Super God-Level Top Student

The cameras at the venue started following Qiao Ze immediately, projecting the blackboard he was heading to onto the big screen.

Otherwise, except for the people in the first five rows, no one in the back would be able to see the content clearly.

"Yang-Mills Theory describes the dynamics of gauge fields as embodied in the equations satisfied by the field strength tensors of gauge fields. Seeking a direct solution is extremely difficult. Neither the existing mathematical tools nor the subdivision method I previously proved for the existence of solutions to the Yang-Mills Equations are sufficient to complete this task; therefore, another approach must be taken."

To that end, I have designed a rather special algebraic structure, which I have named Super Helical Space Algebra. In order to solve it smoothly, the first step I took was to reinterpret the dynamics of gauge fields within the Super Helical Space Algebra.

So next I need everyone to understand these basic concepts: superspiral gauge covariant derivative, superspiral field strength tensor of gauge fields, source terms of the spatial gauge fields, and several important curvature parameters that only work in superspiral space..."

Without deliberately quieting the room, when Qiao Ze began to write on the board and start introducing his latest research findings, the noisy venue instantly fell silent, with everyone's eyes fixed on the large screen.

Especially those bigwigs in the front row...

At that moment, it felt like their brains were exploding!

Indeed!

It was new mathematics!

Of course, this only seemed reasonable.

Because any known mathematical tool had already been tried by the mathematicians attracted by this proposition, it was simply not possible to solve the problem.

But Super Helical Space Algebra?

Wasn't that an enormous leap?

"Alright, having understood these mathematical concepts, we can now transform the Yang-Mills Equations, much like the familiar Fourier transform. This step is very simple. The transformed version of the original Yang-Mills Equations in superspiral algebra space is as follows:

[ D_\\mu F^{\\mu\\nu}+\\alpha \\nabla_\\mu(\\beta F^{\\mu\\nu})= j^\\nu ]."

...

The mathematical heavyweights in the audience stared blankly at the derivation process on the big screen.

Many of them seemed to have recaptured the feeling they had when they were in school.

The only problem was that the vast majority of them were past the age of learning, with a clearly severe decline in the capacity to absorb new knowledge. Qiao Ze on stage had no intention of accommodating these elderly folks; he not only wrote rapidly but also couldn't be bothered to add an extra sentence to something that could be explained in one.

As for the many students attending today, their brains were still young and should have been able to keep up with the pace, but the problem lay in their serious lack of knowledge.

Even though Super Helical Space Algebra was a brand-new field of algebra, this field was built upon the foundation of algebraic geometry known to predecessors.

Without a profound understanding of subjects such as Hilbert space, the Hamiltonian in quantum mechanics that describes the system, topological matter studies, topological insulators, etc., it's also very difficult to comprehend these so-called "simple concepts" within the Super Helical Space Algebra.

Especially regarding computations in ultra-high dimensions, conducting higher-order multiplication operations in superspiral algebra space is highly abstract.

Regrettably, Qiao Ze might be an exceptionally distinguished scholar, but he certainly was not a competent professor, he didn't even care whether the audience below could understand what he was talking about.

"Next are several important formulas regarding Super Helical Space Algebra, starting with the Taylor expansion of the Super Helical Derivative. Assuming (D) is the superspiral derivative operation in superspiral algebra space; then for any smooth function (f), the Taylor expansion of the superspiral derivative can be written as:

[ f(x +\\delta x)= f(x)+ Df(x)\\delta x +\\frac{1}{2} D^2f(x)(\\delta x)^2 +\\ldots ]

Here, (D^2) represents the second order of superspiral derivative. From this, we can calculate the superspiral expansion of the field strength tensor:

Considering the gauge field (A^\\mu) in superspiral algebra space, whose field strength tensor is (F^{\\mu\\nu}= D^\\mu A^\\nu - D^\\nu A^\\mu), the superspiral expansion of the field strength tensor can be expressed as:

[ F^{\\mu\\nu}(x)= F^{\\mu\\nu}_0(x)+ D F^{\\mu\\nu}_0(x)\\delta x +\\frac{1}{2} D^2 F^{\\mu\\nu}_0(x)(\\delta x)^2 +\\ldots ]

Here, (F^{\\mu\\nu}_0) is the initial field strength tensor of the gauge field. Next is the curvature tensor expansion in superspiral space; considering the curvature tensor (R) in superspiral algebra space, it can be expressed as the commutator of superspiral derivatives. Hence, the expansion of the curvature tensor can be written as:

[ R(x)= R_0(x)+ DR_0(x)\\delta x +\\frac{1}{2} D^2R_0(x)(\\delta x)^2 +\\ldots ]

Here comes the crucial part, (R_0) is the initial curvature tensor in superspiral algebra space. Next, we will perform differential operations on the superspiral field according to these formulas, thereby yielding this result:

[ Df(x)=\\lim_{\\delta x \\to 0}\\frac{f(x +\\delta x)- f(x)}{\\delta x}]...
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Swoosh swoosh swoosh...

As Qiao Ze rapidly wrote a series of expansion formulas on the board, the audience finally became noisy again.

"My God... I want to protest! Can't he speak more slowly?"

As soon as one person started shouting out suddenly, it immediately drew many voices of agreement.

"No, it's not a matter of speaking faster or slower! If you want people to understand such a new mathematical system, you shouldn't start with examples that are so difficult! It should go from easy to hard!"

"Yeah, can't we start with a few simple examples? Why analyze the Yang-Mills Equations right away? Why not start from single-variable nonlinear equations?"

Some shouted out without regard to the rules, while others took the opportunity to whisper among themselves.

"Daniel, do you understand?"

"I think this report is not fair to people of our age!"

"Well then... Edward?"

"There's only a thin line between understanding and not understanding math, my advice is, first take pictures of these processes."