On I.M. Gelfand from A. Dynin
In 1954 Gelfand, fresh from the atomic project, was in the height of his creative powers. In particular, he was very enthusiastic about infinite-dimensional Schwinger variational equations of quantum field theory. He got an idea to approximate their solutions using lattice approximations by solutions of partial differential equations of increasing finite dimensions instead of finite difference equations! This method was announced in Gelfand-Minlos Doklady note "Solution of quantum field equations" the same year reprinted in Gelfand Collected Papers, Volume 1, 462-465, Springer, 1987.
Famously Gelfand presented his idea at the Landau Seminar at the Institute of Physics Problems to be completely demolished. Landau claimed that, for starters, that mathematical idea was physically useless, and also not new since it was a version of Feynman path integral. Actually, the latter was just a consolation prize since Landau did not care about Feynman path integral whatsoever.
Nevertheless I. M. was proud of the independent discovery and told me about it 40 years later when I invited him to a conference in Ohio state university.
There were no follow up publications promised in that Gelfand-Minlos note. However, this idea has been realized via second quantized Galerkin approximations in my recent solution of the Yang-Mills Millennium problem in the framework of nuclear Gelfand-Kree triples.
In some sense this is a fulfillment of Gelfand’s prophecy given by him at the 1956 Functional Analysis conference at Moscow State University. In his plenary lecture on problems and perspectives of Functional Analysis, Gelfand proclaimed the great future for Grothendieck nuclear spaces and von Neumann operator algebras.
--Alexander Dynin, December 2012
From Natalia Zamolodchikov December 2009
Words on the Epoch of Gelfand Anatoly M. Vershik, October, 2009
Biographic Sketch Simon Gindikin, 1991
A Tribute to I. M. Gelfand for His 80th Birthday I. M. Singer, 1993
from Doron Zeilberg Rutgers University (October 6, 2009)
from A. Zelevinsky (October 6, 2009: in Russian only)