Mathematician and statistician (1905–2000)For other people named Henry Mann, see Henry Mann (disambiguation).

Henry Berthold Mann (27 October 1905, Vienna – 1 February 2000, Tucson) was a professor of mathematics and statistics at Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") U-statistic of nonparametric statistics. Mann published the first mathematical book on the design of experiments: Mann (1949).

Contents

• 1 Early life of a number theorist
• 2 Statistics
• 3 Later life
• 4 Publications
• 5 References

Early life of a number theorist

Born in Vienna, Austria-Hungary, to a Jewish family, Mann earned his Ph.D. degree in mathematics in 1935 from the University of Vienna under the supervision of Philipp Furtwängler. Mann immigrated to the United States in 1938, and lived in New York, supporting himself by tutoring students.

In additive number theory, Mann proved the Schnirelmann–Landau conjecture on the asymptotic density of sumsets in 1942. By doing so he established Mann's theorem and earned the 1946 Cole Prize.

Statistics

In 1942 the Carnegie Foundation awarded Mann a fellowship to learn statistics while *isting the operations research group of Harold Hotelling at Columbia University. His group also supported Abraham Wald, and Wald and Mann collaborated on several papers. In statistics, Mann is known for the ("Mann–Whitney") U-statistic and its *ociated hypothesis test for nonparametric statistics. Collaborating with Wald, Mann developed the Mann–Wald theorem of asymptotic statistics and econometrics.

Mann wrote the first mathematical book on the design of experiments Mann (1949), whose principles allowed later statisticians to design and to *yze customized experiments. Like contemporary "self-help" and "how to" books, the earlier books gave easy-to-follow examples but little theory beyond exhortations to follow three principles of Ronald A. Fisher—to "replicate", to "establish control" (for example with blocking), and to "randomize" (*ignment of treatments to units). Earlier books provided useful examples of designed experiments along with the design's *ysis of variance, but no basis for constructing new designs for new problems, according to Johnson (1951).

According to Denis Conniffe:

Ronald A. Fisher was "interested in application and in the popularizationof statistical methods and his early book Statistical Methods for Research Workers, published in 1925, went through many editions andmotivated and influenced the practical use of statistics in many fields ofstudy. His Design of Experiments (1935) statistical technique and application. In that book heemphasized examples and how:to:design experiments systematically froma statistical point of view. The mathematical justification of the methodsdescribed was not stressed and, indeed, proofs were often barely sketchedor omitted altogether ..., a fact which led H.:B.:Mann to fill the gaps with a rigorous mathematical treatment in his well known treatise, Mann (1949)."

Later life

In 1946 Mann returned to Ohio State University, where he served as a professor mathematics until his retirement in 1964. Mann then became a professor at the U.S. Army's Mathematics Research Center at the University of Wisconsin–Madison 1964–1971. Mann was professor at the University of Arizona from 1971–1975. His doctoral students include George Marsaglia and William Yslas Vélez.

Publications

• Mann, Henry B. (1942). "A proof of the fundamental theorem on the density of sums of sets of positive integers". Annals of Mathematics. Second Series. Annals of Mathematics. 43 (3): 523–527. doi:10.2307/1968807. ISSN:0003-486X. JSTOR:1968807. MR:0006748.
• Mann, H. B.; Whitney, D. R. (1947). "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other". Annals of Mathematical Statistics. 18 (1): 50–60. doi:10.1214/aoms/1177730491. MR:0022058. Zbl:0041.26103.
• Mann, H.:B. (1949). *ysis and design of experiments: *ysis of variance and *ysis:of:variance designs. New:York,:N.:Y.: Dover Publications,:Inc. pp.:x+195. MR:0032177.
• Mann, Henry B (1955). Introduction to algebraic number theory (With a chapter by Marshall:Hall,:Jr.). Columbus, Ohio: The Ohio State University Press. pp.:vii+168. MR:0072174.
• Mann, Henry B. (1976). Addition theorems: The Addition theorems of group:theory and number:theory (Corrected reprint of:1965 Wiley:ed.). Huntington, New York: Robert:E. Krieger Publishing Company. ISBN:0-88275-418-1. MR:0424744.

References