About a century ago Hilbert initiated his program to secure the foundations of mathematics and to establish once for all the indubitability of mathematical truth. After 100 years of stormy developments, both undermining and reinstalling parts of his program, it is now the time to re-evaluate Hilbert's questions for the 21st century. Unlike in past decades where mathematics and computer science evolved along divergent lines, this renewed approach requires the attention and combined effort of mathematicians and computer scientists. We plan to fruitfully combine recent advances in constructive mathematics, computational complexity, and algorithm design to approach the following questions: Can abstract mathematics be used to work for the concrete? How can abstract mathematical proofs be transformed into finite methods, and eventually into efficient algorithms? Building a strong team of mathematicians and computer scientists and closely collaborating with leading experts we plan to initiate a new 'Hilbert Program for Actual Computation'. The main output of the project will be theoretical investigation in form of high quality research papers. By organizing a workshop we will discuss our new approach with a broad audience of mathematicians, computer scientists, and philosophers.
Abstract Mathematics for Actual Computation: Hilbert's Program in the 21st Century
BENINI, MARCO
2014-01-01
Abstract
About a century ago Hilbert initiated his program to secure the foundations of mathematics and to establish once for all the indubitability of mathematical truth. After 100 years of stormy developments, both undermining and reinstalling parts of his program, it is now the time to re-evaluate Hilbert's questions for the 21st century. Unlike in past decades where mathematics and computer science evolved along divergent lines, this renewed approach requires the attention and combined effort of mathematicians and computer scientists. We plan to fruitfully combine recent advances in constructive mathematics, computational complexity, and algorithm design to approach the following questions: Can abstract mathematics be used to work for the concrete? How can abstract mathematical proofs be transformed into finite methods, and eventually into efficient algorithms? Building a strong team of mathematicians and computer scientists and closely collaborating with leading experts we plan to initiate a new 'Hilbert Program for Actual Computation'. The main output of the project will be theoretical investigation in form of high quality research papers. By organizing a workshop we will discuss our new approach with a broad audience of mathematicians, computer scientists, and philosophers.
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