Grothendieck's mathematics is a radical way of looking at mathematics that is centered around the concept of creating structures out of nothing. It involves developing new ways to think about geometry, algebra, and number theory that allow mathematicians to explore previously unknown territory. One of the most famous results in Grothendieck's mathematics is his proof of the Weil conjectures, which are a set of mathematical problems that had been open for decades. The proof was so groundbreaking that it was awarded the prestigious Fields Medal.