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:
(wait 30-60 seconds to see the display).
Quote of the day (refresh browser to select another):
Mathematicians normally think that they possess absolute truth. They read God's thoughts. They have absolute certainty and all the rest of us have doubts. Even the best physics is uncertain, it is tentative. Newtonian science was replaced by relativity theory, and then---wrong!---quantum mechanics showed that relativity theory is incorrect. But mathematicians like to think that mathematics is forever, that it is eternal. Well, there is an element of that. Certainly a mathematical proof gives more certainty than an argument in physics or than experimental evidence, but mathematics is not certain. This is the real message of Godel's famous incompleteness theorem and of Turing's work on uncomputability. -- G. Chaitin, from "The Creative Life: Science vs. Art" Online article.
The complete list of quotes is available
This website is a repository of information on experimental and computer-assisted mathematics. It is operated by
- David H. Bailey, Lawrence Berkeley Laboratory, and University of California, Davis
- Jonathan M. Borwein, University of Newcastle, Newcastle, Australia
For additional news, see Math Drudge blog news.
- 23 Oct 2013: Bailey and Borwein, together with Marcos Lopez de Prado and Qiji Jim Zhu, launched a website and blog devoted to financial mathematics. The site includes papers, news and a blog, where financial mathematics and related issues are discussed. The objective is to help readers distinguish between mathematically sound techniques of and the unfortunately much larger body of highly questionable methods that sadly pervade the finance community and financial news. For details, see Financial Math site.
- 25 Jul 2013: An article by Bailey and Jon Borwein, together with Andrew Mattingly and Glenn Wightwick of IBM Australia, has appeared in the Notices of the American Mathematical Society. The article is featured on the cover of the August 2013 issue, which can be seen here.
- 4 Mar 2013: Bailey was quoted in Quanta (the Simons Foundation news column) and in a Wired news report on the increasingly complexity of mathematical and scientific computation, and the need for reproducibility in the field.
- 1 Jan 2013: The article "Closed Forms: What They Are and Why We Care," co-authored by Jonathan Borwein and the late Richard E. Crandall, appeared in the Notices of the American Mathematical Society. The PDF of the article is available Here.
- 20 Dec 2012: Our colleague Richard Crandall unexpectedly passed away from leukemia. A brief summary of Crandall's remarkable career is available in our Math Drudge article.
- 20 Nov 2012: The Bailey-Borwein Huffington Post article on the age of the Earth has been read at least 250,000 times (extrapolating from 2500 "Likes").
- 1 Feb 2012: A new book, "Exploratory experimentation in mathematics: Selected Works," with papers by Bailey and Borwein has been published -- see Books.
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. Please send any comments or questions for this site to:
All material is copyrighted by David H. Bailey and Jonathan M. Borwein (c) 2014.
Acknowledgement of support
Bailey's research has been supported in part by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. Borwein's research is supported in part by MITACS, by the Australian Research Council and the University of Newcastle.
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.
For details on the authors' books on experimental mathematics, see
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:
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:
The 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:
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:
For a list of websites of numerous commercial firms that offer mathematical software and (free) online tools, see the Commercial site page:
Courses and tutorials
For information of some courses and tutorials in the area of experimental mathematics, see the Courses page:
For a list of websites of mathematical societies and journals in the general area of experimental and computational mathematics, see the Institutional site page:
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:
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:
Here are some recent papers by Bailey and/or Borwein in the area of experimental mathematics, plus a few others of interest:
For some freely downloadable software for experimental math research, see the Software page:
Here are some recent presentations by Bailey and Borwein in the area of experimental mathematics: