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):
Several years ago I was invited to contemplate being marooned on the proverbial desert island. What book would I most wish to have there, in addition to the Bible and the complete works of Shakespeare? My immediate answer was: Abramowitz and Stegun's Handbook of Mathematical Functions. If I could substitute for the Bible, I would choose Gradsteyn and Ryzhik's Table of Integrals, Series and Products. Compounding the impiety, I would give up Shakespeare in favor of Prudnikov, Brychkov And Marichev's of Integrals and Series ... On the island, there would be much time to think about waves on the water that carve ridges on the sand beneath and focus sunlight there; shapes of clouds; subtle tints in the sky... With the arrogance that keeps us theorists going, I harbor the delusion that it would be not too difficult to guess the underlying physics and formulate the governing equations. It is when contemplating how to solve these equations - to convert formulations into explanations - that humility sets in. Then, compendia of formulas become indispensable. -- Michael Berry, "Why Are Special Functions Special?", available at Physics Today, Apr 2001.
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.
- 10 May 2014: In a column today, John Rekenthaler, Vice President of Research for Morningstar, presented a synopsis of our "Pseudo-Mathematics" paper. He relayed our recommendation that it would "behoove the investment community to adopt a similar policy" to one now being promoted in the pharmaceutical industry, namely to make all test results public.
- 28 Apr 2014: The present authors' paper was mentioned in a Pacific Standard article by Ryan Jacobs. It quotes one of us saying, "What you end up doing is that the models that you derive or you select tend to just focus on idiosyncrasies of the data, and don't have any real fundamental forward predictive power."
- 23 Apr 2014: After the talk by Bailey and Marcos Lopez de Prado at the "Battle of the Quants" meeting in New York City in March (see below), Bailey was invited to do a video interview for Institutional Investor Journals. This video is now available online Here.
- 17 Apr 2014: The present authors were featured in a Barron's article by Brendon Conway. We were quoted as saying, "The higher the number of configurations tried, the greater is the probability that the backtest is overfit."
- 16 Apr 2014: The present authors were featured in a Financial Times article by Stephen Foley. He summarizes our paper by saying, "The authors' argument is that, by failing to apply mathematical rigour to their methods, many purveyors of quantitative investment strategies are, deliberately or negligently, misleading clients." If you cannot view the article due the pay wall, a PDF copy is available Here.
- 11 Apr 2014: The present authors were featured in a Bloomberg News article. It quotes one of us as saying, "We strongly suspect that such back-test overfitting is a large part of the reason why so many algorithmic or systematic hedge funds do not live up to the elevated expectations generated by their managers."
- 10 Apr 2014: The paper "Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance," written by the present authors together with Marcos Lopez de Prado and Qiji Jim Zhu, was published by the American Mathematical Society. It is available free of charge from the AMS website, or from the SSRN website (preprint version).
- 26 Mar 2014: On Tuesday March 26, 2014, Bailey and Marcos Lopez de Prado jointly presented a talk How to spot backtest overfitting at the Battle of the Quants meeting in New York City.
- 12 Mar 2014: An article by Bailey and Borwein, entitled "Pi day is upon us again, and we still do not know if pi is normal," has appeared in the American Mathematical Monthly. A preprint copy is available here.
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: