IntroductionPart 1: The General Environment of Contemporary Mathematics: The Specificity of Modern and Contemporary Mathematics; Advanced Mathematics In the Tracts of Mathematical Philosophy; Toward a Synthetic Philosophy of Contemporary Mathematics;Part 2: Case Studies: Grothendieck; Eidal Mathematics; Quiddital Mathematics; Archeal Mathematics; Part 3: Synthetic Sketches: Fragments of a Transitory Ontology; Comparative Epistemology and Sheafification; Phenomenology of Mathematical Creativity; Mathematics and Cultural Circulation
Fernando Zalamea is Professor of Mathematics at the Universidad Nacional de Colombia.
This book, elegantly and clearly translated by Z.L. Fraser provides, for the Anglophone world, insight into Zalamea's renewal of philosophy through mathematical (and synthetical) means.-Tzuchien Tho, MUTE
Zalamea's book is thematically vast. It is truly astounding to behold the rich range of mathematical themes that are touched upon, arguably including all of the most important objects of contemporary exploration.-Giuseppe Longo, Speculations
This is a weighty and daring book. It proposes a new philosophy of mathematics, based on a detailed knowledge of the most recent work in advanced mathematics, and constructed in explicit contrast with the traditional analytical approach ... this new synthetic and open-minded approach is no doubt worthy of attention, and philosophers who dare to make an effort will surely reap the reward.-Paloma Perez-Ilzarbe, MathSciNet