Graph, Wall, Tome

The Graph

Ed Witten concisely described present knowledge of physics in one paragraph from his 1987 essay Physics and Geometry.

If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Space-time is a pseudo-Riemannian manifold \(M\), endowed with a metric tensor and governed by geometrical laws. (ii) Over \(M\) is a vector bundle \(X\) with a nonabelian gauge group \(G\). (iii) Fermions are sections of \((\hat{S}{+} \otimes V_{R}) \oplus (\hat{S}{-} \otimes V_{\tilde{R}})\). \(R\) and \(\tilde{R}\) not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference \(\Delta\) in some underlying theory. All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to interpreted in quantum mechanical terms.

Edward Witten, Physics and Geometry

The Wall

Jim Simons commissioned a stone wall at Stony Brook to display history’s most important equations.

The Tome

Sir Roger Penrose wrote an extensive book to provide an overview of physics and its mathematical roots.