A Closed Future for Mathematics?

abernard102@gmail.com 2014-09-20

Summary:

"In a blog post on Computational Knowledge and the Future of Pure Mathematics Stephen Wolfram lays out a vision that is in many ways exciting and challenging. What if all of mathematics could be expressed in a common formal notation, stored in computers so it is searchable and amenable to computer-assisted discovery and proof of new theorems? As a former mathematician who is now a programmer, it is I think inevitable that I have had similar dreams for a very long time; anyone with that common background would imagine broadly the same things. Like Dr. Wolfram, I have thought carefully not merely about the knowledge representation and UI issues in such a project, but also the difficulties in staffing and funding it. So it was with a feeling more of recognition than anything else that I received much of the essay. To his great credit, Dr. Wolfram has done much – more than anyone else – to bring this vision towards reality. Mathematica and Wolfram Alpha are concrete steps towards it, and far from trivial ones. They show, I think, that the vision is possible and could be achieved with relatively modest funding – less than (say) the budget of a typical summer-blockbuster movie. But there is one question that looms unanswered in Dr. Wolfram’s call to action. Let us suppose that we think we have all of the world’s mathematics formalized in a huge database of linked theorems and proof sequences, diligently being crawled by search agents and inference engines. In tribute to Wolfram Alpha, let us call this system Omega'. How, and why, would we trust Omega? There are at least three levels of possible error in such a system. One would be human error in entering mathematics into it (a true theorem is entered incorrectly). Another would be errors in human mathematics (a false theorem is entered correctly). A third would be errors in the search and inference engines used to trawl the database and generate new proofs to be added to it ..."

Link:

http://esr.ibiblio.org/?p=6252

From feeds:

Open Access Tracking Project (OATP) » abernard102@gmail.com

Tags:

oa.new oa.comment oa.mathematics oa.databases oa.tools oa.search oa.open_science

Date tagged:

09/20/2014, 16:49

Date published:

09/20/2014, 12:49