Functional analysis, scientific computing, algebra and mathematical physics.
More specifically: operator algebras, real and complex C*-algebras,
numerical linear algebra, ring theory,
condensed matter physics, topological
Professor Terry Loring
Worries about inventions degrading eductation
"Your invention will enable them to hear many things
without being properly taught, and they will imagine that they have come
to know much while for the most part they will know nothing."
--The god Thamus, as quoted by Socrates, regarding the dangerous
invention of writing.