Taking a broader view ---------------------
As Michel Broué, one of his colleagues, writes: "There is no doubt in the minds of mathematicians around the world that, if a relatively civilized humanity survives five hundred years from now, not only will Alexandre Grothendieck be remembered, but his work will be regarded as a revolution in thought at least comparable in scope to those bequeathed by Newton or Einstein."
According to Grothendieck, to solve a given problem, one need only rise above it and view it from a height where the walls no longer exist. The higher we climb into abstraction, the easier it becomes to overcome the difficulties.
The solution appears when we generalize, because creating concepts opens up new ways of seeing things. This is how he introduced, among other things, schemes, toposes, motives, sites and étale cohomology—a wealth of concepts now used throughout algebraic geometry and many other branches of mathematics.
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