184.

Starting from the 2001st floor, Cheng Li is actually working hard.

Because he had to get to the 3000th floor before the battle.

And this left him with only about 21 hours.

It is undoubtedly difficult to reach the 3000th floor in 21 hours.

Starting from the 1500 floors, the difficulty of the math problems in each subsequent layer increases dramatically.

In the end, Cheng Li sometimes has to be stuck for half an hour for a question, which is also normal.

But fortunately, most of the questions are barely within the scope of Cheng Li's ability.

Moreover, the greatest luck is that after the baptism of epiphany on the 2000th floor, Cheng Li's understanding of mathematics and his mathematical skills have also been greatly improved and improved.

I'm afraid Cheng Li didn't expect that his current level of mathematics can be comparable to some high-level mathematicians before his crossover.

Even some mathematicians don't have a solid foundation.

After all, Cheng Li has gone through, from the 10th century BC to the modern 21st century, the entire history of mathematics, the baptism of thousands of questions, and the condensation of epiphany.

There is even that mysterious information, which brings Cheng Li endless inspiration.

This is the real reason why the level of mathematics has improved by leaps and bounds.

With such a huge improvement, Cheng Li can overcome obstacles in the sea of increasingly difficult questions after the 2000th floor, just like in a muddy swamp, moving forward with difficulty.

More than 2,000 questions have been done, and Cheng Li also has a summary of the distribution law of the question bank of this arithmetic tablet.

The question bank of the arithmetic tablet, from the low level to the high level, is also getting more and more difficult, and the more difficult the questions are in the back, and the difficulty of each question is also increasing.

At the lower level in the front, there may be more than a dozen questions of the same type.

However, after the 2000 layer, the questions of each question are highly condensed and highly generalized, and have the characteristics of typical problems in a certain field.

Since the development of mathematics on the earth has always been linear, the level of the entire mathematical community has increased with the passage of time.

So in fact, the question bank that Cheng Li randomly got this time is completely the history of the development of mathematics on the earth.

The first - 500th floors are ancient Chinese mathematics before the 14th century AD.

Floors 501-999 are the 14th-16th centuries A.D., European Renaissance mathematics.

Floors 1000-1500 are mathematics in the 17th century, starting with the creation of calculus.

Floors 1501-1999 are the 18th century AD, the mathematics of the analytical era.

And the 2000th - 2500th floors are about mathematics in the 19th century.

Mathematics in the 19th century was a period of nirvana in the history of mathematics.

At the end of the 18th century, there was a lot of pessimism in both mathematics and physics.

At that time, in the field of physics, many people thought that they had studied almost all the natural physical energy, and the rest was just a matter of tinkering. Some even think that physicists may not have anything to do in the future.

From the current point of view, this is undoubtedly a kind of thinking of sitting in a well and watching the sky.

Mathematics has always been closely linked to physics, so this pessimistic thinking of physicists has also spread to mathematics.

So much so that the famous mathematician and physicist Lagrange wrote to D'Alembert in 1781: "It seems to me that the mine of mathematics has been dug very deep, and unless new veins are discovered, it will be abandoned...... It is not impossible that the situation of mathematics in the Academy of Sciences will one day become the same as that of Arabic in the universities today. ”

A report from the Collège de France also "predicted" that "in almost all branches of mathematics, people are held back by insurmountable difficulties." Refinement seems to be the only thing that can be done next, and all these difficulties seem to announce that our analytical power has actually been exhausted. ”

Such pessimistic arguments were prevalent at the end of the 18th century.

However, in the 19th century, contrary to the pessimistic expectations of people at the end of the last century, mathematics entered a period of unprecedented rapid development in the 19th century.

Therefore, the mathematics of the 19th century can be called the period of nirvana.

In these 500 problems from the 2001st to the 2500th floor, Cheng Li encountered many classic problems about 19th-century mathematics.

For example, the solvability of algebraic equations and the discovery of groups.

Algebra gained a new lease of life due to the introduction and development of the concept of groups. This makes the research object of algebra not only algebraic equations, but more of the study of the operation relations of various abstract "objects", which is also the foundation of later set theory and logic.

In addition, there is also the problem of quaternion super-complex numbers, which is also a headache for Cheng Li.

Since the middle of the 19th century, the emergence of Boolean algebra has completely entered a completely new field of algebra - the field of logic.

For the first time, people discovered that logic could also be calculated. And this is also the source of the theoretical basis for the birth of computers in later generations.

In addition to algebra, in the field of geometry, 19th-century geometry can even be described by the word subversive.

Until the 19th century, geometry was the domain of Euclid, and it was believed to be the truth.

It's as if people at that time believed in Newtonian mechanics as the truth in the field of physics.

However, in the 19th century, it was vaguely discovered that Euclid's geometry was not so perfect.

In particular, Euclid's Fifth Catholic:

"A little beyond a known straight line, you can and can only make a straight line parallel to the known straight line. ”

After entering the 19th century, many people vaguely felt that Euclid's public establishment was a bit problematic.

But the authority of the classics makes people afraid to make public statements about non-Euclidean geometry.

As a result, Gauss, who had the reputation of "the king of mathematics" at that time, although he already had a theoretical idea of non-Euclidean geometry, but because he was afraid of being attacked by the world, he did not publish any works on non-Euclidean geometry during his lifetime.

In fact, the term "non-Euclidean geometry", that is, "non-Euclidean geometry", was coined by Gauss.

However, even a man of high moral standing as Gauss did not dare to openly express his views in this regard, so you can imagine how difficult it was to challenge authority at that time.

Fortunately, a mathematician named Lobachevsky, with very firm and radical remarks, was not afraid of authority to publish his book "On the Principles of Geometry" in 1829, which was the first published non-Euclidean geometry literature in history.

The problem encountered by Cheng Li on the 2177th floor of the arithmetic tablet is from "On the Principles of Geometry".

The question on Layer 2177 is:

Ask, how can it be proved that by a point outside the straight line, more than one but at least two straight lines can be drawn parallel to a known straight line. ”

The proof process that Cheng Li spent 10 minutes writing at that time was to overthrow Euclide's fifth postulate and develop a completely new geometry from this alternative postulate - non-Euclidean geometry!