>>10834031Academia successful(big industrial money, high grant research, new horizon for science with experiments)
Quantum field theories, Gauge theories,condensed matter physics, mathematical biology, particle elemental, neutron/light transport, fluid mechanics.
Math Use in Academia successful
Sympletic geometry/topology, Functional Analysis / operator theory, PDE on Riemann geometry, lie algebras, K-Theory, non-commutative geometry, Geometric Analysis.
Pure(no applications) Hard Math but Academia approved
Langrans program, algebraic geometry, arithmetic geometry, algebraic K-Theory.
Academia Autism(No Applications in real world, some people say are complete fraud or impossible)
Quantum computers, String Theory.
Academia Math Autism (New fundaments mathematics / abstractions, math community found it worthless)
Higher topos theory, Higher Algebra, anabelian Geometry, Type Theory.
Math Higher Autism(Only few people believe is real)
Inter-universal Teichmüller theory
https://en.wikipedia.org/wiki/Inter-universal_Teichmüller_theory