**Griffith Evans**' father was George William Evans and his mother was Mary Taylor. It was a family in which mathematics played a major role for George Evans was a mathematics teacher at the English and Latin High School in Boston. In fact George Evans had published a number of school level mathematics texts including *Algebra for schools* which had given him a good reputation as a teacher of mathematics.

Griffith attended the school at which his father taught and completed his studies there in 1903 at the age of sixteen. He then entered Harvard University and showed outstanding ability. He was awarded his first degree, the A.B., in 1907 and he had the good fortune to have been taught by several outstanding mathematicians, including Osgood, Coolidge and Bôcher. It was under Bôcher's supervision that Evans began research at Harvard, being awarded his Master's degree in 1908 and his doctorate in 1910. His doctoral dissertation *Volterra's integral equation of the second kind with discontinuous kernel* was published in the *Transactions of the American Mathematical Society* in two parts in 1910 and 1911.

Already before completing his Ph.D., Evans had been employed as an instructor at Harvard in session 1909-10. He won a Sheldon Travelling Fellowship from Harvard which enabled him to spend 1910 to 1912 studying in Europe. Most of this time Evans spent in Rome studying with Volterra but he also had an interest in applied mathematics and so he spent a summer in Berlin studying with Planck.

Evans returned to the United States in 1912. He was now in the happy position of being sought by several of the top universities. In particular the Massachusetts Institute of Technology tried to encourage him to accept an appointment as did the University of California at Berkeley. However he accepted an offer form a third institution, namely the Rice Institute in Houston, Texas. The decision was not made lightly by Evans from which of these institutions to accept a post but he felt that Rice offered him the greatest opportunities.

Appointed as assistant professor in 1912, Evans was promoted to full professor at Rice in 1916. In 1917 he married Isabel Mary John on 20 June and they had three children, all sons. This, of course, was the period of World War I and Evans was commissioned as a captain in the Air Branch of the U.S. Signal Corps during 1918-19. Rider writes in [1]:-

His scientific assignments concerning bomb trajectories and sights, and anti-aircraft defences took him to England, France, and Italy. With the help of Volterra, Evans facilitated the enrolment of U.S. military personnel in special wartime courses in Italian universities.

Evans did a fine job of attracting visiting professors to Rice during his time there, including Menger and Rado. He also made many visits himself including Belgium, France and Italy. During a visit to the University of Minnesota in 1921 he met Fisher who convinced him of the need to develop statistics in the United States.

The University of California at Berkeley continued to try to attract Evans, and he taught there during the summer terms of 1921 and 1928. He turned down an attractive offer from them in 1927 and he also turned down several offers from Harvard. However, in 1933 the University of California at Berkeley made him an offer which was so attractive that he accepted it.

Basically he was given the explicit mandate to revitalise and improve the mathematics department and set up a programme for graduate studies. In the summer of 1934 Evans left Rice and began his task at Berkeley as chairman of the mathematics department. The article [3] shows why and how Evans was successful in building a world class centre there. Although at first he favoured appointing unemployed Americans, he soon changed to reap the benefits from the availability of mathematicians expelled from Europe and also from the changes to American science policy that resulted from World War II. In particular he appointed Lewy, Neyman and Tarski among fifteen appointments he made from 1934 to 1949.

During World War II Evans again undertook work related to the war effort. As well as serving on the Applied Mathematics Panel of the National Defense Research Council, he also acted as a consultant on the design of guns for the Office of the Chief of Ordnance in Aberdeen, Maryland. For his war work he was awarded the Distinguished Assistance Award of the War Department and the Presidential Certificate of Merit.

Evans was chairmen of the mathematics department at Berkeley for fifteen years, ending his term in 1949. He retired in 1955 but lived to see the new mathematics building at Berkeley named Evans Hall in 1971.

His work dealt with potential theory, functional analysis, integral equations and the problem of minimal surfaces, the Plateau Problem. It was built on the foundations provided by Lebesgue, Volterra, Fréchet and Poincaré. Zund writes in [4] of his contributions to potential theory:-

He pioneered the use of general notions of integration and measure theory in this area, and his interests lay in application and development of new techniques rather than in deep structural theorems. These include the theories of harmonic and superharmonic functions, the Poisson-Stieltjes integral, the logarithmic potential, the discovery of the precursor of Sobolev spaces in1920 ...,generalisations of Heni Poincaré's "sweeping out" process, the theory of capacity, and finally an ingenious theory of multiple-valued harmonic functions(1947,1951).

In fact the work referred to here on multiple-valued harmonic functions was a generalisation of his own work on the problem of minimal surfaces which he published on from the 1920s. He had proved, among many other results, that among the surfaces with a fixed boundary, there is a surface of minimal electric capacity.

Evans also wrote on mathematical economics, in particular on monopolies, competition and cooperation, taxation, profit, prices, etc. Rider writes in [1]:-

Evans formulated a model of the economy as a whole and posed the problem of defining an aggregate variable in terms of microeconomics components. His1924paper on the dynamics of monopoly, which introduced time derivatives in demand relations, was recognised as the beginning of dynamic theories of economics.

Among the important texts he wrote were *Functional equations and their applications* (1918), *The logarithmic potential* (1927), and *Mathematical Introduction to economics* (1930).

Evans received many honours for his mathematical contribution. He was vice-president of the American Mathematical Society in 1924-26 and vice-president of the Mathematical Association of America in 1932. He served as vice-president for mathematics of the American Association for the Advancement of Science in 1931-32 and vice-president for economics of the American Association for the Advancement of Science in 1936-37. He was elected to the National Academy of Sciences in 1933 and was president of the American Mathematical Society in 1939-40.

**Article by:** *J J O'Connor* and *E F Robertson*

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