[FOM] Funding Opporunity

[Harvey Friedman]

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.

For more information, please view the PDF announcement http://www.templeton.org/emails/2010_funding_priorities/foundational_questions_in_the_mathematical_sciences/JTF-FP-Mathematics-n.pdf?utm_source=JTF+E-Mail+List+Manager&utm_medium=email&utm_term=http%3A%2F%2Fwww.templeton.org%2Femails%2F2010_funding_priorities%2Ffoundational_questions_in_the_mathematical_sciences%2FJTF-FP-Mathematics.pdf&utm_content=http%3A%2F%2Fwww.templeton.org%2Femails%2F2010_funding_priorities%2Ffoundational_questions_in_the_mathematical_sciences%2FJTF-FP-Mathematics.pdf&utm_campaign=Grant+Opportunity%3A+Foundational+Questions+in+the+Mathematical+Sciences

or visit the website at http://www.templeton.org/what_we_fund/2010_funding_priorities/foundational_questions_in_the_mathematical_sciences/index.html

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