*To*: isabelle-users <isabelle-users at cl.cam.ac.uk>*Subject*: [isabelle] Funding Opportunity*From*: Jeremy Avigad <avigad at cmu.edu>*Date*: Wed, 17 Mar 2010 16:38:17 +0100*User-agent*: Thunderbird 2.0.0.23 (X11/20090817)

Dear Isabelle users, Harvey Friedman asked me to post the announcement below. Jeremy ****** Subject: Grant Opportunity: Foundational Questions in the Mathematical Sciences There is a grant opportunity in (A) foundations of: mathematics, mathematical sciences, computer science; (B) artificial intelligence; (C) and related fields. The John Templeton Foundation accepts research proposals that directly or indirectly address the following questions: (1) What are the limits of mathematics in advancing human knowledge? (2) What have the difficulties of AI taught us about the nature of mind and intelligence? Deadline for the initial inquiry is April 15, 2010. Please feel free to pass the information on to others who might be interested in the grant opportunity.

ADDITIONAL INFORMATION The Grant Program is co-chaired by Barry Cooper and myself, with Barry focused on the AI component, and myself focused on the LIMITS OF MATHEMATICS component. I have chosen to add some additional information that may be of some use in your decision to make an initial inquiry by April 15, 2010. With regard to question (1): we are interested in funding selected research projects that address (1) directly or indirectly. Here is a sample of some research thrusts that are of interest. But feel free to propose your own ideas that genuinely address (1) directly or indirectly, in ways not included in A-E below. Proposals will be judged according to their relevance to (1), their conceptual and technical soundness, and their feasibility. A. Limits of mathematics within mathematics. This includes exploring the boundary of algorithmic decidability/undecidability of basic mathematical problems. This also includes explorations into the boundary of provability and unprovability of basic mathematical problems within fundamental formal systems. These are well explored areas, so we will emphasis the development of novel ideas. B. Limits of mathematics within biology and physics. This includes investigations as in A above, but related to the behavior of idealized biological and physical systems. The level of biological and physical realism is of particular interest. C. Limits of mathematics within probability and statistics. This includes investigations into the logical foundations of probability and statistics of the kind that can be used to address limits of mathematics. D. Limits of computation in mathematical modeling. This includes investigations into the limits of computational methods in approximating physical reality due to round off, instability, and so forth. E. Limits of mathematics within mathematical economics. This includes investigations into limits of computational methods and decidability/ provability in the realm of game theory and models of economic behavior. F. Limits of certainty in mathematics. This includes practical and theoretical investigations into just how certain we are or can be about mathematical assertions. G. Limits of certainty in software. This includes practical and theoretical investigations into how certain we are or can be that software meets mathematical requirements. Sincerely Yours, Harvey M. Friedman Distinguished University Professor of Mathematics, Philosophy, and Computer Science The Ohio State University Columbus, Ohio

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