Just turned over a new leaf and became a wise and intelligent student

Chapter 430: Ranking of Mathematicians
Deligne actually intended to tell Xu Qingshan that Grothendieck was also coming.

But just now on the other end of the phone, they had a quarrel for a while. The old man was becoming more and more childish at his age, and he insisted that Deligne keep it a secret.

In the old man's own words.

"I want to see if the younger generation can still recognize me after I've been out of the game for so long."

There's nothing I can do because of my seniority.

And Grothendieck is willing to return to politics, which is a good thing for everyone.

You should know that Grothendieck, who is 83 years old, is the only remaining true god of the times among contemporary mathematicians. His historical status can be ranked in the top ten, and his academic status can be firmly in the top five.

It is important to note here the distinction in the ranking of mathematicians' status.

It is mainly divided into historical status and academic status.

The historical status of a great mathematician is generally judged based on three aspects: public influence, expert influence and academic achievements.

For the general public, the most popular thing is the seating arrangement of people in historical positions. The position of the mathematician they admire in this mathematics gathering hall is the key point that makes everyone stand up and speak passionately.

Sometimes, just for the ninth or tenth ranking point, two groups of people would quarrel and start a World War III.

In fact, everyone has their own preferences for the great mathematicians in the history of mathematics.

Especially in the mathematics circle, it is more likely to have fanatical worship of top mathematicians.

However, since mathematics is a very broad subject with many fields and various aspects, there are always many controversies in the evaluation of the status of mathematicians due to the lack of unified standards.

In addition, some mathematicians’ own problems also easily lead to the ranking order.

Just like Lord Bull who dominated the history of human science.

Newton is not only the father of modern physics, but also one of the top three in the history of mathematics. If science is a religion, it is not an exaggeration to call Newton the god of the history of science.

But Lord Niu himself doesn't like mathematics very much.

He is able to rank in the top three in the history of mathematics, and part of his influence comes from his achievements in physics. In terms of academic achievements, although Niu Jueye created the unique calculus, the calculus tool is versatile enough, but the depth, that is, the completion of analysis, is not enough.

Someone may ask here, who has a higher historical status than Sir Alex Ferguson?

If we only talk about the historical status of the field of mathematics, there should be no dispute about the first place.

NO.1 [Gauss]

If you interview an ordinary person and ask him to name a mathematician first, I believe more than half of them will say Gauss's name first.

Gauss is almost synonymous with mathematics.

Hundreds of years of word of mouth, the public's perception of him as a mathematical genius, and his comprehensive strength in depth, breadth and completeness have established his historical position as No. 1.

Gauss's "Discovery of Arithmetic" is the culmination of elementary number theory, the source of algebraic number theory, and the most influential and academically valuable great monograph of the 18th century.

The intrinsic differential geometry of surfaces he discovered inspired the emergence of Riemannian geometry and laid the foundation for the system of differential geometry.

As for the normal distribution in probability theory that Xu Qingshan had done in the early stages of his academic career, those were all relatively minor studies of Gauss.

You should know that before 1840, Gauss had achieved the best results in the four major fields of number theory, geometry, algebra and analysis mathematics at that time.

He is the absolute GOAT, the god who dominates the era.

His comprehensiveness and highly integrated research make him the undisputed number one in the history of mathematics.

Also regarded as the top masters of mathematics, Riemann and Poincare were slightly inferior in the field of algebra, Grothendieck, Hilbert, Noether, Abel, and Galois were relatively weak in geometric topology, Euler did not do enough in terms of overall rigor, abstraction, and standardization, and Cauchy was several levels lower in the importance of his results.

And the subsequent comers only "each" surpassed Gauss in various fields.

It can also be said that Gauss is the last mathematician in the history of human mathematics who dominated his time.

This is why Deligne and his companions are so eager to establish a super school that can accommodate their names.

Because only in this way can they be remembered by history and by mankind.

The Göttingen School, founded by Gauss and developed by Riemann, is a school that has two of the world's top mathematicians. It is the highest hall that many people dream of.

It’s just that Gauss is the mathematician with the highest historical status in human history.

But he has one most fatal and biggest black spot.

That is, he never had an independently created, most important landmark achievement in modern mathematics.

Yes.

The first person in history did not have the top iconic achievements that he independently created.

We can count the most important landmark achievements in modern mathematics, including Riemann geometry, non-Euclidean geometry, group theory, complex analysis, theory of elliptic functions, theory of complex variables, rigorous foundations of analysis, etc.

Neither is completely determined by Gauss.

Even in the field of number theory, where Gauss is recognized as the strongest, all his works on number theory combined are not as important as Riemann's, which only has eight pages of Riemann hypothesis.

of course.

Now the No. 1 status in number theory is waiting to be refreshed.

Xu Qingshan successfully solved the Riemann hypothesis and proposed new mathematical tools, although he cannot have the same historical status as Riemann simply by solving the Riemann hypothesis.

We can only mention the field of number theory and the special proposition of the Riemann hypothesis.

Xu Qingshan has successfully matched that thousand-year-old genius. As long as he can propose the next future proposition of number theory based on the Riemann hypothesis, he will undoubtedly become the number one person in number theory in ancient and modern times.

The reason why Riemann is great is not just because he proposed the Riemann hypothesis, but more because of the various contributions he made to the entire mathematical community, including Riemann integral, Riemann geometry, Riemann hypothesis, manifold theory, Riemann zeta function and so on.

But in the process of proving the Riemann hypothesis, Xu Qingshan also demonstrated his solid academic foundation in other fields.

He has been recognized worldwide as one of the most intuitive young mathematicians of our time.

Because after being exposed to a mathematical tool in a short period of time, it can successfully find the direction for the expansion and in-depth development of this tool.

This is also why Deligne and others are so optimistic about Xu Qingshan that they even went so far as to bring out old man Grothendieck to support Xu Qingshan.

Because they really saw hope in Xu Qingshan to surpass Gauss.

The transcendence here refers to Gauss before 1840, the Gauss who was invincible in the unified academic world and the leader in four major fields.

Not just in terms of academic level, but also in terms of influence.

They hope that when people in the future mention mathematics, the first name they think of is Xu Qingshan.

Of course, in terms of historical status, Euler, who ranks second, is also regarded as the embodiment of mathematics, just like Gauss.

If we only talk about public influence, Euler can be compared with Gauss to see who has greater influence.

It's just that due to the times, Euler was a little earlier than Gauss, and the current judging criteria are based on the scope of influence of modern mathematics. Therefore, in terms of breadth and depth, Euler's academic influence is inferior to Gauss.

As for the ones following the No. 3 [Lord Niu], they are two ancient Gudens who have risen to prominence by relying on their public influence.

NO.4 [Euclid] and NO.5 [Archimedes].

The reason why the two old Dengs are placed fourth and fifth is out of respect for their historical status.

The two of them can be regarded as the founders of ancient times who laid the foundation for the complete system of mathematics.

Euclid's research has been around for more than 2500 years and still permeates the knowledge base today. The public influence of his mathematical research is the most lasting. In the field of popularizing mathematics, Euclid is second to none. In particular, the creation of the axiom system has become the basis for the theorization of mathematics. Even a slight defect in the parallel axiom in this system directly gave rise to the birth of non-Euclidean geometry, becoming a breakthrough for the explosion of modern mathematics.

As for Archimedes, he is one of the three greatest mathematicians in the world, along with Prince Gauss and Lord Niu. It is impossible that anyone would think that his influence on mathematics is not good, right? The source of the calculus system, the geometry works.
Interestingly.

Mr. Ji is the exact opposite of Mr. Niu, who inherited his great calculus legacy.

Niu Jueye was obsessed with physics and mechanical inventions, and thought they were more interesting than mathematics. However, Mr. Ji thought that mechanical inventions were inferior to pure mathematics, so he didn't want to write a book on mechanical inventions at all.

However, it was this teacher who didn't like mechanical theory who came up with a lot of mechanical inventions that could rapidly promote the development of productivity in human society. The most classic of these is the principle of lever.

I can only say that people are like this.

But a genius is a genius, and a master is a master. Whether it is Lord Niu or Teacher Ji, they have achieved unprecedented achievements in physics and mathematics that are difficult for future generations to surpass.

After leaving the top five, the last five can be regarded as the leaderboard of modern and contemporary mathematics.

If only the current time point is used as the evaluation standard.

The last five are considered to have officially started the academic evaluation stage.

Because such historical status lists are not static.

The closer a mathematician is to modern times, the less advantage he or she has on this kind of list.

Because their research needs to be continuously promoted and developed by future generations, and finally cover the entire world and the entire academic circle.

This is the only way to develop professional influence.

However, compared with their predecessors, Xu Qingshan's generation has another advantage, that is, the advantage of the Internet.

Young scholars like Xu Qingshan, after achieving great academic achievements, can quickly promote his academic achievements and enhance his personal reputation through the Internet and various wide-area media.

At the same time, it can also create real-time academic hotspots around the world.

In the past, if mathematicians wanted to promote their theories and achieve a top academic achievement, they would need to write letters to their friends and submit their papers to various other academies of sciences. Only after a lengthy review and verification would they have the opportunity to stand on the stage of a large conference and promote their mathematical theories to the world's top mathematicians.

The research, development, and finalization of an important academic achievement may take as short as four to five years or as long as several decades.

There are many great mathematicians who, due to insufficient academic completion, could only leave some of their discoveries as manuscripts, and they never completely solved the academic problems they left behind until their death.

Here we have to mention our dear Mr. Gauss again.

After Gauss's death, his students and assistants found his mathematical notes.

If his notes, filled with various conjectures and problems, had been published at the time, they would have advanced the development of mathematics by at least half a century.

Teacher Gao is somewhat obsessive-compulsive and a perfectionist.

He basically doesn't want to publish it unless it is completed to perfection.

But this also shows that Professor Gao’s research in these areas is not deep enough.

And it is very likely that it is because Teacher Gao's energy is too dispersed and he is unable to take care of too many aspects.

In his notebooks, he studied the problem of solving higher-order equations, but later discovered that the credit for group theory belonged to Galois and Abel.

Professor Gao discovered the bi-periodicity of elliptic functions at a relatively early time, but he did not conduct in-depth research and only recorded some ideas. Later, Abel and Jacobi completed their work on elliptic functions to a very high degree and directly opened up a new field!

Gauss explained his ideas on non-Euclidean geometry in his notes, but his simple explanation was far inferior to that of Lobachevsky and Bolyai in terms of academic completion.

The basic geometry problem that Gauss thought would make him bald had already been solved by his student Riemann before he died and before his notes were published.

The least squares method and quadratic reciprocity were also discovered by Legendre during the same period. He also had to share the invention of the normal distribution with others.
Perhaps Mr. Gao's fate is somewhat unstable.

As a result, the current core development directions of modern mathematics have little to do with Professor Gao’s research and the notes he left behind.

Teacher Gao has laid a comprehensive foundation for everyone.

But it was someone else who built the flourishing edifice of modern mathematics on these soils.

Of course, this is not necessarily a bad thing for mathematicians.

This means that they at least have the possibility of surpassing Teacher Gao.

who?

At present, the person who is closest to this goal is Grothendieck.

There is a very interesting data.

The most important breakthroughs in contemporary mathematics all come from Graham's algebraic geometry, including Fermat's Last Theorem solved by Mr. Andrew Wiles and Weil's conjecture solved by Deligne.

So far, more than half of the Fields Medals are directly or indirectly related to Greenspan’s work.

As the greatest mathematician of our time, if no greater mathematician creates mathematical tools and new mathematical ideas that can replace Mr. Greenwich, then a hundred years later, Mr. Greenwich will be able to strive for the No. 1 position.

after all.

This person, like Riemann, was able to directly impact the top ten in the history of mathematics when he was alive.

Moreover, the old man has not yet reaped the benefits of the Internet era.

If Gauss was comprehensive in all fields and the best in his time, then Mr. Ge was the one who took one direction to the extreme.

The ultimate in algebraic geometry, abstraction, and structuring.

When a direction is pushed to its knowable limit, it will have super strong radiation ability, radiating to algebra, geometry, number theory, analysis, topology and so on.

And Xu Qingshan already has such a possibility.

(End of this chapter)