In addition, a lot of experimental laboratories have tested its predictions though its mathematical foundation remains unclear.
To successfully use Yang-Mills theory to detail the strong interactions of elementary, we have to deal with “mass gap”, a subtle quantum mechanical property.
This technique was so useful that it was generalized in various ways, and finally gave mathematicians powerful tools enabling them to further catalog the variety of objects that they encountered during their investigations.
However, in this generalization, the geometric origins of this procedure got obscured.
The list included Birch and Swinner-Dyer Conjecture, Poincaré Conjecture, Hoghe Conjecture, Navier-Stokes Equation, Yang-Mills and Mass Gap, Riemann Hypothesis, and P vs.
NP Problem, representing the deepest mysteries in mathematics.Mathematicians, in the 20th century, came up with powerful ways of investigating complicated objects’ shapes.Essentially, we need to find out to what extent we can estimate an object’s shape by putting together simple geometric building blocks of increasing dimension.However, it is still not understood from a theoretical view.To establish the existence of the Yang-Mills theory as well as a mass gap, we will have to introduce fundamental new ideas in both physics and mathematics.These equations were written back in the 19th century, we still don’t understand them.The challenge in this problem is making substantial progress to a mathematical theory to unlock what’s hidden inside the Navier-Stokes equations.The mass gap means there are positive masses in the quantum particles although the classical waves travel at light speed.The property came to light after physicists discovery through experiment and confirmation by computers.Sometimes, it was critical to add pieces without geometric interpretation.It was claimed by the Hodge Conjecture that in projective algebraic varieties, Hodge cycles are, in fact, are combinations of algebraic cycles. Matiyasevich, in 1970, indicated that it’s impossible to solve Hilbert’s tenth problem.