On Tue, Jul 26, 2011 at 9:00 AM, Bill Hart <goodwillh...@googlemail.com>wrote: > > Regarding rigor, mathematics itself went through a phase where > informal arguments were displaced with formal ones. Likewise, informal > computer programs will eventually give way to formally verified ones, > and this will naturally be embraced by mathematicians. You are right > that this will not directly have an effect on Number Theory > computations as they are currently done because people will continue > to use computers as a tool to investigate conjectures and collect > numerical evidence and so on. They care little about whether the > program is correct. >
When doing such investigations, we care greatly that the data we get is correct. We just don't care so much that the program producing it be *proven* correct in a formal and technically rigorous sense. When people begin justifying their programs in their papers, (which > will of course also be electronic in the future), then the field will > become more academically sound and eventually the problems it > currently has will become a thing of the past. At the moment the field > (if you can even call it that) has a serious image problem. People > speak about working on computation in whispers as though it is sinful. > There are other things happening in the world of mathematics that are helping with this image problem. For example, I was just at FoCM 2011 [1] and did not get this impression about computation, and there was a very wide range of mathematics represented (everything from numerical PDE's to Computational Topology to Number Theory). And there were certainly some well respected mathematicians among the participants (e.g., Steven Smale, Gunar Carlson, etc.). The people who build communities (major conference series / proceedings volumes) like the FoCM organizers are helping. [1] http://www.damtp.cam.ac.uk/user/na/FoCM11/workshops.html > This is possibly something you don't encounter as a computer > scientist. > > Bill. > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
