The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Concrete and Abstract in Mathematics, was "What's wrong with education..."
Replies: 2   Last Post: Jun 14, 1996 1:03 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
john baez

Posts: 57
Registered: 12/6/04
Re: Concrete and Abstract in Mathematics, was "What's wrong with education..."
Posted: Jun 14, 1996 1:03 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply



In article <Dsyrpn.5I1@mv.mv.com> Alberto C Moreira <junkmail@moreira.mv.com> writes:
>baez@guitar.ucr.edu (john baez) wrote:

>Also, you're talking at a level far beyond that which I was addressing.
>When doing mathematical research, one probably has to use whatever tools
>one has at his/her disposal, but learning it is another story. And when
>we're talking about teaching students, do we want to emphasize informal
>thought?


I suspect we should emphasize formal thought and informal thought and
the road between the two: formal thought without the backing of
informal thought tends to be lacking in zest, while informal thought
without the backing of formal thought tends to bog down in vagueness.

>Logic itself is your frame, or isn't it ? I'm not at that level, but I
>have difficulty seeing any kind of mathematics that doesn't anchor
>itself in a logical frame. I know that category theory people, just
>like lambda calculus people, like to see category theory as a formal
>system par with set theory and others. But all three of them are still
>based on a logic system, or at least I do so far believe.


Certainly once one starts proving theorems in category theory one can,
just like in set theory, formalize the reasoning with the help of an
axiomatic system, and it's good to know how to do this.

>>Think of how Ed Witten won the Fields Medal, the biggest
>>math prize of all! His reasoning was not formal, and in many cases we
>>still don't know how to make it formal --- but his discoveries were


>I'm
>not familiar with the work of Ed Witten, are his proofs "informal",
>in the sense that they don't fit within a logic system ?


Yes, they are informal. He is primarily a physicist, yet he won the
highest prize in mathematics, the Fields Medal. Many of his arguments
and computations have been formalized by other mathematicians, and many
of them have not yet been fully formalized. They have revolutionized
many subjects.









Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.