324 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1959 
Perhaps the most radical step in U.S. mathematical education has 
been taken by the University of Illinois’ experimental high school. 
There, under the guidance of a member of the university’s mathematics 
department, a professor of education, Max Beberman, has introduced 
a completely new mathematics curriculum. It starts with an informal 
axiomatic approach to arithmetic and algebra and proceeds through 
aspects of probability theory, set theory, number theory, complex num- 
bers, mathematical induction, and analytic geometry. The approach 
reflects the rigor, abstractness, and generality of modern mathematics. 
To make room for some of the new concepts, Beberman and his ad- 
visers have had to reduce the amount of time spent drilling on such 
techniques as factoring algebraic expressions. 
So far the experiment has been very stimulating to students—partly, 
of course, because of the very fact that the course isan experiment. In 
the college entrance examinations of 1957, the first group of students 
to complete 4 years of the [linois course made some of the highest 
scores in the nation. 
While 12 other high schools have now experimentally adopted the 
Illinois mathematics curriculum, it is not likely to be widely used for 
some time. The reason is that most high-school teachers have to be 
completely retrained to teach it. With Carnegie Foundation support, 
the University of Illinois has begun to train high-school teachers from 
many States to teach the new curriculum. 
For many years it has been hard for a would-be teacher to learn 
what mathematics he needs to teach any serious high-school course. 
Prof. George Polya of Stanford explains: “The mathematics depart- 
ment [of a university] offers them tough steak they cannot chew, and 
the school of education vapid soup with no meat in it.” The National 
Science Foundation has helped more than 50 colleges and universities 
set up institutes where high-school teachers can study mathematics for 
a summer or even a full academic year. 
OPPORTUNITY AHEAD 
However many mathematicians there may be, there will always be 
a need for more first-rate minds to create new mathematics. This will 
be true of applied mathematics as well as pure mathematics. For ap- 
plied mathematics now presents enough of an intellectual challenge to 
attract even academic men who pride themselves on creating mathe- 
matics for its own sake. One young assistant professor, recently of- 
fered $16,000 by industry, is seriously thinking of abandoning his uni- 
versity career. He explains: “I think that the problems in applied 
mathematics would offer me just as much stimulation as more basic 
research.” 
