Experimental Mathematics Website

<== This is a picture from the interactive geometry package Cinderella showing the behavior of 10,000 starting values in the rectangle [0,1]x[h-1,h+1], where h is the height of the horizontal line, after six iterations of the algorithm which reflects a point x in the sphere then reflects the outcome in the line and then averages the result y with x. It is an accessible prototype for a remarkable image reconstruction algorithm known variously as Douglas-Ratchford, Lion-Mercier, Fienup's method, and "divide-and-concur." Some related graphics can be generated and displayed at these URLs: Expansion Reflection (wait 30-60 seconds to see the display).

Quote of the day (refresh browser to select another):

There exists today a very elaborate system of formal logic, and specifically, of logic applied to mathematics. This is a discipline with many good sides but also serious weaknesses. ... Everybody who has worked in formal logic will confirm that it is one of the technically most refactory parts of mathematics. The reason for this is that it deals with rigid, all-or-none concepts, and has very little contact with the continuous concept of the real or the complex number, that is with mathematical analysis. Yet analysis is the technically most successful and best-elaborated part of mathematics. Thus formal logic, by the nature of its approach, is cut off from the best cultivated portions of mathematics, and forced onto the most difficult mathematical terrain, into combinatorics. -- John von Neumann, 1948, quoted in L. Blum, P. Cucker, M. Shub and S. Smale, Complexity and Real Computation, Springer-Verlag, New York, 1998.

The complete list of quotes is available here.

This website is a repository of information on experimental and computer-assisted mathematics. It is operated by

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Additional information, in alphabetical order:

  1. Acknowledgement of support. Borwein's research is supported in part by MITACS, by the Australian Research Council and the University of Newcastle.
  2. Books. Bailey and Borwein have authored numerous books on mathematical and scientific computation. For details on the authors' books on experimental mathematics, see:
  3. CARMA. Jonathan Borwein leads the Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA) at the University of Newcastle, Australia. The researchers in this centre are very active in experimental mathematics and applied computational mathematics in general. Here is an index to the experimental mathematics resources at the CARMA site:

  4. Disclaimer and copyright. Material on this site is provided for research purposes only and does not necessarily reflect the views or policies of the authors' respective institutions or funding agencies. All material is copyrighted by David H. Bailey and Jonathan M. Borwein (c) 2016.

  5. Financial Mathematics website and blog. Bailey and Borwein, together with their colleagues Marcos Lopez de Prado of Hess Energy Trading Co. and Qiji Jim Zhu of Western Michigan University, have recently written a series of papers in mathematical finance, with the objective of helping researchers and investors distinguish mathematically sound techniques from the unfortunately much larger body of questionable techniques that sadly pervade the finance community and financial news. Here is a website with additional information:

  6. Commercial sites. For a list of websites of numerous commercial firms that offer mathematical software and (free) online tools, see the Commercial site page:

  7. Conversation articles. Bailey and Borwein have also authored a series of articles for The Conversation, an international forum of academic research and discussion based in Melbourne, Australia. A listing of these articles is available here:

  8. Courses and tutorials. For information of some courses and tutorials in the area of experimental mathematics, see the Courses page:
  9. Huffington Post articles. Bailey and Borwein have authored a series of articles for the Huffington Post, a very widely read online news and discussion forum based in the U.S., with over 9000 contributors and many thousands of regular readers. It was recently named the world's most influential blog/news site in an article in the U.K. Guardian. A listing of the articles by Bailey and Borwein is available here:

  10. Institutional sites. For a list of websites of mathematical societies and journals in the general area of experimental and computational mathematics, see the Institutional site page:
  11. Math Drudge blog. The new "Math Drudge" blog is now online. It contains essays, philosophical musings, interesting quotes and exercises, all in the realm of mathematics, computing and scientific research. New items are posted on average every two weeks.

  12. News. For some recent news articles in the general area of mathematics, computing, science and finance, see the News page:
  13. Non-commercial software and tools. For a list of websites of non-commercial organizations that offer mathematical software and (free) online tools, see the Non-commercial site page:
  14. Other sites of interest. For a list of numerous other websites with interesting and useful information relevant to mathematics in general and computational mathematics in particular, see the Other site page:

  15. Papers. Here are some recent papers by Bailey and Borwein:

  16. Press reports. Here are some recent press reports mentioning Bailey and/or Borwein:
  17. Software. For some freely downloadable software for experimental math research, see the Software page:

  18. Talks. Here are some recent presentations by Bailey and Borwein: