Related papers: Editor's column (on an article by Jaffe and Quinn)
This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between…
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
There is no mysterious link between mathematics and physics, because both of them are human inventions designed to study the world.
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
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…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore,…
We briefly comment (in italian) on present relations between the traditional philosophy and modern positive sciences, in particular exact sciences.
This paper replies to the comment by Jefimenko: "Causal equations for electric and magnetic fields and Maxwell's equations: Comment on a paper by Heras" [Am. J. Phys. 76, 101-101 (2008)]."
This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…