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Foundational Questions in the Mathematical Sciences

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Mathematics is the language of nature and provides the basis for modern scientific discovery. It has always been integral to research in the physical sciences, engineering, and information technology. But today mathematical modeling and meta-mathematical explorations are transforming research in a range of other fields, from biology, neuroscience, and medicine to economics, sociology, ethics, and theology. Mathematics is thought to hold the key to unlocking the deep mysteries of such subjects as creativity, information, complexity, emergence, intelligence, and the limits of knowledge.

The Foundation's 2010 Funding Priority on "Foundational Questions in the Mathematical Sciences" focuses on two large issues in this exciting domain. The first concerns Gödel's Incompleteness Theorems and related developments in the mathematical sciences that remain the subject of great scholarly discussion. Stanley Jaki once argued that the theorems place strict limits on human understanding of the universe. Freeman Dyson sees them as a guarantee that there will always be new things to discover. Roger Penrose claims that they defeat the goals of artificial intelligence and show that the human mind can never be emulated by a Turing machine.

In a related vein, the Foundation also wishes to encourage scholarly inquiry into the promise and limits of artificial intelligence (AI). Three decades ago, there was huge optimism about the quest for AI. All manner of philosophical conundrums were posed in expectation of the rapid development of super-human artificial intelligence. Today, however, the subject has largely faded from public view, in part because the field encountered new problems and discovered that older ones were harder to solve than anyone imagined.

In order to deepen understanding of these issues, the Foundation invites researchers to explore one or more of the following Big Questions:

  1. 1What are the limits of mathematics in advancing human knowledge?
  2. 2 What have the difficulties of AI taught us about the nature of mind and intelligence?

Budget range and term for individual projects: From $50,000 to $400,000 and for up to two years.

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