Abstract

The paper is devoted to the analysis and identification of new philosophical aspects of the problem of justification of modern mathematics according to which to the end of the 20th century the most exact of sciences had experienced new shocks associated with the crisis of excessive complexity of the mathematical theories. In the context of justification of mathematics philosophical conclusion consists in the fact that from a methodological point of view for general assessment of whether mathematics is developed or not just the lack of crises is more negative phenomenon than its too long trouble-free state. Accomplished fact is that a computer can be regarded as one of the serious revolutionary technological inventions of the last century, which has had a huge influence on mathematics. In this development of progress of contemporary mathematics, more precisely, in its instrumental technologies the new philosophical problems are revealed - this is the role of computers and the new standards of mathematical thinking. In addition, with the development of contemporary mathematics and the emergence of increasingly complicated and long proofs, they lose their methodological advantage - the property of visibility and convincingness. Within the philosophy of mathematics this problem has not been discussed yet, possibly because the leading mathematicians haven’t expressed their opinions on the subject. After that, we can wait for a methodologically important period clarifying details, which can make the process itself foundations of mathematics philosophical consummation as the crisis complexity; in mathematics it is not a ‘systemic crisis‘ carrying the potential danger of the destruction of all mathematical knowledge