Grothendieck and the Evolution of Cohomology

This chapter explores the groundbreaking developments in cohomology theories for algebraic varieties spearheaded by Alexander Grothendieck, emphasizing his innovative approach amidst the skepticism of his contemporaries. It examines the accessibility of mathematical texts, contrasting Grothendieck's more self-contained writing style with that of Ser, as well as the influence of mathematical correspondence and social upheaval on their ideas. The chapter also reflects on Grothendieck's personal journey amidst the competitive landscape of 20th-century French mathematics, culminating in his decision to withdraw from the public sphere.