Oliver Dimon Kellogg

Oliver Kellogg studied as an undergraduate at Princeton University. There he attended lectures by Fine who fired his interest in mathematics. After receiving his A.B. in 1899, Kellogg continued his studies for a Master's Degree at Princeton. He was awarded the Master's Degree in 1900 and received a Fellowship to allow him to study in Europe.

Kellogg spent a year at the University of Berlin, then moved to Göttingen to work for his doctorate. He attended lectures by Hilbert who suggested he undertake research on the Dirichlet problem for plane regions bounded by a finite number of plane curves which met at points where the boundary was not differentiable. Fredholm had just published a major work on the Dirichlet problem but Fredholm's methods did not apply to the regions which Hilbert suggested Kellogg investigate.

In 1902 Kellogg published his first paper giving a direct proof of Fredholm's inversion formula. In January of the following year he received his doctorate for his dissertation Zur Theorie der Integralgleichungen und des Dirichlet'schen Prinzips on the Dirichlet problem but he remained in Germany to the end of the academic year, returning to the United States to take up the post of instructor in mathematics at Princeton. During these years he published two further papers which developed from the work of his thesis.

However Kellogg soon became less than happy with these papers. Partly he had failed to answer the questions Hilbert had asked him to solve though this was understandable since they were much harder than Hilbert had realised. Secondly some of Kellogg's results were incomplete and others were incorrect. Again it is hard to criticise him too much over this since very similar errors were later made by both Hilbert and Poincaré.

Kellogg was appointed to the University of Missouri in 1905 where, despite a heavy teaching and administrative load he was able to publish impressive papers on potential theory. In 1912 he published the important work Harmonic functions and Green's integral.

Although he would return to potential theory, Kellogg next published a number of papers on sets of real orthogonal functions. However his work was disrupted by World War I when he was assigned as scientific advisor to the United States Coast Guard Academy at New London, Connecticut. At the end of the war he was appointed to Harvard University.

In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a_n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1. In fact the answer is given by

a_n+1= a_n(a_n+ 1) where a₁= 1.

Kellogg also wrote a number of papers on the existence of certain sets of functions in analysis as well as generalisations of polynomials due to Sergi Bernstein.

Kellogg continued to work at Harvard until his death which resulted from a heart attack which he suffered while climbing.

Birkhoff writes in [1]:-

His quick, generous nature and unusual charm of personality were united with a versatile and original mind. The full story of Kellogg's many successful efforts to help others would be an extraordinary one ... in order to judge his mathematical achievements, it is necessary not only to consider his published work but to take into account his modesty and his readiness to share his nascent ideas with others.

Texto original por: J J O'Connor and E F Robertson

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JOC/EFR November 1997	School of Mathematics and Statistics University of St Andrews, Scotland
The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Kellogg.htm