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Dear David and Gregory:

	Here are some comments on your draft proposal.

	1. The phrase "special group" is somewhat mysterious.  Better
"Institute for Symbolic Computation in Mathematics" or perhaps
``... in Applied Mathematics'' or even " ... in Mathematics, Physical Science
and Engineering".

	2. The main reason why you can do such an institute better
than other people who might be interested is your ability to understand
mathematical, physical and engineering problems and the mathematical
techniques for their solution.  This includes your contacts with
the mathematicians and physicists who have the problems.

	There are other people who know more about the available computers,
programming languages and symbolic manipulation systems.  However, none
of them are strong enough mathematically to make the bridge in a reliable
way.

	3. Nevertheless, you need such people in the Institute.  If
you could get Fateman, he would be ideal.  However, I think his
problem with SDF funding going away is only a temporary setback,
and while I don't know for sure, I don't think he has any long
term problem at Berkeley.

	4. The main problem with Kahn and DARPA generally is to
convince them that very strong mathematical ability is important to
the project.  You also have to convince them that you have it, but
that can be done by appropriate references.

	Here is a slight revision of your draft.

First draft

Preliminary Proposal

	The Institute for Symbolic Computation in Mathematics, Science and
Engineering will be an interdisciplinary research laboratory associated
with Columbia University.  It will consist of a core group of faculty,
dedicated reseachers and computer facilities and will be open to students,
postdocs and trainees from universities, relevant companies, national labs
and armed services.

	One of the reasons for the urgent need for such an
interdisciplinary group lies in the opportunity to rethink the interaction
between mathematical and computer science achievments.  Recent
breakthroughs in Pure and Applied Mathematics were not adequately
translated into new computer designs, techniques and algorithms.
Similarly the availability of powerful computers did not lead to easier
interaction of many mathematical and physical problems.  One interesting
bottleneck is an important area of numerical methods, whose constructions
do not reflect the greatly enhanced capabilities of computers and computer
programming.  A new basis for interaction between the scientist and the
computer is provided by Symbolic Mathematical Computations (a technical
offshot of the more general concept of Artifical Intelligence).  Symbolic
Comutations are important not only because they eliminate heavy
programming for the scientists, but because they, combined with the powers
of sypercomputers, allow scientists to tackle difficult problems of
Mathematics, Physics and Computer Science.  Among the particular areas,
where research on applications of Symbolic Computations is progressing, we
can name: algebraic function computations, integration in finite terms,
symbolic differential algebra computations, solutions of algebraic
differential equations, power series manipulations, gauge lattice
computations, computational Topology, computations in Algebraic Geometry,
finite elements and grids and VLSI design.

	There are a few existing Computer Algebra systems and a few are
under development now.  The next natural step in the development of an
advanced Symbolic Computational system is the combination of existing
language capabilities with the capabilities of supercomputers.  It is
important to combine the advantages of modern LISP-family languages with
vector-languages and parallel processing to bring about large-scale
symbolic computations.  We speak, for example, about power series
(asymptotic power series) manipulations with 10↑7 terms, about large (of
order 1000 by 1000) determinants with symbolic entries, and about
applications of these symbolic computations to numerical implementation in
the form of numerically stable fast computational schemes.

	The group will try to draw its strength from all interested pure
and applied mathematicians, who have important problems to solve, and from
computer scientists interested in the development of various symbolic
systems.