Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn

  title={Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn},
  author={Michael Francis Atiyah and Armand Borel and Gregory J. Chaitin and Daniel Friedan and James Glimm and Jeremy Gray and Morris W. Hirsch and Saunders Maclane and Benoit B. Mandelbrot and David Ruelle and Albert S. Schwarz and Karen K. Uhlenbeck and Ren{\'e} Thom and Edward Witten and Christopher Zeeman},
  journal={Bulletin of the American Mathematical Society},
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 mathematics and theoretical physics. 
A Defence of Mathematical Pluralism
We approach the philosophy of mathematics via an analysis of mathematics as it is practised. This leads us to a classification in terms of four concepts, which we define and illustrate with a variety
What Lakatos Could Teach the Mathematical Physicist
This contribution portrays the various stances taken in the Jaffe-Quinn debate from the perspective of Imre Lakatos philosophy of mathematics that seems most suitable for a debate concerning mathematical growth.
Physical Mathematics and the Future
These are some thoughts meant to accompany one of the summary talks at Strings2014, Princeton, June 27, 2014. This is a snapshot of a personal and perhaps heterodox view of the relation of Physics
The effectiveness of mathematics in physics
In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader
On the Tension Between Physics and Mathematics
  • M. Rédei
  • Physics, Education
    Journal for General Philosophy of Science
  • 2020
Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The paper looks at how the tension has been perceived and articulated by some physicists,
The Effect of Computers on Pure Mathematics
The philosophical implications of the computers in mathematics are investigated by recounting the controversy following the proof of the Four-Colour Theorem, then the famous Jaffe-Quinn discussions, and the discipline called experimental mathematics is examined.
“The End of Proof”? The Integration of Different Mathematical Cultures as Experimental Mathematics Comes of Age
The question of how distinct mathematical cultures can coexist and blend into a common understanding that allows for cultural convergence while preserving heterogeneity is approached.
Mathematical Explanation: Problems and Prospects
Since this issue is devoted to the interaction between philosophy of mathematics and mathematical practice, I would like to begin with an introductory reflection on this topic, before I enter the
The Applicability of Mathematics
Since its publication in 1960, Wigner’s paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’ has attracted comment from scientists, applied mathematicians and philosophers
What's experimental about experimental mathematics?
The role of the computer in the mathematical experiment is outlined and the impact of high speed computing on mathematical research within the emerging sub-discipline of experimental mathematics is described.


“Theoretical mathematics”: toward a cultural synthesis of mathematics and theoretical physics
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
The Limits of Mathematics - Course Outline and Software (Abstract)
  • G. Chaitin
  • Computer Science
    Analysis of Dynamical and Cognitive Systems
  • 1993
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information
Quantum field theory and the Jones polynomial
It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones
Exhibiting Randomness in Arithmetic using Mathematica and C
In this book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic, and the software used to construct it.
Claims and accomplishments of applied catastrophe theory
Catastrophe theory seems to have made no significant contributions to biology and the social sciences, and to have no advantage over other better-established mathematical tools which have been used to better effect.
The partition function of degenerate quadratic functional and Ray-Singer invariants
The partition function of degenerate quadratic functional is defined and studied. It is shown that analytic torsion and similar invariants can be interpreted as partition functions of quadratic
Information-Theoretic Incompleteness
  • G. Chaitin
  • Mathematics, Computer Science
    World Scientific Series in Computer Science
  • 1992
We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a self-delimiting program for enumerating the set of theorems of the
Catastrophe Theory, Selected Papers 1972-1977
bocker News-Union Star, Feb. 15, 1971. [51] C. Daniel and F. S. Woods, Fitting Equations to Data. New York: Wiley, 1971, p. 32. [52] Conversations with George Barkley, Brunswick Town Supervisor
Les singularites des applications differentiables
© Association des collaborateurs de Nicolas Bourbaki, 1956, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. implique l’accord avec les conditions