A few things struck me after reading Isaacson’s biography of Einstein. Someone who comes up with a unified field theory would need both a very wide and deep understanding of all 4 forces (Strong, Electromagnetic, Weak and Gravity) and have an intuitive/uncommon ability/feel for the interaction of these forces on each other. Moreover, that person would need the right mathematics to solve a unified field theory equation. Without Riemann’s tensor analysis that wouldn’t have been possible.
“By imposing metrics on manifolds Riemann invented differential geometry and took non-Euclidean geometry far beyond his predecessors. Riemann’s other masterpieces include tensor analysis, and the theory of functions. His generalized notions of distance and curvature described new possibilities for the geometry of space itself. Several important theorems and concepts are named after Riemann, e.g. the Riemann-Roch Theorem, a key connection among topology, complex analysis and algebraic geometry. He was so prolific and original that some of his work went unnoticed (for example, Weierstrass became famous for showing a nowhere-differentiable continuous function; later it was found that Riemann had casually mentioned one in a lecture years earlier). Like his mathematical peers (Gauss, Archimedes, Newton), Riemann was intensely interested in physics. His theory unifying electricity, magnetism and light was supplanted by Maxwell’s theory; however modern physics, beginning with Einstein’s relativity, relies on Riemann’s curvature tensor and other notions of the geometry of space.”