First relationship between geometry and physics appeared with the invention of General Relativity, theory of gravitation. It was realized that equation of motion for the gravitational field coincides with the curvature tensor of Riemannian geometry equal to zero. Then it was realized that equation of motion for a particle interacting with gravitational field coincides with equation of geodesics of the Riemannian geometry with specially chosen metric. Also, it is worth noting that action functional for the gravitational field could not be constructed by the methods of field theory because those methods required to add infinite number of terms to the action in order to get conserved energy momentum tensor. On the other hand geometrization principle gave a simple action; its density is the scalar curvature of the Riemannian geometry. Because of this discovery, that theory of gravitation has its own underlying geometry, gave such a fruitful result as construction of the theory of gravitation, this discovery has been lifted to the so called geometrization principle, stating that every fundamental theory has its own underlying geometry.

Next step was to find underlying geometry for electromagnetism and unify it with gravitation. A. Einstein has been involved in solving this problem. However, he has failed as many scientists who tried to geometrize electromagnetism in the framework of Riemannian geometry.

H. Weyl was the first (1918) who proposed to geometrize electromagnetism in the framework of Riemannian geometry with changing length of the curve. As it is described in the Pauli's book "Theory of Relativity" this theory failed to comply with experiments.

Next (1921) was T. Kaluza (Sitzsungsber. d. Preuss. Akad. d. Wiss (1921) 966), who proposed five dimensional theory, again underlying geometry was chosen Riemannian one. (We note that A. Einstein (as one of the editors of SZ) has published this paper only after keeping it during one year). This theory has unobserved dilaton field and charge/mass problem. As it is noted by T. Kaluza this theory is not applicable even to electrons because of the charge/mass problem.
We notice an attempt to oppose dissemination of new ideas on this direction even by A.Einstein in 1921.

Later, Einstein has been involved in solving this problem ( A. Einstein and Mayer, Berl. Ber. (1931) 541 and (1932) 130, A. Einstein and P. Bergmann, Ann. Math. 39 (1938) 683, A. Einstein, V. Bargmann and P. Bergmann, Theodore von Karman Anniversary Volume, Pasadena (1941) 212, A. Einstein, Ann. d. Phys. 102 (1930) 685). However, his attempts did not give a satisfactory theory.

In 1960, E. Schrodinger made an attempt to solve this problem ("Space-Time Structure", Cambridge University Press, 1960) by adding antisymmetric part to the metric and identifying it with electromagnetic force. This idea also did not lead to a satisfactory theory.

From 1960 to 2002 there were various attempts to solve this problem in the framework of Riemannian geometry with various metrics. Attempts to solve this problem in the framework of the so called Finsler geometry did not give any satisfactory results. It is worth noting that the so called Finsler geometry is actually Riemannian geometry with a specially choosen metric.

Finally, this problem was solved by S. S. Shahvediyev in 2002. He has shown that actually this problem cannot be solved in the framework of Riemannian geometry with any metrics because of the different physical properties of electromagnetic interactions. He proposed a new geometry which is an underlying geometry for Electromagnetism. This theory is formulated in four dimensional spacetime and does not include any additional fields. Using this new geometry a new unified model of electromagnetism and gravitation is proposed which predicts that electromagnetic field is a source for gravitational one.

However, S. Shahverdiyev's works has been suppressed by already established scientists. These are scientists (mostly old ones) who devoted about 20-30 years to solve the same problem using different approaches. I have summarized their attempts to sabotage S. Shahverdiyev's works in a separate page. Take a look to Masterpieces of Charlatanism