(The remaining 4 problems seem to be outside the scope of SS.) It is of utmost importance to note that the nature of the ideas and consequently of the solutions is very radical and it would take painstaking efforts to fully understand and appreciate the solutions proposed. Also it has to be considered that according to Conmathematics (Conceptual Mathematics) : the superultramdoern mathematical science, the superultramodern scientific solutions to the problems are, though apparently philosophical, in fact, mathematical. Virtually all of the 3 problems are such that they demand revolutionary changes in the current (modern/ultramodern) sciences. And SS is thought to be an appropriate change. I shall state the problems exactly as they are stated on the website of the CMI. However, the statements are the ones which are brief and not the ones that are official and descriptive. This choice is out of the revolutionary nature of the solutions which makes it senseless to consider the conventional or orthodox symbolic patterns which essentially make the (official) statements look complicated and descriptive.
1. Yang - Mills Theory
The laws of quantum physics stand to the world of elementary particles in the way that Newton's laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics.
SS solution :
I suppose that light, for example, is a classical wave and photon, for example, is a quantum particle. It