4 ms·

Meh, I think he just didn't explain what a "scheme" is very well. Compare it the NY Times piece. From that, I immediately understand that it is an elegant gen

by chubot 12y ago

Meh, I think he just didn't explain what a "scheme" is very well. Compare it the NY Times piece. From that, I immediately understand that it is an elegant generalization of solutions to polynomial equations. http://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html?_r=1 http://www.nytimes.com/2014/11/25/science/the-lives-of-alexa... Compare it to: ''The proper foundations of the enlarged view of algebraic geometry were, however, unclear and this is how Grothendieck made his first, hugely significant, innovation: he invented a class of geometric structures generalizing varieties that he called schemes. In simplest terms, he proposed attaching to any commutative ring (any set of things for which addition, subtraction and a commutative multiplication are defined, like the set of integers, or the set of polynomials in variables x,y,z with complex number coefficients) a geometric object, called the Spec of the ring (short for spectrum) or an affine scheme, and patching or gluing together these objects to form the scheme. The ring is to be thought of as the set of functions on its affine scheme.'' Sorry, this writing is just awkward. I can see why the editors of Nature rejected it. I think the audience of Hacker News is closer to mathematics than the audience of nature (programming being more closely related to math than biology). I doubt that anyone in this thread unfamiliar with schemes was able to get much useful from Mumford's obituary. I don't even see many comments on the exposition.

snowwrestler 12y ago
To me the difference is that the rejected obit attempts to summarize how Grothendieck's innovations worked mathematically, but what most readers want to know is why they are important. This is similar to the insight in the tech world that customers don't buy technology because it is built well, they buy it because it solves a problem for them.
- flatfilefan 12y ago
  "most readers want to know is why they are important". This happened to me in my second year studying physics and applied math. The math teacher did not know how to explain the importance of the math around the eigenvalues etc. Only a year later when taking quantum mechanics we got to the applications of that math. However in hindsight I hope he was trolling me :-) otherwise we need a separate curriculum for math teachers to get in touch with the reality :-)

by chubot 12y ago

snowwrestler 12y ago

To me the difference is that the rejected obit attempts to summarize how Grothendieck's innovations worked mathematically, but what most readers want to know is why they are important. This is similar to the insight in the tech world that customers don't buy technology because it is built well, they buy it because it solves a problem for them.

flatfilefan 12y ago
"most readers want to know is why they are important". This happened to me in my second year studying physics and applied math. The math teacher did not know how to explain the importance of the math around the eigenvalues etc. Only a year later when taking quantum mechanics we got to the applications of that math. However in hindsight I hope he was trolling me :-) otherwise we need a separate curriculum for math teachers to get in touch with the reality :-)