Free Web NovelChapter 913: Chapter 468: You Motherf... Really Are a Genius!_2
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Upon returning to the dormitory, Zhao Yi thought about the International Congress of Mathematicians and felt a slight regret.
The International Congress of Mathematicians was an excellent venue for mathematical exchange, bringing together the world’s top mathematicians. He had gained a lot from his visit four years ago; the mathematical presentations there always had some eye-catching highlights or brought some inspiration.
"It seems like it has been a long time since I’ve studied mathematics."
"Normally the Fields Medal recipients would be invited to give a talk at the conference. Or maybe I could have asked Fan Lei to give a talk on my behalf?"
Zhao Yi thought about it and then shook his head.
Fan Lei?
Give a lecture? frёeweɓηovel.coɱ
The guy couldn’t even understand research papers, let alone present one. Perhaps even if he were to read from a paper, there would be some symbols he wouldn’t understand, leading him to read the content incorrectly.
Moreover, it had indeed been a long time since he had studied mathematics, and he didn’t have any results to show for it.
As the thought grew in his mind, coupled with some recent downtime while waiting for the Aviation Group’s acceptance, he unconsciously pondered mathematics.
He quickly remembered a topic—Yang-Mills Existence and Mass Gap.
While researching the Boundary Theory of particles and shaping the energy composition of spectating particles, Zhao Yi had taken an interest in the ’Yang-Mills Existence and Mass Gap’ problem.
It was an extremely complex issue in mathematical physics.
Yang Zhenning and Mills conducted research in mathematical physics together, aiming to describe the behavior of fundamental particles with the mathematically unifying core forces of electromagnetism, weak force, and strong force.
In the theory of electromagnetism, overall gauge symmetry corresponds to charge conservation, and if this overall gauge symmetry is also required to hold locally, the entire electromagnetic theory can be obtained.
So the question arose.
What if this idea was extended to other fields? For example, the strong and weak forces? Is it possible to likewise impose some overall symmetry locally to directly generate the relevant theories of the strong and weak forces?
This is the famous non-Abelian gauge field theory, also called Yang-Mills theory.
Yang-Mills theory is generally considered to be an important achievement beyond the discovery of parity non-conservation laws, that is, beyond Yang Zhenning’s Nobel-winning work.
In current quantum physics, the strong force is described using Yang-Mills theory. Quantum physics has theoretically unified weak force and electromagnetism, and the unified electroweak force is also described using Yang-Mills theory.
The Yang-Mills Existence and Mass Gap problem, one of the Millennium Prize Problems, originated from Yang-Mills theory. The formal statement of the problem is: Prove that for any compact, simple gauge group, the Yang-Mills equations in the four-dimensional Euclidean space have a solution that predicts the existence of a mass gap.
This problem is related to the basic explorations of gauge particles and clarifies aspects of nature not yet fully understood by the physics community.
The reason Zhao Yi thought of this problem was mainly because the Yang-Mills problem is related to the Boundary Theory of particles. Yang-Mills theory describes the relationships in microscopic standpoints’ interactions through symmetry and mathematical equations, while the Boundary Theory of particles explains the origins of microphysical phenomena through the energy composition of particles.
As descriptions of the principles behind microphysics, both inevitably have many overlapping areas.
If one delved further into the exploration of the energy composition of particles, it would inevitably lead to field force issues and necessarily involve Yang-Mills theory, and perhaps even the proof of the theory.
Zhao Yi hoped to conduct further research. His study of particle mathematics, like other theoretical physicists, aimed to achieve the unification of the four fundamental forces.
After thinking deeply for several days, he still temporarily gave up on the research of the Yang-Mills problem, mainly because he had not laid a solid foundation. Solving this problem would require more than a short period of research.
It was much more complex than solving the Goldbach Conjecture or Fermat’s Last Theorem.
During the continuous contemplation process, he noticed another issue and immediately became interested.
Because of "Derivation Law".
Zhao Yi now had a good understanding of "Derivation Law", and he found it to be a very effective ’logical deduction’ ability. Unlike normal logical thought processes, "Derivation Law" could find the ’most likely’ pathway based on given conditions instead of listing many possibilities.
This ability was useful for research and development, and it seemed to be very helpful in solving mathematical problems too.
Zhao Yi wanted to truly test the application of "Derivation Law" and found an excellent logical deduction problem—
The NP-complete problem.
It was the first of the seven Millennium Prize Problems.
The mathematical community was interested in the NP-complete problem mainly because it was a pure logic issue.
The correct statement of the NP-complete problem is: NP=P?. Whether P (deterministic polynomial-time algorithms) applies to NP (nondeterministic polynomial-time algorithms)—the problem’s statement seems complex, but a simple explanation makes it clear.
NP stands for nondeterministic polynomial-time algorithms.
Some problems can be directly solved with a formula, while others cannot.
For example, what is the next prime number?
The answer to this problem can only be found through guesswork and verification, verifying that a certain subsequent number is prime amounts to solving the problem.
