal.com]

to both of you, my advice is RTFP!

[rdore.livejournal.com]

Sorry, but you quoted just enough to make me think the person is a crackpot, not enough to make me actually interested in reading it.

[gustavolacerda.livejournal.com]

since you are concerned with the persons who wrote it, the following may be relevant:
http://en.wikipedia.org/wiki/Arthur_Jaffe
http://en.wikipedia.org/wiki/Frank_Quinn

[rdore.livejournal.com]

Do be honest, I really just don't care enough to read the paper. The quote just struck me as wild enough I felt I ought to object to it on principle.

[stepleton.livejournal.com]

Sounds interesting! I can't read it right now since I'm busy, but what does "basing" mean? Establishing ambitious, less-than-fundamental axioms (e.g. Assuming Poincare's conjecture is true... [and yes, we don't have to assume anymore]) and then just seeing what that lets us do? Then hoping that rigorous proof fills in the gaps later?

[dachte.livejournal.com]

Multiple cognitive parse failures in second sentence....

any *other* science
a clarity and reliability unmatched

Ouch. Sounds neo-platonist.