Related papers: Joseph Carter Corbin: Arkansas's "Profound Mathema…
A short essay on the life and mathematical heritage of Coble. A substantially edited version will be part of the series of biographical memoirs of past members of the National Academy of Sciences. Version 2: minor changes. Version 3. Typo…
This contribution to the book in honour of J.S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered appropriate to share with…
The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…
It is with pleasure and pride that I introduce this special section in honor of Ingram Olkin. This tribute is especially fitting because, among the many profound and far-reaching contributions that he has made to our profession, Ingram…
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.
An invited plenary given at the founding meeting of the Southern African Association for Research in Mathematics and Science Education in 1992.
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
This article is firstly a historic review of the theory of Riemann-Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert's 21st problem and Plemelj's work associated with it. The secondary…
The traditional calculus-based introduction to statistical inference consists of a semester of probability followed by a semester of frequentist inference. Cobb (2015) challenges the statistical education community to rethink the…
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties.…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…
The authors discuss the role of controversy in mathematics as a preface to two opposing articles on computational complexity theory: "Some basic information on information-based complexity theory" by Beresford Parlett [math.NA/9201266] and…
The emergence of Boris Struminsky's January, 1965 paper with a footnote that introduced a new quark quantum number now known as color caused a response [arXiv:0908.2772] that is seen, perhaps contrary to what it was intended to convey, to…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
Roger Carter (1934--2022) was a very well known mathematician working in algebra, representation theory and Lie theory. He spent most of his mathematical career in Warwick. Roger was a great communicator of mathematics: the clarity,…
These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has…
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…