Chapter 1109 Final Stage
Lu Zhou had no idea that his project had become a betting war between two old men.
If he had known about this, he would definitely make a bet himself.
After Lu Zhou stopped Dean Qin from hosting a farewell ceremony, he and w.a.n.g Peng drove Faltings and Schultz to the airport. Then, Lu Zhou returned to his Zhongshan International mansion.
On the other hand, Schultz had gone through the airport security check and boarded the plane. He put on his seatbelt and looked outside the window, as if he was thinking about something. He saw the ground slowly disappear from his sight as he spoke.
“Time is flying by, I can’t believe I’ve stayed here for a month already.”
Professor Faltings, who was sitting next to him, wasn’t interested in talking about the pa.s.sage of time. Faltings had closed his eyes and spoke.
“We have to work hard when we get back.”
Schultz smiled and said, “Of course.”
Geniuses were often proud and arrogant people.
Schlutz was one of them.
In fact, the reason he was going back wasn’t only because of his students; he could have easily contacted his students via the Internet.
The real reason…
He was certain Lu Zhou knew the real reason.
On the final stage of heroism, it wouldn’t make sense to form a hierarchy structure; there was only one person who would be remembered by history.
While the initial non-creative work had already been done.
As for who could put down the final tile, the most difficult tile…
That would depend on individual talent.
Everyone knew this.
This was a compet.i.tion.
Even though Schlutz knew the odds of him winning were slim, he still wanted to give it a try.
He knew that Professor Faltings had the same idea.
Schultz felt the adrenaline rus.h.i.+ng in his chest as he squeezed his fist.
“… This is getting me excited.”
…
The plane back to Germany was lost in the sky.
Lu Zhou, who was back home, was sitting in his study room.
Just like Professor Schultz, Lu Zhou was also full of adrenaline.
However, it was for a different reason.
“Finally, this is the last step…”
Lu Zhou looked at the draft papers on his table and the fully-written whiteboards next to his bookshelves. He took a deep breath and smirked.
There was only one step left to unify algebra and geometry.
After that, he would enter the world of level 10 mathematics.
According to the rewards of the legendary mission, the Void Memory would reveal secrets about the system.
He was full of excitement!
Lu Zhou reached out and picked up a pen. He then looked at a blank piece of draft paper and thought back to his conversations with Perelman and the others over the past month. He began thinking about this final proposition.
Abstract geometry was an insanely complicated thing.
Most people wouldn’t even be able to learn geometry, much rather less do research.
After all, the abstract meaning behind numbers could be changed by modifying the number base, but the abstract form of geometry couldn’t be described with just a few words and symbols.
Not only did it require creative thinking, but it also required a strong spatial imagination and an understanding of abstract concepts.
Therefore, the unification of numbers and geometry was a proposition that combined different abstract concepts.
Take the simple one-variable polynomial with an obvious geometric explanation as an example.
Its dimension was 1, which meant it was a curve. But if one considered its complex form, its dimension was two, making it a surface.
The contrary was also true.
Grothendieck’s theory gave a complete framework. He believed that in some sense, integers were curves, while each point on the curve would respond to a prime number.
His theory was successful, and combined with the topology tools he created, he was able to derive many useful methods and mathematical proofs, which could solve many algebraic geometry problems.
When Witten was studying string theory, he tried to use the Jones polynomial to explain the Chern–Simons theory, which greatly inspired him.
This was the reason M-theory was born.
What Lu Zhou was doing now, was to expand this framework and extend it to the entire field of algebra and geometry, covering the Langlands program, motive theory, and even coh.o.m.ology theory…
This meant the birth of a new mathematical foundation!
While Grothendieck’s standard conjectures would have predicted half of the new foundation.
As for the other half, they were so complex no one dared to think about them.
[Let X be a non-singular projective cl.u.s.ter on the algebraic closed domain k. When we take k→C, we get a complex manifold X(C)…]
Lines of equations were written on the page, giving a simple outline of the proof framework.
Lu Zhou looked at the page and mumbled to himself quietly, “Abstract all coh.o.m.ology into a geometrically composed set, subst.i.tute Cq(D,k) corollary 4, by using the Fold method…
“The geometric figures abstraction set forms a map to n.
“… This is the most likely solution.”
There was a s.h.i.+ne in his eyes as his pen suddenly began to move.
The traces of ink were like rivers, converging onto the ocean of paper, turning into beautiful mathematical calculations.
Time quickly pa.s.sed by.
Sounds of the pen gliding on the paper were heard.
Lu Zhou was in a flow state. He had totally forgotten about the pa.s.sage of time or even his own existence. He was absorbed in the ocean of mathematics.
It was almost like he wasn’t completing a proof.
It was almost like he was writing a symphony about the universe.