Prof. Jonathan of the University of Newcastle in Australia (and one of the co-bloggers of this site) has been interviewed in International Innovation, a publication devoted to be a leading portal for scientific dissemination. Borwein’s interview, and the accompanying discussion of experimental mathematics, are available here.
Here are a few excerpts:
Borwein describes experimental applied mathematics:
Experimental applied mathematics comprises the use of modern computing technology as an active agent of research for purposes of gaining insight and intuition, discovering new patterns and relationships, testing and conjectures, and confirming analytically derived results, much in the same spirit that laboratory experimentation is employed in the physical sciences. It is closely related to what is known as ‘experimental mathematics’ in pure mathematics, as has been described elsewhere, including by the late Herb Wilf in the Princeton Companion to Mathematics.
Commentary on “experimental math-odology”:
The key findings of Borwein’s study have thus far been nothing short of spectacular — particularly the results on the structure of short, random walks and flights; randomness of the distribution of digits of numbers; and other technical areas, including the creation of fast algorithms used for hard image reconstruction issues. However, it is the evolution of the study’s methodological underpinnigns that Borwein finds most exciting. He calls it ‘experimental mathodology’, a name derived from a fortuitous misspelling of ‘methodology’ (Borwein liked it and decided to keep it). These underpinnings are: gaining insight and intution, discovering new relationships, visualising math principles, testing (especiallly falsifying conjectures), exploring a possible result to see if it merits formal proof, computing and thereby replacing length hand derivations, and confirming analytically derived results.
Borwein comments on the future of experimental mathematics:
I expect much more emphasis on advanced visualisation in two and three dimensions as illustrated in the description of my recent work on Pi and other fundamental constants. I am heavily involved in attempts to make computational science research more reproducible and reliable. … This is an enormous task as it requires much more robust code than is currently available, which no one wishes to pay for, and a series of culture changes.
The full interview and discussion are available here.