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."
傑作在於認知到有一個特殊的「存在」隱藏於任一代數方程(或方程組)，將之稱為
「計畫」。解的空間不過就是這個計畫的投影或是影子。此外，他發現這些計畫
背後有一個豐富的世界，其中它們交互作用，互相關聯。
"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."
將大師創作用在壞事上也屢見不鮮。例如NSA應用橢圓曲線的相關演算法在使用者電腦
植入後門。
https://goo.gl/NsLBkb
這個怪咖原本連家人都不見的。
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."
在代數幾何上的貢獻被應用到數論、分類理論、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應用代數幾何方法證明出費馬最後定裡。
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."
一個人抵上十幾位數學大師。
http://www.math.columbia.edu/~woit/wordpress/?p=7335