Joseph Warren Dauben (born 29 December 1944, Santa Monica) is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York. [1] He obtained his PhD from Harvard University.
His fields of expertise are the history of science, the history of mathematics, the Scientific Revolution, the sociology of science, intellectual history, the 17th and 18th centuries, the history of Chinese science, and the history of botany.
Dauben is a 1980 Guggenheim fellow. [2]
He is a fellow of the American Association for the Advancement of Science, and a fellow of the New York Academy of Sciences (since 1982). [3]
Dauben is an elected member (1991) of the International Academy of the History of Science [4] and an elected foreign member (2001) of German Academy of Sciences Leopoldina. [5]
In 1985–1994 Dauben served as the chair of the Executive Committee of the International Commission on the History of Mathematics. [6]
Dauben delivered an invited lecture at the 1998 International Congress of Mathematicians in Berlin on Karl Marx's mathematical work. [7]
The creator of non-standard analysis, Abraham Robinson was the subject of Dauben's 1995 book Abraham Robinson. It was reviewed positively by Moshé Machover, but the review noted that it avoids discussing any of Robinson's negative aspects, and "in this respect [the book] borders on the hagiographic, painting a portrait without warts." [8]
In 2002 Dauben became an honorary member of the Institute for History of Natural Science of the Chinese Academy of Sciences. [3] [9]
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers.
Abraham Robinson was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics.
The German National Academy of Sciences Leopoldina, short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the Academia Naturae Curiosorum until 1687 when Emperor Leopold I raised it to an academy and named it after himself. It was since known under the German name Deutsche Akademie der Naturforscher Leopoldina until 2007, when it was declared to be Germany's National Academy of Sciences.
I. Bernard Cohen was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton and Benjamin Franklin.
Ivor Owen Grattan-Guinness was a historian of mathematics and logic.
John Robison FRSE was a British physicist and mathematician. He was a professor of natural philosophy at the University of Edinburgh.
David Neil Corfield is a British philosopher specializing in philosophy of mathematics and philosophy of psychology. He is Senior Lecturer in Philosophy at the University of Kent.
George Jiří Klir was a Czech-American computer scientist and professor of systems sciences at Binghamton University in Binghamton, New York.
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below.
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover.
Revolutions in Mathematics is a 1992 collection of essays in the history and philosophy of mathematics.
Donald Angus Gillies is a British philosopher and historian of science and mathematics. He is an Emeritus Professor in the Department of Science and Technology Studies at University College London.
Adolph-Andrei Pavlovich Yushkevich was a Soviet historian of mathematics, leading expert in medieval mathematics of the East and the work of Leonhard Euler. He is a winner of George Sarton Medal by the History of Science Society for a lifetime of scholarly achievement.
Donald Lyman Burkholder was an American mathematician known for his contributions to probability theory, particularly the theory of martingales. The Burkholder–Davis–Gundy inequality is co-named after him. Burkholder spent most of his professional career as a professor in the Department of Mathematics of the University of Illinois at Urbana-Champaign. After his retirement in 1998, Donald Burkholder remained a professor emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign. He was a member of the U.S. National Academy of Sciences and a fellow of the American Mathematical Society.
Wilhelmus Anthonius Josephus Luxemburg was a Dutch American mathematician who was a professor of mathematics at the California Institute of Technology.
Christoph J. Scriba was a German historian of mathematics.
Hans-Ludwig Wußing was a German historian of mathematics and science.
Peter Jaques Roquette was a German mathematician working in algebraic geometry, algebra, and number theory.
Jürgen Renn is a German historian of science, and since 1994 Director at the Max Planck Institute for the History of Science in Berlin.
Barbara I. Wohlmuth is a German mathematician specializing in the numerical solution of partial differential equations. She holds the chair of numerical mathematics at the Technical University of Munich (TUM).
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