Barry Mazur

"Hodge cohomology, algebraic de Rham cohomology, crystalline cohomology, the étale ℓ-adic cohomology theories for each prime number ℓ ... A strategy to encapsulate all the different cohomology theories…"

"Number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"

"Sometimes the mathematical anti-Platonist believes that headway is made by showing Platonism to be unsupportable by rational means, and that it is an incoherent position to take when formulated in a p…"

"Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category which in some intuitive sense “softens algebraic geometry” so as to allow fo…"