... never heard of the man before in my life. He received a Fields medal in 1966, that's roughly equivalent to a Nobel Prize for mathematics. Silly me.
"...The mere enumeration of Grothendieck 's best known contributions is overwhelming: topological tensor products and nuclear spaces, sheaf cohomology as derived functors, schemes, Ktheory and GrothendieckRiemannRoch, the emphasis on working relative to a base, defining and constructing geometric objects via the functors they are to represent, fibred categories and descent, stacks, Grothendieck topologies (sites) and topoi, derived categories, formalisms of local and global duality (the 'six operations'), étale cohomology and the cohomological interpretation of Lfunctions, crystalline cohomology, 'standard conjectures', motives and the 'yoga of weights', tensor categories and motivic Galois groups. It is difficult to imagine that they all sprang from a single mind. ..."
It looks as though I haven't got a clue to what mathematics ( algebra ) is about. It is however possible that the concepts are in my mind that I only have to match the words. Like with groups and rings. Once you understand the concept it becomes so trivial that you think you have always known what a group was, or a Galois group for that matter.
Monday, April 18, 2005
Saturday, April 9, 2005
Paradox of Life...
Maybe Matthew R. Watkins is a true genious, perhaps someone who lost direction in his life. I feel as if I never had any direction in my life or am I still searching? That's a paradox since I have found what I have been looking for.
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Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)