``Theorems for a price: tomorrow's semi-rigorous mathematical culture''. (Appeared in the Notices of the Amer. Math. Soc. v. 40, no. 8 (Oct. 1993) 978-981. Reprinted in the Math. Intell. v. 16, no. 4 (Fall 1994) 11-14.)

This is the `semi-rigorous manifesto' that lead George Andrews to write a counter-manifesto (``The death of proof? semi-rigorous mathematics? you've got to be kidding'',(ibid p.16-19). I am sure that this `controversy' will seem comical to our grandchildren (perhaps it already is to our children.) Semi-rigorists would be analogous to what Hasidic Jews are now. The Hasidic movement, started in the 18th century by Baal Shem Tov, was condemned by the then mainstream `mitnagdim' (opposers) as a dangerous heresy. Now Hasidic Jews are the epitome of ultra-orthodoxy.

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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 Feb. 11, 2009) All the links below are broken. I am keeping them for historical reasons.

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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