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experienced, seek and think I know about, Thom was not after the logical proofs of
geometry but rather viewed mathematical theorem and proof work as activity
derived from intuitive experience with geometric relations as the thought forms that
represented real Reality. Though a Field’s Medal winner in mathematics (recall that
it is the Nobel Prize in mathematics awarded every four years at the International
Congress of Mathematics) and for his life time, one of the most brilliant and fecund
mathematicians in the world, so many mathematicians admit that they got the seeds
of their life work from his throw away remarks, Thom, with a little smile and his eyes
twinkling, admitted to me with apparent pleasure that “I have never proven any
theorem in my life.” All his discoveries came from insightful moments of grace and
the courage to pursue them. Riding back from Paris late one night on a train that
didn’t stop at IHES’s town of Bures sur Yvette, I watched him use the red
emergency phone to call the train’s engineer to stop the train suddenly for our exit. I
loved him, in part, because he had the courage to believe in and act on my kind of
intuitively realizable, experiential God.

In keeping with his characteristic style of generalizing mathematical systems
beyond their carefully defined specifics, Thom defined the concept of singularity
very broadly, speaking of them as distinctive and noteworthy things, points where
the usual or expected properties, laws and definitions fail, where smooth and
continuous processes become discontinuous. For Thom, these were the settings for
the unexpected and miraculous. He believed that his work and that of many others,
now and in the future, would indicate that the set of miraculous singularities were
finite, systematic, universal and describable. Most importantly for our purposes,
Thom believed them to be archetypal. It was through the structure of archetypal
singularities that he regarded inside and outside realities as mutually reflective.

I was blessed by hours of discussion with him during his car travels to
lecture around France. Thom often asked me to accompany him as he drove from
IHES to various branches of the University of Paris. He used these times to
exercise my geometrically flavored, mathematical intuitions. He used words to
create visualizable structures without the diagrammatic aid of a blackboard. He
used mental topological structures created by the properties of imagined motions,

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