Related papers: Problems with Popper
J. Hadamard's ideas about the correct formulation of the problems of mathematical physics have been analyzed. In this connection various interpretations of the directly related Banach theorem about the inverse operator has been touched. The…
The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the…
Philosophical analyses of causation take many forms but one major difficulty they all aim to address is that of the spatio-temporal continuity between causes and their effects. Bertrand Russell in 1913 brought the problem to its most…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
Kolmogorov's Calculus of Problems is an interpretation of Heyting's intuitionistic propositional calculus published by A.N. Kolmogorov in 1932. Unlike Heyting's intended interpretation of this calculus, Kolmogorov's interpretation does not…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new…
The question of the authorship of Shakespeare's plays has long been debated. The two leading contenders are W. Shakspere (1564-1616) and Edward de Vere the 13th Earl of Oxford (1550-1604). Here I note that Shakespeare's references to…
Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the…
The parts contributed by the author in recent discussions with several physicists and mathematicians are reviewed, as they have been occasioned by the 2006 book "The Trouble with Physics", of Lee Smolin. Some of the issues addressed are the…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
In 1693, Isaac Newton answered a query from Samuel Pepys about a problem involving dice. Newton's analysis is discussed and attention is drawn to an error he made.
John Mather is a great scholar who was dedicated to mathematics in his whole life. His works in mathematics can be characterized as original and foundational. He laid out the foundation of singularity theory while he was a graduate student.…
The paper (in French) presents a survey of Hilbert's Epsilon operator focusing on the intensional aspects of its semantics. It comments on some epistemological problems, from Albert Lautman in the 1930s to John Bell, Grigori Mints, Barry…
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
This essay offers a brief biography of Paul Erd\H{o}s and summarizes his approach to mathematics. This is further elucidated by a discussion of Erd\H{o}s' simple proof of Bertrand's Postulate.
E731 in the Enestrom index. Originally published as "Solutio problematis ob singularia calculi artificia memorabilis", Memoires de l'academie des sciences de St-Petersbourg 2 (1810), 3-9. For $z$ the distance from the origin, and $v$ a…
This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many…
The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of Analysis and Partial Differential Equations in…