[FOM] 827: Tangible Incompleteness Restarted/1

[Harvey Friedman]

On Wed, Sep 25, 2019 at 2:30 AM Timothy Y. Chow
<tchow at math.princeton.edu> wrote:
>
> Harvey Friedman wrote:
> > But I have found a somewhat surprising reaction against graphs and
> > cliques among many mathematicians. Notable is the statement made to me
> > by a Fields Medalist when asked if they knew what a graph is. ANSWER: No
> > I don't, and I never want to know what a graph is. So the interesting
> > question here is just what did this Fields Medalist know about graphs to
> > make them never want to know what a graph is? Let me repeat for
> > emphasis:
> >
> > WHAT DID THIS FIELDS MEDALIST KNOW ABOUT GRAPHS TO MAKE THEM NEVER WANT
> > TO KNOW WHAT A GRAPH IS?
> >
> > The answer to this question should reveal a lot about the current
> > mathematical environment.
>
> The obvious way to try to find out the answer to this question is to ask
> the Fields medalist in question.  Did you try that?
>
Not going to happen.

> Contempt for subfields of mathematics is often correlated to a perception
> that those subfields are largely disconnected from the rest of
> mathematics.  There are certainly large chunks of graph theory that are
> disconnected in this way (ironically, I'm using a graph-theoretic metaphor
> to describe the situation).  It could be that this is what the Fields
> medalist was saying.
>
Core mathematicians with this kind of attitude need to look at
themselves in the mirror. After all, the general view among core
scientists is that core mathematics is largely disconnected from the
rest of science. I'm pretty sure that core mathematicians do not enjoy
being marginalized by the general scientific community any more than
discrete mathematicians enjoy being marginalized by core
mathematicians.

And the idea that the present state of mathematics is of some
fundamental importance in the history of ideas seems ridiculous. One
has no intellectually honest choice but to take into account the
general intellectual interest of mathematical notions and results.
Graph theory is in fact very well connected with a number of major
areas outside of core mathematics, notably the structure of the
internet, computer architecture, etcetera.

Harvey Friedman


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