  We propose a funding scheme for theoretical research that does not rely on
project proposals, but on recent past scientific productivity. Given a
quantitative figure of merit on the latter and the total research budget, we
introduce a number of policies to decide the allocation of funds in each grant
call. Under some assumptions on scientific productivity, some of such policies
are shown to converge, in the limit of many grant calls, to a funding
configuration that is close to the maximum total productivity of the whole
scientific community. We present numerical simulations showing evidence that
these schemes would also perform well in the presence of statistical noise in
the scientific productivity and/or its evaluation. Finally, we prove that one
of our policies cannot be cheated by individual research units. Our work must
be understood as a first step towards a mathematical theory of the research
activity.
