MatheRealism is the position that the amount of information in the universe places a limit on the possible contents of mathematics. Its supporters claim it as a philosophical foundation of mathematics.

The argument proceeds as follows. The number of atoms is about $10^{80}$ and will remain so forever, limited by the horizon of observation and notwithstanding the expansion of the universe; the remaining part of the universe is causally disconnected from us. The number of elementary particles is less than $10^{100}$ . Although every atom has infinitely many eigenstates, only a finite number of them can be distinguished (due to the uncertainty relation of quantum physics). Further the eigenstates, with exception of the ground state, have a limited life time. All this leads to the result that only a finite number of bits can be stored in the universe. A conservative estimate is $10^{100}$ bits, but in any case there is an upper limit of information L.

According to MatheRealism only such numbers exist which are computable or can be identified uniquely and addressed individually by any other means. In particular, the supporters of this view claim that any irrational number which cannot be represented by less information than is contained by its infinite string of bits, cannot get addressed at all and that even most natural numbers cannot get addressed because their most economical representation requires more information than L. According to MatheRealism, a number which cannot be represented, addressed, or used otherwise does not exist. This implies that infinite sets do not exist.

Note: Although all available numbers have a finite contents of information, there is not a greatest number, because, by useful abbreviations, numbers as large as desired can be represented by means of little information.

The expression MatheRealism is touching on materialism. It may not be mixed up with the notion "realism" of current philosophy of mathematics which in fact is an idealism.

Literature W. Mückenheim: Die Mathematik des Unendlichen, Shaker, Aachen 2006.