often we think : are new fundamental concepts being developed in Math ?
the answer is affirmative. Here is a quote from Prof. Alon Amit :
New mathematical concepts and principles are invented every week. Most are minor, some very much so. A few are important. Even fewer are found to have a legacy that lasts years.
A few random examples:
1. Floer homology was born around 1988. Its inventor, Andreas Floer, committed suicide three years later, but his theory is very much an active field of research.
2. The Jones Polynomial was discovered in 1984 by Vaughan F. R. Jones and completely revolutionized knot theory, low-dimensional topology and significant portions of theoretical physics.
3. Related to that, Chern-Simons theory was introduced in 1974.
4. Train tracks were invented in 1992 by Bestvina and Handel. They are important tools in the study of surface homeomorphisms and free groups.
5. Grigory Margulis came up with the genius idea of building expander graphs from Lie groups with property T. This was in 1975, and the principle he laid down is still being studied and developed.
6. In the theory of computation, Probabilistically checkable proofs were invented in 1990 (implicitly) or 1992 (explicitly).
7. Vertex operator algebras were defined by Borcherds in 1986.
8. Oded Schramm discovered the Schramm–Loewner evolution in 2000. It is a central object of study in modern probability theory.
Although fundamental, they are not so much easy to understand. So we should not run after them.
