- CARMA COLLOQUIUM
- Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
- Title: Experimental Computation and Visual Theorems: Part I
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Wed, 21st May 2014
In these two talks chapter I want to talk, both generally and personally, about the use of tools in the practice of modern research mathematics. To focus my attention I have decided to discuss the way I and my research group members have used tools primarily computational (visual, numeric and symbolic) during the past five years. When the tools are relatively accessible I shall exhibit details; when they are less accessible I settle for illustrations and discussion of process.
Long before current graphic, visualisation and geometric tools were available, John E. Littlewood, 1885-1977, wrote in his delightful Miscellany:
A heavy warning used to be given [by lecturers] that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety. Some pictures, of course, are not rigorous, but I should say most are (and I use them whenever possible myself).
Over the past five years, the role of visual computing in my own research has expanded dramatically. In part this was made possible by the increasing speed and storage capabilities - and the growing ease of programming - of modern multi-core computing environments. But, at least as much, it has been driven by paying more active attention to the possibilities for graphing, animating or simulating most mathematical research activities.
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