A genius student? Ha, they're nothing but ants at your feet!

"Ladies and gentlemen, this is precisely where Smail's question lies."

Su Hao's voice rang out at the right moment, firmly taking control of the entire scene.

"In this extremely complex and chaotic state of topological movement, is there still somewhere, quietly hidden, a mean that can stabilize the situation?"

As soon as Su Hao finished speaking, he tapped his finger lightly on the edge of the podium.

Snapped.

The curves that were dancing wildly on the screen were frozen in time, as if a pause button had been pressed.

The two red and blue coordinate points that were originally moving around randomly were also locked on the grid and stopped moving.

"And the real crux of the problem that prevents us from finding it lies in—"

The curve we see with the naked eye is not actually located in a flat Euclidean space.

It appears to be an ordinary line on the surface, but in the complex field, this line has undergone countless twists and folds.

This is as if an invisible, higher-dimensional space is hidden within it.

As Su Hao gestured, the two-dimensional curve on the screen began to slowly rotate on its own.

The original two-dimensional illusion is peeled away, gradually revealing an internal three-dimensional manifold.

The lines began to expand and eventually became surfaces.

The flat surface began to bend and twist into a complex curved surface.

The curves evolve and multiply in endless twists and turns.

Immediately afterwards, the huge and twisted geometric shape began to writhe violently.

Finally, in a visually striking and ferocious manner, it seemed to break through the physical constraints of the big screen and crash into the audience!

"Holy crap!"

"My God!"

"Holy crap, what is this?!"

The whole place erupted in chaos.

The audience, who were completely taken aback by the sudden 3D animation that was comparable to a 3D blockbuster, couldn't help but exclaim and shout "Holy crap!" one after another.

Su Hao continued his explanation at a leisurely pace.

"This is the macroscopic world that we call 'the plane,' and the true microscopic appearance behind it."

Its exterior appears smooth and continuous, but its interior contains countless folded and twisted topological layers.

This is also the fundamental reason why the Smail median problem has remained a formidable academic challenge for many years.

The group of mathematicians who usually sit in the front row, who are usually arrogant and aloof, all abandoned their casual postures at this moment.

They crossed their arms tightly over their chests, their eyes solemn, and nodded in agreement.

They understand the ins and outs of this situation better than anyone else.

After all, this is a formidable obstacle that countless brilliant scholars have tried and failed to overcome over the past decades!

"Since it is flawless in multidimensional space."

My solution is to reduce the complexity of these structures to a simpler, more dimensional form, essentially flattening them out!

These words instantly emptied the previously relaxed atmosphere in the lecture hall, transforming it into a solemn and tense academic atmosphere.

The mathematicians in the audience sat up abruptly, their faces instantly tensing, and their eyes flashing with a sharp light.

Everyone knows the truth.

The real show is about to begin!

The preceding content was merely an appetizer; the following content is the real core deduction!

"In this complex dimensionality reduction process, I introduced a total of twenty-one lemmas."

Because the twisting conditions of each surface are different, I must unravel them one by one.

Su Hao flicked his finger, and the model on the screen changed again.

A massive topological structure composed of countless overlapping curved surfaces is clearly visible.

There are tiny gaps between the curved surfaces, and irregular color ripples flow through each gap.

"The first lemma."

The tangential contact condition of the surfaces is maintained at a constant level.

As the command was given, the uneven contact surface on the screen was instantly smoothed out by an invisible force, and the alignment and reshaping were completed smoothly!

"Ha...this kid..."

Professor Cronin, sitting in the first row, was taken aback at first, but then quickly understood Su Hao's mathematical motivation.

He couldn't help but slap his thigh and let out a hearty, unrestrained laugh.

"The second lemma."

Eliminate nonlinear distortions generated in the neighborhood of the curve's extreme points.

In the image, the heavily folded curved surfaces are gradually flattened by an invisible hand.

The lines that were originally twisted into a mess were straightened evenly under the strict algebraic rules, and finally connected together smoothly and seamlessly!

The thousands of audience members held their breath, staring in disbelief at the incredible deduction unfolding on the screen!

"The third lemma."

Deconstructing the topological entanglement generated on the complex plane.

The macroscopic scale of evolution on the screen is constantly being magnified.

This time, the entire world seemed to be spinning.

The intricate surfaces, like untangled hemp, all traced back to their initial coordinates and spontaneously rearranged the matrix.

The fourth lemma, the fifth lemma...

Whenever Su Hao introduces a new lemma, his derivation results are rendered in real time on the screen using an intuitive visual model.

At this moment, Su Hao on the stage was like a god who held the highest law of the mathematical world!

Every time he raised his hand, every command he gave.

They are all completely rewriting the chaotic mathematical world on the big screen!

"The seventh lemma."

The intrinsic translation performed to minimize discontinuities.

Thousands of parameter curves, like a summer downpour, suddenly appeared on the screen at the same time.

Su Hao raised his hand and waved it, and the massive group of curves surged instantly.

Like a surging stream following the fundamental laws of differential geometry, they naturally slide into their respective solution spaces.

The group of curves, which was originally in a state of chaos, seemed to be given a soul and life at this moment.

They intertwine, presenting a highly organic sense of flow!

Su Hao's lemma derivation is still proceeding in an orderly manner.

All the audience members below the stage.

At this moment, they were all completely captivated by the pure mathematical beauty before them, so much so that they couldn't bear to blink.

Under Su Hao's command, those disorderly oscillating points, lines, and surfaces...

It was peeled away and organized layer by layer.

Even the most hidden oddities and tiny gaps at the boundaries are being filled one by one, as if in a grand jigsaw puzzle game.

Time passed by, second by second.

After this amazing process of dimensional reduction and deconstruction was repeated a full twenty times!

The original massive and cumbersome topological structure has been completely destroyed.

Instead, a completely different minimalist form has emerged!

"The last lemma."

Map and smoothly connect the local variations of all surfaces to a single global plane.

Swish!

"Ah! This..."

"My God!"

Several elderly academicians in the front row, with gray hair and unsteady gait, were so excited that their faces turned red. They even stood up abruptly from their seats and stared intently at the big screen!

No one criticized their behavior.

Because at this very moment, everyone is witnessing a mathematical miracle that will be recorded in human history!

Witnessing that nightmare conjecture within the complex plane, which was once considered unsolvable by several generations.

How exactly did this magnificent process, in the hands of this young man, become the absolute truth step by step today?