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).

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On the other hand, I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research. Only those who realize the immense efforts and, above all, the devotion without which pioneer work in theoretical science cannot be achieved are able to grasp the strength of the emotion out of which alone such work, remote as it is from the immediate realities of life, can issue. What a deep conviction of the rationality of the universe and what a yearning to understand, were it but a feeble reflection of the mind revealed in this world, Kepler and Newton must have had to enable them to spend years of solitary labor in disentangling the principles of celestial mechanics! Those whose acquaintance with scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a skeptical world, have shown the way to kindred spirits scattered wide through the world and through the centuries. Only one who has devoted his life to similar ends can have a vivid realization of what has inspired these men and given them the strength to remain true to their purpose in spite of countless failures. It is cosmic religious feeling that gives a man such strength. A contemporary has said, not unjustly, that in this materialistic age of ours the serious scientific workers are the only profoundly religious people. -- Albert Einstein, New York Times Magazine, 9 Nov 1930, pg. 1-4, reprinted in Albert Einstein, Ideas and Opinions, Crown Publishers, Inc. 1954, pg. 36-40.

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 David H. Bailey, Lawrence Berkeley Laboratory (retired), and University of California, Davis (DHB website). Please send any comments or questions for this site to:

Disclaimer and copyright. Material on this site is provided for research purposes only and does not necessarily reflect the views or policies of the author's institutions or any other organization. All material is copyrighted by David H. Bailey (c) 2020.

Math Scholar blog. The "Math Scholar" blog contains essays, philosophical musings, interesting quotes and exercises, all in the realm of mathematics, computing and modern science. New items are posted on average every two weeks:

Math Drudge blog (older). This blog was co-authored by Bailey and the late Jonathan Borwein, prior to Borwein's death in August 2016.

Jonathan Borwein Memorial site. In the wake of Jonathan Borwein's untimely death in August 2016, this site contains a blog of remembrances of Jon by family, friends and colleagues, together with a compendium of Jon's publications, talks and reviews of his work by others.

Mathematical Investor blog. The Mathematical Investor blog is devoted to financial mathematics and abuses of mathematics in the field:

Additional information, in alphabetical order:

  1. Books. Bailey and Jonathan Borwein (now deceased) have authored numerous books on mathematical and scientific computation. For details on the authors' books on experimental mathematics, see:
  2. Commercial sites. For a list of websites of numerous commercial firms that offer mathematical software and (free) online tools, see the Commercial site page:

  3. 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:
  4. 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:
  5. 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:

  6. Software. For some freely downloadable software for experimental math research, see the Software page: