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 limits 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 an American historian of science. He taught at Harvard University for 60 years, 1942–2002, becoming the first chair of its Department of the History of Science when it was established in 1966, and he mentored notable students including George Basalla, Lorraine Daston, and Allen G. Debus. He was the author of many books on the history of science and, in particular, on Isaac Newton, Benjamin Franklin, and Howard H. Aiken. He made a full English translation of Newton's Principia Mathematica and was the second chief editor of the history of science journal Isis.
The Courant Institute of Mathematical Sciences is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the Stern School of Business and the economics department of the College of Arts and Science.
Ivor Owen Grattan-Guinness was a historian of mathematics and logic.
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.
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.
Marjorie Lee Senechal is an American mathematician and historian of science, the Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College and editor-in-chief of The Mathematical Intelligencer. In mathematics, she is known for her work on tessellations and quasicrystals; she has also studied ancient Parthian electric batteries and published several books about silk.
Peter Jaques Roquette was a German mathematician working in algebraic geometry, algebra, and number theory.
Klara Nahrstedt is the Ralph and Catherine Fisher Professor of Computer Science at the University of Illinois at Urbana–Champaign, and directs the Coordinated Science Laboratory there. Her research concerns multimedia, quality of service, and middleware.
Jürgen Renn is a German historian of science, and since 2022 Founding Director of the Max Planck Institute of Geoanthropology in Jena.
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).
Moritz Epple is a German mathematician and historian of science.
Umberto Bottazzini is an Italian historian of mathematics, writing on the history of mathematics and the foundations of mathematics.
