The Courtyard House: Xu Damao's Aunt is the Queen of Women

But the little queen is a bit upset!

Looking at Liu Hao and He Xiaomeng, there was a familiar feeling, a familiar feeling. When the older sister was studying mathematical problems with Liu Hao, wasn't she just like that?

He Xiaomeng only thought for a few seconds, her long eyelashes trembled, and she answered immediately.

"The essence comes from the symmetry of the functional equation of the zeta function, which is deeply bound to the Fourier transform and the Poisson summation formula. At a deeper level, it is the dual structure of the prime number distribution and the additive and multiplicative groups."

"The current global deadlock is that it is impossible to establish a strong causal relationship between the critical line and the zero-point distribution, the control methods after analytical extension are insufficient, and there is a lack of unified topological invariants."

The answer was concise, precise, and impeccable.

Liu Hao's pupils contracted slightly; this was the depth of understanding of a world-class mathematician.

He continued to escalate the situation, his tone becoming even more serious.

"So, regarding the Hodge conjecture, what tool do you think is most likely to break through it? Layer theory? Cohomology? Or algebraic topology?"

He Xiaomeng spoke softly as always, yet every word she uttered was precious.

"Using any one of them alone is not enough; we must unify the hybrid Hodge structure, topological K-theory, and probabilistic homology to construct a new closed-chain class correspondence."

"The equivalence between Hodge classes and algebraic classes is essentially the complete overlap of geometric and algebraic structures in high-dimensional space. This path requires redefining cohomology functionals from the bottom up."

Liu Hao fell silent. He Yingjie and Zhu Mei were completely burying a genius!

What a load of rubbish! He Xiaomeng should just become a disciple of Qian Xuesen or Guo Moruo.

He Xiaomeng's understanding of the most cutting-edge framework of modern mathematics has reached the same level as Ye Xi's.

But he wasn't done yet; he turned his attention directly to theoretical physics, this time tackling truly top-tier problems.

"Okay, let's leave the math for now. I have a question for you: In general relativity, besides the exact solutions of the Schwarzschild, Kerr, and Resner-Nordstrom field equations, is it possible for new axisymmetric vacuum solutions to exist? And where does the derivation lead?"

This is a cutting-edge question that even physics professors might not be able to answer.

He Xiaomeng raised her eyes, her gaze clear and firm, her voice still soft and sweet, but the contents of her voice made Liu Hao's heart pound.

"Yes, we can start with the generalization of Kerr's metric, introducing complex structures and twist symmetry to construct spin-symmetric solutions under the vacuum Einstein equations. More importantly, these new solutions can directly correspond to the unified model of angular momentum and charge of black holes, providing a rigorous mathematical foundation for the hairless theorem."

Liu Hao exclaimed "Holy crap!" and decided to leave He Xiaomeng with Teacher Ye Xi and Teacher Guo.

He Xiaomeng's socially awkward and adorable personality is perfect for scientific research.

He took a deep breath and threw out the most cutting-edge and tricky questions.

"The hairless black hole hypothesis, proposed just last year, how do you think it needs to be proven? From which angle can we get it to fruition the fastest?"

He Xiaomeng knew that Liu Hao was testing her, and she also wanted to prove her abilities to Liu Hao.

After a moment's thought, she began to speak clearly and logically.

"Starting with the topological invariants and field equation constraints of steady-state black holes, we first prove that the external geometry of steady-state black holes is uniquely determined by only three quantities: mass, charge, and angular momentum. Then we prove that all higher-order multipole moments are eliminated by the gravitational field itself. Finally, we use differential topology to lock the event horizon topology, thus completing the uniqueness proof."

"Moreover..." she paused, then continued, "This proof can be directly linked to the topological conclusions of the Poincaré conjecture on three-dimensional manifolds, and the mathematical tools are completely interchangeable."

Liu Hao is completely baffled. He has managed to accurately pinpoint the most cutting-edge physics research paths in the world solely through self-study.

He continued to test even more difficult problems in quantum field theory.

He had previously been completely ignorant of this knowledge, having only mastered six out of seven orifices; he had never even heard of it.

It was Ye Xi who showed him the information, like feeding an AI, which enabled him to integrate and master so much knowledge.

"Regarding the divergence problem in quantum electrodynamics, what do you think is the real direction for a solution? Is renormalization alone sufficient?"

He Xiaomeng shook her head: "It's not enough. Renormalization is just a means of processing in effective theory, not a fundamental solution."

"The real way out is to establish a rigorous mathematical foundation for quantum field theory, using operator algebra, functional integration regularization, and topological field theory to unify the three and eliminate the source of ultraviolet divergence, rather than passively canceling it out."

"If it can be combined with the analytical control methods of the Riemann Hypothesis, it is even possible to transform the divergent term into a symmetric term of the zero of the ζ function, thus completely eliminating infinity from the mathematical foundation."

Upon hearing this, Liu Hao was completely shocked.

This can no longer be described as genius; this is the visionary perspective that establishes a new school of thought!

Ye Juan listened intently. She had originally thought that Liu Hao and her older sister were already geniuses, but now she realized that He Xiaomeng, who was usually timid and docile and would only cry when she was wronged, was the real genius buried in the dust.

Having examined the matter to this point, Liu Hao was completely certain that He Xiaomeng didn't just know a little bit; she was a true genius.

He Xiaomeng asked cautiously, "Brother Hao, did I say something wrong?"

"No, you're a genius! A prodigy!"

Hearing such high praise, He Xiaomeng hurriedly waved her hand: "I... I can't be considered a genius at all, Brother Hao, don't flatter me."

Liu Hao looked at He Xiaomeng, whose ears were bright red and who looked shy, and couldn't help but laugh.

Just moments ago she could calmly discuss world-class problems with him, but now she has reverted to that soft-spoken, timid little girl, afraid of saying the wrong thing.

This contrast is so adorable! No wonder the little queen likes to tease her.

"Brother Hao, I...I was just...thinking about it randomly in private...Did I...say something wrong...? Please don't look at me like that, I'm a little scared..."

When He Xiaomeng saw Liu Hao and Ye Juan staring intently at her, she nervously clenched her hands together, her beautiful face filled with helplessness, like a frightened kitten, completely different from the genius who had just been pointing out the flaws in the world and hitting the pinnacle of mathematics and physics.

Liu Hao stepped forward, his voice carrying for the first time an undisguised solemnity and appreciation.

"You are absolutely right, not a single word is wrong. Every problem, every path, and every framework you mentioned is the most cutting-edge, core, and unsolvable breakthrough in the international academic community today."

"I'm testing you so much not to make things difficult for you, but to confirm one thing."

Liu Hao looked at He Xiaomeng with a serious and intense gaze.

"You are a peerless genius in both physics and mathematics who was buried in the steel rolling mill. Your talent is no less than Sister Xi's, and you are even better in terms of a systematic view of physics."

Ye Juan also came to her senses and grabbed He Xiaomeng's hand.

"Xiaomeng, my goodness! You've been hiding this so well! How is your brain even structured? You actually understand all that difficult stuff!"

He Xiaomeng blushed even more from the praise, lowered her head and whispered, "I just...like...reading books when I have nothing to do...I'm really not that good..."