Alexander Polyakov (a Princeton University theoretical physicist) caught a glimpse into the future of quantum theory back in 1981. There were many mysteries to solve, including the wiggling strings and the binding of quarks to protons. Alexander Polyakov was able to see the future of quantum theory in 1981.He wrote that science has many methods and formulae which can be used to solve seemingly different problems in the introduction of a four-page letter in Physics Letters B. We need to learn how to handle sums on random surfaces.Original story reprinted by permission of Quanta Magazine. This independent publication published by the Simons Foundation has an editorial independence and aims to increase public understanding of science. It covers research developments and trends in mathematics, the physical and the life sciences.The proposal of Polyakov was powerful. He proposed a formula in his paper that described how to calculate averages for a chaotic surface called the Liouville field. This was essential for understanding the behavior of theoretical objects called strings, and creating a simplified model explaining quantum gravity.Polyakov would struggle for years to find solutions to other theories of physics. However, he didn't fully understand the mathematics behind the Liouville fields.A group of mathematicians have accomplished what many scientists thought impossible over the past seven years. They have published a trio of important publications that recast Polyakov's formula in fully rigorous mathematical language. This has proven that the Liouville field accurately models the phenomenon Polyakov believed it would.Vincent Vargas, a French mathematician and coauthor of the research, shared that it took 40 years to understand four pages. He was a member of the French National Center for Scientific Research.These papers bridge the gap between mathematics and physics by breaking new ground within probability theory. The paper also addresses philosophical questions about the objects that are central to the most popular theories of fundamental physics, the quantum fields.This is a great example of mathematical physics, according to Xin Sun, a University of Pennsylvania mathematician.Infinite FieldsToday, fieldsobjects that fill space and take on different values depending on where they are located are the key actors in physics.A single field in classical physics tells you everything about the force pushing objects around. Consider Earth's magnetic field. The movement of a compass needle reveals the influence of the fields (its strength, direction) at each point on the planet.Quantum physics also has fields. The quantum theory's deep randomness makes matters more complex. Quantum theory says that Earth does not generate one magnetic field but many. While some may look similar to the classical physics field, others are completely different.However, physicists want to make predictions, which are predictions that match exactly, in this instance, what a mountaineer sees on a compass. The difficult task of quantum field theory (QFT) is to combine the many forms of a quantum field into one prediction. This model shows how one or more of the infinitely variable quantum fields interact and act.QFTs are the fundamental language of particle physics, thanks to a lot of experimental support. One such QFT is the so-called standard model. It depicts fundamental particles like electrons, which are fuzzy bumps formed from an infinite number of electron fields. Although it has passed all experimental tests, other groups might be close to finding the first holes.Many QFTs are used by physicists. Others, like the standard model of physics, strive to model real particles moving through four dimensions of the universe (three spatial dimensions plus one time dimension). Other describe exotic particles in bizarre universes, ranging from two-dimensional flatlands down to six-dimensional super-worlds. Although their connection to reality is distant, physicists continue to study them in order for them to be able provide insight into our world.