322 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1959 
Still, a great deal of industrial mathematics is done by physicists 
and engineers who have switched to mathematics after graduation. 
And there is also room for people with bachelor’s and master’s de- 
grees, particularly in programing computers to perform calculations. 
Different companies use mathematicians in different ways. Some 
incorporate them in research teams along with engineers, physicists, 
metallurgists, and other scientists. But a growing number have set 
up special mathematics groups, which carry out their own research 
projects and also do a strictly limited amount of problem solving 
for other scientific departments. 
The oldest and most illustrious industrial mathematics department 
was set up in 1930 by Bell Telephone Laboratories. It started with 
six or eight professional mathematicians and grew slowly until after 
the war. Then in 10 years it doubled in size. Today the depart- 
ment has about 30 professional mathematicians, half of them with 
Ph. D.’s in mathematics, the rest with Ph. D.’s in other sciences. The 
department has made outstanding contributions to mathematics. 
Notable is information theory, which was developed during and after 
the war by Claude Shannon as a mathematical model for language 
and its communication. 
CRISIS IN EDUCATION 
The demand for mathematicians of every sort is rapidly outstrip- 
ping the capacity of the U.S. educational system. Swelling enroll- 
ments in mathematics courses are already beginning to tax college 
and university mathematics departments. At Princeton, for 
example, the mathematics majors have for years numbered only 5 to 
10, but 19 members of last year’s junior class elected to major in 
mathematics. To complicate matters further, the good college and 
university departments no longer require their professors to teach 
12 to 15 hours a week. So that the teachers can also do research, the 
average classroom time has been reduced to 9 hours in most schools, 
and to less than 6 in some of the best universities. Yet the serious 
mathematics student now needs more training than ever before. If 
he wants a good job in industry or in a top university, he must have 
a doctor’s degree; and if he wants to excel in research, he should have 
a year or two of postdoctoral study. 
There is a great deal to be mastered in modern mathematics, but 
surprisingly it is relatively easier to learn than most of the mathe- 
matics traditionally taught in high school and college, despite its 
abstractness and complexity. One change that would obviously help 
would be to start teaching the important modern concepts and tech- 
niques earlier. The way mathematics is taught now, complains John 
G. Kemeny of Dartmouth, “it is the only subject you can study for 14 
