Аннотация:The present paper is devoted to several major changes in how the foundations of mathematics are understood – changes that have been taking place in the post-Gödelian intellectual landscape. The foundationalist and speculative approaches of the previous historical period first gave way to the “no foundations” approach and, next, to two concurrent trends of “anthropological” and “practical” approaches to the foundational problem. An attempt is made to demonstrate that each of the two recent trends can be interpreted in terms of communication with both human and non-human agents.