Sr) ANNUAL REPORT SMITHSONIAN INSTITUTION, 1959 
tion, They have laid foundations for Operations Research techniques 
that businessmen use to schedule production and distribution. They 
have created an elaborate theory of “information” that enables com- 
munications engineers to evaluate precisely telephone, radio, and tele- 
vision circuits. They have grappled with the complexities of human 
behavior through game theory, which applies to military and business 
strategy alike. They have analyzed the design of automatic controls 
for such complicated systems as factory production lines and super- 
sonic aircraft. Now they are ready to solve many problems of space 
travel, from guidance and navigation to flight dynamics of missiles 
beyond the earth’s atmosphere. 
Mathematicians have barely begun to turn their attention to the 
biological and social sciences, yet these once purely descriptive 
sciences are already taking on a new flavor of mathematical pre- 
cision. Biologists are starting to apply information theory to inher- 
itance. Sociologists are using sophisticated modern statistics to 
control their sampling. The bond between mathematics and the life 
sciences has been strengthened by the emergence of a whole group 
of applied mathematics specialties, such as biometrics, psychometrics, 
and econometrics. 
Now that they have electronic computers, mathematicians are solv- 
ing problems they would not have dared tackle a few years ago. In 
a matter of minutes they can get an answer that previously would 
have required months or even years of calculation. In designing 
computers and programing them to carry out instructions, further- 
more, mathematicians have had to develop new techniques. While 
computers have as yet contributed little to pure mathematical theory, 
they have been used to test certain relationships among numbers. 
It now seems possible that a computer someday will discover and 
prove a brand-new mathematical theorem. 
The unprecedented growth of U.S. mathematics, pure and applied, 
has caused an acute shortage of good mathematicians. Supplying 
this demand is a knotty problem. Mathematicians need more train- 
ing than ever before; yet they cannot afford to spend more years in 
school, for mathematicians are generally most creative when very 
young. A whole new concept of mathematical education, starting as 
early as the ninth grade, may offer the only escape from this dilemma. 
CONVENIENCE OF THE OUTLANDISH 
The applied mathematician must be a creative man. For applied 
mathematics is more than mere problem solving. Its primary goal 
is finding new mathematical approaches applicable to a wide range 
of problems. The same differential equation, for example, may de- 
scribe the scattering of neutrons by atomic nuclei and the propaga- 
