Good insights, but, for those familiar with pragmaticism and category theory and various issues in foundation, proof theory, etc. the perspective isn't new. Some chapters are rather like introductions to works of seminal contemporary mathematicians with flowery language.

While the book is rather about what future philosophy of mathematics should do, a call to a re-orientation of philosophy of mathematics, it is the rediscovery of Albert Lautman and indication of his unique modern Platonistic metaphysics implicitly present is of pivotal importance, at least for me. The extreme structuralization in contemporary mathematics and its power of organization indicates a brand-new schema for a new version of Pythagoreanism and thus a new version of Platonism to be founded. This should be an ambitious and fruitful project.

Becomes repetitive and pointless when it goes to the end. Again, for those with enough background, an 50-pages essay should have been sufficient.