.dvi version (for previewing)
Note added Nov. 6, 1996: For a beautiful, much deeper, analysis of the ideas here, as well as for an ambitious and courageous attempt at initiating a unified philosophy and methodology of Experimental Mathematics, see the article `Making sense out of Experimental mathematics' by Borwein, Borwein, Girgensohn, and Parnes in the Math. Intell. 18(4) (Fall 1996), 12-18. [The expanded version was available from the link http://www.cecm.sfu.ca/preprints/1995pp.html, but is currently (Feb. 11, 2009) broken]
Note added Sept. 20, 1998: For a deep and critical discussion of my point of view, as well as those of Chaitin and the Borwein's, by a professional philosopher of mathematics, I recommend Patrick Peccatte's very interesting article on quasi-empiricism (in French).
Added Nov. 27, 1998: Patrick Peccatte drew my attention to the English summary of the above article , with feedback, that appeared in the FOM forum.
Added Dec. 29, 1998: I was interviewed about the views expressed in this article by John Rieger of the National Public Radio's Beyond Computing Program (click on the Sept. 4, 1998: `Can computers change the way we think?' program).
Added Feb. 15, 1999: Leo Corry wrote a fascinating article about Hilbert, Bourbaki, and Eternal Truth, that has a couple of pages, at the end, about my `philosophy'. Read Leo Corry's Fascintaing Article.
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