1942, the middle of World War II, and the greatest increase occurred in 1948, the middle of the relatively peaceful years between that war and the Korean one.

Forty-one different nations representing all the con- tinents were in the sample. Of these, six accounted for nearly 70 percent of the total. In rank order, these were the United States, USSR, Italy, France, Germany, and England. Each of these nations held the same rank order position year by year over the time period.

Since larger populations presumably have a greater chance of producing more mathematicians, and thereby more mathematics, mathematical production was standardized by population size. Using the stan- dardized mathematical production index, the leading nations in rank order were the following: Switzerland, Belgium, Norway, Israel, Netherlands, and Hungary.

Research mathematics was published in many dif- ferent languages including Esperanto, Gaelic, Dutch, and Hebrew. Of the 26 languages represented in this study, however, five account for nearly 92 percent of the total publications. In order, these are English (43 percent), French (16 percent), Russian (13 percent), German (11 percent), and Italian (8 percent). These five languages held the same relative positions through time. All the Scandinavian languages com- bined accounted for only 0.5 percent of the total, and all the Asian languages combined for only 0.6 percent. Publications in Japan during the 1940s were predom- inately in German, and during the 1950s in English.

The five specialities in order of frequency of publi-

cation were analysis (52 percent), geometry (20 per- cent), algebra (14 percent), number theory (9 percent), and topology (7 percent). This rank order was main- tained through time. When the percentage of publi- cation by speciality within the United States was com- pared to the percentage distribution of mathematicians by speciality and to the number of doctoral degrees awarded by mathematical speciality, both number the- orists and analysts published more than would be ex- pected, whereas geometers and algebraists published less.

Nations seemed to have speciality predilections. For example, the United States published more in to- pology and less in geometry than would be expected. Italy overpublished in geometry, and England and Germany in number theory. The Soviet Union pub- lished more in analysis and, like the United States, little in geometry.

Mathematical publication has been mostly a solitary activity, the work of one person. Indeed, single author papers accounted for over 92 percent of the published work. However, during this period there was a statis- tically significant trend toward joint authorship. The United States and Japan were especially likely to pub- lish coauthored papers, and those papers were most likely to be in English, although no particular speciality was more social than any of the others.

Department of Sociology Ohio State University Columbus, Ohio 43210

A N e w V i e w of Two Old Friends

Until a few years ago one understood complex func- tions only by studying their Laurent series or their Weierstrass factorizations. A "picture" of the function (Its modulus? Its real and imaginary parts?) seemed i r re levant . . , besides, pictures were too hard to draw.

The computer (and plotter) have changed all that. Pictures provide a means for retrieving the essential facts about a function. How often have you seen a

student draw the graph of e x to recall what happens for large or small values? With the ability to plot by computer, perhaps we ought to provide students of Complex Function Theory with the same help we pro- vide students of Calculus.

Below are the graphs (of the modulus) of two old friends from a first course in complex functions. Rec- ognize them? (Answer on page 80.)

7 8 THE MATHEMATICAL INTELLIGENCER VOL. 6, NO. 1, 1984