NEW USES OF THE ABSTRACT—BOEHM BPA 
a fast computer takes a full hour to test each n. The fact that a ma- 
chine has failed to find an exception does not, of course, prove the 
Fermat theorem, although it does perhaps add a measure of assur- 
ance that the theorem is true. 
But it is possible for a computer to produce a mathematical proof. 
Allen Newell of Rand Corp. and Herbert A. Simon of Carnegie Tech 
have worked out a program of instructions that tells a high-speed 
computer how to work out proofs of some elementary theorems in 
mathematical logic contained in “Principia Mathematica,” a three- 
volume treatise by Alfred North Whitehead and Bertrand Russell. 
The Newell and Simon program is based on heuristic thinking—the 
kind of hunch-and-analogy approach that a creative human mind 
uses to simplify complicated problems. The computer is supplied 
with some basic axioms, and it stores away all theorems it has previ- 
ously proved. When it is told to prove an unfamiliar theorem, it first 
‘ries to draw analogies and comparisons with the theorems it already 
knows. In many cases the computer produces a logical proof within 
a few minutes; in others it fails to produce any proof at all. It 
would conceivably be possible to program a computer to solve 
theorems with an algorithmic approach, a sure-fire, methodical pro- 
cedure for exhausting all possibilities. But such a program might 
take years for the fastest computer to carry out. 
Although most mathematicians scoff at the idea, Newell and Simon 
are confident that heuristic programing will soon enable computers to 
do truly creative mathematical work. They guess that within 10 
years a computer will discover and prove an important mathematical 
theorem that never occurred to any human mathematician. 
HELP WANTED 
But computers are not going to put mathematicians out of work. 
Quite to the contrary, computers have opened up so many new 
applications for mathematics that industrial job opportunities for 
mathematicians have more than doubled in the last five years. About 
one-fourth of the 250 people who are getting Ph. D.’s in mathematics 
this year are going into industry—chiefly the aircraft, electronics, 
communications, and petroleum companies. In 1946 only about one 
in nine Ph. D.’s took jobs in industry. 
While most companies prefer mathematicians who have also had 
considerable background in physics or engineering, many companies 
are also eager to hire men who have concentrated on pure mathe- 
matics. Starting pay for a good young mathematician with a fresh 
Ph. D. now averages close to $10,000 a year in the aircraft industry, 
about double that of 1950 (and about double today’s starting pay in 
universities). 
