Gelfand

Many people consider mathematics to be a boring and formal science.
However, any good mathematics always has in it: beauty, simplicity, exactness, and crazy ideas.

Working as an applied mathematician, I realized the importance of the resolution of singularities while working with non-linear partial differential equations in late 1950s.
I understood that we have to deal with a sequence of resolutions (blow-ups), by changing variables and adding new ones.
So, I was fully prepared to embrace the great result of Hironaka.
We studied his paper for a year.
Hironaka's theorem seems to have nothing to do with non-linear PDE.
But for me it shows the unity of mathematics.
Let me emphasize here that we still do not have a "Hironaka" theory for non-linear PDE.

http://www-math.mit.edu/conferences/unityofmathematics/program.html