Talk:Experimental mathematics

Is the Four Color Theorem an example of Experimental Mathematics?
I don't believe so. I've never heard the term used to refer to a computer-aided proof, so I believe the use of the term in this context is wrong. The Experimental Mathematics entry should also be changed to reflect this. Can someone provide a reference to show the use of the term "experimental mathematics" to refer to a computer-aided proof?

I've also added this to the Four Color Theorem talk page. I will remove the first definition of experimental mathematics unless someone gives a reference for it. --C S 07:10, Sep 22, 2004 (UTC)

Mention of specific algorithm
I removed the following from the article:


 * One major tool of experimental mathematicians is the PSLQ algorithm, which searches for integer relations. Named one of the top ten algorithms of the century by "Computing in Science and Engineering" magazine, PSLQ was used to discover a previously unknown formula which may be employed to directly calculate arbitrary binary digits of Pi.

Due to the brevity of the article, the PSLQ algorithm is given a disproportionate emphasis. There are other integer relations algorithms; I realize perhaps they aren't as important, but to single out a particular integer relation algorithm over the quite diverse and non-standard toolkits used by researchers seems odd, to say the least.

What this probably shows is that there should be a section, "Tools used" or similar title, which could include this algorithm and other algorithms and resources used by many researchers.

Also, the excerpted paragraph could probably be reworked to be more in the form of an example of a experimental mathematics "success story". Maybe there should be a section for that kind of thing too.

Actually, one thing that I think would be nice is to add a link to an article about PSLQ and the discovery of a formula using it. I'll try and find one to link to. --C S 14:21, Oct 15, 2004 (UTC)


 * I would respectfully point out that the discovery of the Bailey-Borwein-Plouffe Pi formula using PSLQ was the seminal event that launched experimental math as a legitimate field in its own right, and hinted that there might be many simple and profound formulae accessible by brute force computer search, whose direct derivation lay beyond the limits of human ingenuity. As such, I think PSLQ merits mention in the main section of any  article about the origins of experimental math. --66.109.196.249 14:56, 15 Oct 2004 (UTC)


 * Your point is moot since currently the article is *not* about any origins. If you want to create an origins section, then certainly PSLQ would merit mention in it, but again, I must emphasize that your statement makes no sense since there is no mention of how experimental mathematics developed.


 * I removed the original paragraph on PSLQ not because I don't think it's important, but simply because it did not fit in the article, and I don't have the time to create a whole new article, in effect, to blend it in. As I mentioned previously, there should be some of section relating "success stories".  --C S 01:40, Oct 16, 2004 (UTC)

Proposing rewrite
No substantial updates to the contents of this page for over 18 months. I think we can do a lot better. It needs a simple introduction, something on the history of the topic, and some example of results and ongoing research. I propose to do a substantial rewrite in a few days time, unless there are any objections. Gandalf61 14:59, 4 October 2007 (UTC)


 * Okay, finally got round to completing the proposed rewrite. Gandalf61 (talk) 11:06, 31 December 2007 (UTC)

Update
I have added some material regarding some challenging mathematical physical problems, namely analytical solutions of the energy eigenvalues of a special case of the quantum mechanical three-body problem known as the Hydrogen molecule-ion in terms of a generalization of the Lambert W function and also an item related to the relativistic n-body problem. —Preceding unsigned comment added by 24.6.171.96 (talk) 22:11, 19 January 2009 (UTC)

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Not a good sentence if you squint
The following is not a good sentence if you squint at it, and not much of anything if you don't: It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental (in either the Galilean, Baconian, Aristotelian or Kantian sense) exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit."

For my own notes, I rearranged it until I got this:

It has been defined as that branch of mathematics concerned with the codification and transmission of insights through:
 * experimental exploration of
 * conjectures
 * in either the Galilean, Baconian, Aristotelian or Kantian sense
 * and informal beliefs
 * along with careful analysis of the data acquired in this pursuit.

Hmm. Is there a Galilean way to explore informal belief? If so, I've messed this up.

The parse simply shouldn't be this difficult (I only got one that works for me after substantial reduction in unnecessary verbiage). &mdash; MaxEnt 04:45, 12 September 2021 (UTC)