https://goo.gl/912BKL
"Grothendieck’s genius was to recognize that there is a “being” hiding
behind a given algebraic equation (or a system of equations) called a scheme.
The spaces of solutions are mere projections, or shadows of this scheme.
Moreover, he realized that these schemes inhabit a rich world. They “interact
” with one another, can be “glued” together and so on."
杰作在于认知到有一个特殊的“存在”隐藏于任一代数方程(或方程组)，将之称为
“计画”。解的空间不过就是这个计画的投影或是影子。此外，他发现这些计画
背后有一个丰富的世界，其中它们交互作用，互相关联。
"For example, according to published reports, the National Security Agency
inserted a back door in a widely used encryption algorithm based on “
elliptic curves” — mathematical objects illuminated by Grothendieck’s
research."
将大师创作用在坏事上也屡见不鲜。例如NSA应用椭圆曲线的相关算法在使用者电脑
植入后门。
https://goo.gl/NsLBkb
这个怪咖原本连家人都不见的。
https://goo.gl/JrfTyU
"His nominal specialty was algebraic geometry, which combines elements of both
mathematical disciplines, but Grothendieck used his remarkable capacity for
abstract thinking to make advances across the entire spectrum of mathematics.
He developed unifying concepts that could be applied to a variety of avenues
of mathematical thought, including number theory, category theory, functional
analysis and topology."
在代数几何上的贡献被应用到数论、分类理论、泛函分析及拓璞。
"His ideas were instrumental in solving one of the enduring conundrums of
mathematics, Fermat’s Last Theorem. In 1637, Pierre de Fermat had jotted a
mathematical notation in the margin of a book, but its proof had baffled the
world’s greatest mathematicians for more than three centuries.Then in 1995,
the British mathematician Andrew Wiles published a proof. He arrived at his
solution using the principles of algebraic geometry, the field that
Grothendieck had redefined to its foundations."
1995年Andrew Wiles应用代数几何方法证明出费马最后定里。
https://goo.gl/HvQCqc
"Grothendieck was a legend as a math genius in Montpellier. In a display of
his raw talent, Grothendieck was given by two professors with 14 questions
which should have taken at least a year to solve. He was supposed to pick
just one question. However, Grothendieck came back a few months later with
solutions to all of 14 questions."
一个人抵上十几位数学大师。
http://www.math.columbia.edu/~woit/wordpress/?p=7335