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Dear Pat,

I received the airfare reimbursement; thanks.

After all the work I've been putting into writing up my thesis, I can
really sympathize  with the way you feel.   In response to your note,
here are the facts:

1.   The  program  itself  actually  came  up  with  the  concept  of
maximally-divisible numbers. This concept was unknown to me and to my
committee   (including  Knuth).    The   program  noticed  a  certain
regularity in the factorized forms of such numbers.

2. Working then  by hand, I derived  the hairy formula (only  about 1
day's work), and proved it  using calculus.  Neither the statement of
that formula  nor  its proof  is  withn  the scope  of  AM's  current
abilities.

3. This was of interest to Knuth, who then  passed it along to Erdos,
who then said that he dimly recalled a similar study by Ramanujan. It
turns out that  Ramanujan did in  fact define  that same concept  (in
1915),  and  was interested  in  it.    He  never quite  derived  the
relationship  I  did,  but  then again  neither  did  AM  itself.   A
significant feature  of all this  is that  Ramanujan himself was  the
only great modern mathematician who was "self-taught".  He re-derived
most of  known number  theory (and  much new  work) all  by  himself,
before finally getting into a college.

4. One more "new" result was recently formed by  AM.  AM derived what
is  known as  "Goldbach's conjecture"  (every  even number  is either
prime, the square of a prime,  or is representable as the sum of  two
odd primes), and then applied it  to a base of geometric concepts I'd
fed  it  (an  experiment  I  was  performing  on  AM). The  following
interesting result  was  obtained: if  you  have this  collection  of
angles: 0  degrees, 1 degrees,  2 degrees, 3,  5, 7, 11,  13, 17, 19,
23,..., 179 degrees, then  you can approximate ANY  angle (from 0  to
180 degrees)  to  within 1  degree, as  the  sum of  two such  "prime
angles". If our  technology and/or culture were different, this might
be an important and well-known result.

*********************************************************************

My oral exam is scheduled for May 19, so by definition I will  have a
first draft of my  thesis ready before then. At the  moment, I have a
few  chapters in  rough form. I'm  sending them  to you  now, in case
you'd like to look them  over (partly in case you feel the  energy to
include AM  in the  text you're writing,  but mainly just  to provide
feedback to me).

Regards,
Doug