Mathematical Scientists Who Worked in Cross-disciplines

Computer Science, Information Science and Electronics
  • A.N. Kolmogorov (1903-1987). One of the founders of modern probability theory, and leader of the dominant Russian probability school which included A.M. Yaglom, B.V. Gnedenko, among others. He also made some important contributions to statistics and ergodic theory, including the theory for Kolmogorov-Smirnov test and Kolmogorov-Sinai entropy. He is equally influential for work in turbulence (such as K-41), and for developing algorithmic complexity theory.
  • Norbert Wiener (1894-1964). Made fundamental contributions in both pure and applied mathematics and is an excellent example of interdisciplinary and multidisciplinary researcher. What he started in multidisciplinary work in cognitive science and cybenetics 60 years ago remain as important and alive today as ever. His work in probability theory is reviewed nicely by G Kallianpur .
  • John Von Neumann (1903-1957). He was a Hungarian American mathematician who made many contributions in the boundaries of statistics and other disciplines, such as quantum mechanics, ergodic theory, computer science, and stochastic simulation. His development of game theory (with Oskar Morgenstern) was particularly noteworthy since it inspired A. Wald and L.J Savage to develop a modern foundation of statistics.
  • Alfred Renyi (20 March 1921 ?1 February 1970). He was a Hungarian mathematician who made contributions in combinatorics, graph theory, and probability theory. The concepts he developed such as Renyi entropies, the Erdoss-Renyi model for random graphs are still interesting today.
  • Solomon Kullback (1904-1997). Fame in statistics from Kullback-Leibler divergence criterion, he developed information theory as a general approach to statistics in his 1959 book. (The famous AIC and other model selection criteria were developed later on.) he applied statistics to cryptanalysis and became one of the top three cryptanalysts.
  • Johann K. A. Radon (1887-1956). He was an Austrian mathematician. His doctoral dissertation was on calculus of variations (in 1910, at the University of Vienna). Radon is known for a number of lasting contributions, such as his part in the Radon-Nikodym theorem, the Radon measure concept of measure as linear functional. He is especially known for the Radon transform, in integral geometry, based on integration over hyperplanes, which has important application to tomography for scanners (in tomographic reconstruction), which are widely used today in medical imaging. Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz, Austria is named after him.
  • Lai-Sang Young, born in 1952 in Hong Kong. She emigrated to the United States to pursue higher education in mathematics at the University of Wisconsin, Madison (B.A., 1973) and the University of California, Berkeley (M.S., 1976; Ph.D., 1978). She published her first paper as a graduate student in 1977, and conducted doctoral research under the direction of Robert Bowen; resulting a dissertation, entitled Entropy and Symbolic Dynamics of Certain Smooth Systems. Her research and exposition on the statistical aspects of dynamical systems have earned her wide recognitions, such as 2005 AWM Noether award for Women in Mathematics.
  • Glenn Shafer, who developed A.P. Dempster's theory of generalized Bayesian inference to new heights, now known as Dempster-Shafer theory, widely used in artificial intelligence and imprecise reasonings.Theory of Capacity.
  • L.A. Zadeh. Fuzzy logic and fuzzy reasonings.
  • Ulf Grenander (1923-), founder of the Brown Pattern Theory School. He was also fundamental in developing modern time series, co-author with Murray Rosenblatt of a well-known text. His PhD thesis was on inference of stochatic processes, which he developed further for many years, resulting in his milestone book, Abstract Inference.

    Social Studies, Economics

  • Vilfredo Pareto (July 15, 1848 ?August 19, 1923) or Fritz Wilfried Pareto. He discovered the famous 80-20 rule or the so-called Pareto principle, and generalised further to the concept of a Pareto distribution.
  • Corrado Gini (May 23, 1884 - March 13, 1965). Italian statistician, demographer and sociologist who developed the Gini coefficient, a measure of the income inequality in a society.
  • Eugen Slutsky. Slutsky theorem fame in statistics, but he made important contributions to economics such as his famous theory of the summation of random causes as a source of cyclical processes, which also gave rise to the moving averaging process as a general time series model.
  • John Maynard Keynes (1883-1946) Author of Treatise on Probability in 1921, developer of Keynesian economics,authored General Theory of Employment, Interest and Money in 1936. Keynes's theory has been developed in a school, called "neoclassical synthesis".
  • Herbet A Simon (1916-2001), who contributed to causal inference and proposed a skew-distribution model, a stochastic mechanism to explain the power-law, but he was truly an interdisciplinary researcher, pioneering in several fields, including decision making with incomplete information in behavioral economics, proposing the two important concepts of bounded rationality and satisficing.
  • Benoit B. Mandelbrot (1924-). Mandelbrot was born in Warsaw and then moved France, in 1945-47 attended the Ecole Polytechnique, where he studied under Gaston Julia and Paul Levy. Then he studied aeronautics at California Institute of Technology for two years, and finally obtained a Ph.D. in Mathematical Sciences at the University of Paris in 1952. Mandelbrot worked on many problems including applied fields such as information theory, economics, and fluid dynamics, but his focus on two key themes, fat tails and self-similar structure, is constant. Both concepts are, of course, important in statistics, such as time series analysis (long range dependece, extreme value theory) and stochastic process (e.g. L�vy process). In 1975, Mandelbrot coined the term fractal, and in 1982 his book The Fractal Geometry of Nature was published.

    Biological Sciences (Evolution, Genetics, Ecology, neural science)

  • R.A. Fisher (1890-1962). His daily association with scientists and data at the Rothamsted forced him to develop modern statistical techniques for research workers, such as design of experiments to optimize data collection, and analysis of variance as a general technique for analyzing experimental data. As the de facto founder of modern mathematical statistics, he was euqally impressive in his fundamental work in genetics. he is one of the founders of the neo-Darwinian modern evolutionary synthesis along with Sewall Wright, and J.B.S. Haldane. Fisher's book The Genetical Theory of Natural Selection is still widely read today.
  • Gustave Malecot (1911-1998). Mal�cot is considered as one of the founders of modern theoretical population genetics, after Sewall Wright, R.A. Fisher, and J.B.S. Haldane. But because of his writing was in abstract mathematical style and was published in obscure French journals, his work was not widely recognized, except by a few such as Oscar Kempthorne (for example, his 1957 textbook, An Introduction to Genetics Statistics, Wiley, made extensive reference of Malecot's work). Malecot obtained a degree in mathematics from the Ecole Normale Superieure, Paris. He then went on to get a PhD from George Darmois, by clarifying and developing in rigorous probability formulation of R.A. Fisher's 1918 article.
  • J.F.C. Kingman. Widely known for his work on probability and stochastic processes such as the Kingman subadditive ergodic theorem. He has had a long-term side interest in population genetics. In 1982, he published three papers which laid the foundation for modern work on coalescent trees of genes.
  • Pat. A. P. Moran (July 14, 1917 - September 19, 1988). Contributions include dam theory, stochastic evolutionary theory (such as Moran's infinitely many alleles model), and geometrical probability. His statistical study of the Canadian lynx cycle data is particularly noteworthy in time series analysis, and his 1950 biometrics paper "Some remarks on animal population dynamics" raised interesting nonlinear dynamics issues. During the 70s and 80s, the mechanisms which produce limit cycle or chaos (aperiodic, apparrent random behavior), have finally been understood, see a review by Robert M. May.
  • Motoo Kimura (1924-1994). A Japanese biologist who introduced the neutral theory of molecular evolution, who was among the most influential theoretical population geneticists. He had made innovative use of stochastic processes tools including diffusion equations for genetics and other mathematical biology problems.
  • Rick Durret. In his own words, my favorite research topics are stochastic spatial models that arise from questions in ecology, and use of probability problems that arise from genetics. His publications include topics in evolutionaty genetics and stochastic spatial models. His collaborations with Simon A. Levin were especially fruitful, such as this one, and his helpful expository article, on-line tutorial.
  • Simon Tavare. Research interests include stochastic computation, population genetics, and statistical genomics.
  • Richard Cowan. Formerly a researcher at CSIRO and professor of statistics at the University of Hong Kong . He did much work on statistics for cell biology, molecular biology and biochemistry, among other interests.
  • Andrei Yu Yakovlev (1944-2008). Andrei Yakovlev received his Ph.D. degree in biology from the Institute of Physiology, Academy of Sciences, Russia, in 1973, and a Ph.D. degree in mathematics from Moscow State University, in 1981. His contributions include work in cell biology, branching processes, and microarray data analysis.
  • Keith Worsley (1951-2009). Mathematical statistician, applications of statistics reasonings and random field to human brain mapping.

    Geophysics, Meteorology and Turbulence

  • Edward N. Lorenz (1917-2008). American mathematician and well-known meteorologist. He made many fundamental and deep contributions in meterology, such as The nature and theory of the general circulation of the atmosphere (1967), and his life-time interest and study of predictability. He introduced principal component analysis (independent of Hotelling), called empirical orthogonal functions , which is widely used in meterology. He discovered the strange attractor notion and coined the term butterfly effect, which is rooted in his now famous 1963 paper, a story recounted in his 1993 popular book, The Essence of Chaos.
  • Akiva Moiseevich Yaglom (1921-2007), affliated with the Institute of Atmospheric Physics, Russian Academy of Sciences, and since 1992 with MIT. He made many contributions to the mathematical theory of turbulence, including the definitive two-volume book with A.S. Monin, Statistical Fluid Mechanics, Mechanics of Turbulence. He made fundamental contributions to stochastic processes, especially stationary processes, random fields and information theory. He wrote the critically claimed two-volume books Correlation Theory for Stationary and Related Random Functions, Springer 1987. He is a student of A.N. Kolmogorov, and his students included China's Jiang Zepei (Chiang Tse-pei, 江泽培).
  • L. S. Gandin, fundamental in introducing modern statistics such as spatial statistics into modeling meteorological fields, as in data assimilation, to be used with simulating global climate models. Publications include the famous Objective analysis of meteorological fields, 1965, and Averaging of Meteorological Fields, Springer 1997.
  • Georges Matheron (1930-2000). Known for contributions to kriging, co-founder (together with Jean Serra) of mathematical morphology.

    Chemical Sciences, Quality Control, and Measurement

  • W. J. Youden (1900-1971), trained as a chemist (PhD), but went on to have a career in applied statistics. From 1924 to 1948, He was on the staff of Boyce Thompson Institute for Plant Research in Yonkers, New York, where developed his famous Youden square (1937, use of incomplete block replications in estimating tobacco-mosaic virus, Contributions from Boyce Thompson Institute, 9, 50-57, in which he proposed a special BIBD type) as a generalization of Latin square design. Then he was recruited to work at National Bureau of Standards, Wasington DC (now it evolves as National Institute of Standards and Technology, Gaithersburg, Maryland) where he had a highly successful career in promoting and expounding statistics in chemistry and quality control. He is also known for Youden index (1955) and Youden plot (1959).
  • John Mandel (1914-2007). He was trained as a chemist (BA, MS), later on get a PhD in mathematical statistics from the Eindhoven University of Technology in the Netherlands. An expert in interlaboratory studies and statistical applications in quality control and measurements.
  • Herman O.A. Wold (1908-1992). A Swedish statistician (student of Harald Cramer), known for contribution to time series analysis, such as fame in Wold decomposition. He is also known for the Cramer-Wold theorem. His later interest turned to modeling relationships in econometrics and promoted the use of partial least square type "soft" modeling in chemometrics. Svante Wold, one of his three children, collaborated with him and continued his work on chemometrics modeling.

    Copyright: Z.Q. John Lu, 2008.

    References

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