Successfully attracting Hao Peng into his research team is something that Junxin Research has thought about. First, Hao Peng has helped him a lot, although most of them are instructed by Professor Hu. Second, Hao Peng himself is also very talented in mathematics, otherwise he would not be valued by Professor Hu, who is a member of the department. In addition, Junxin has talked with Hao Peng many times, and he is also very optimistic about Hao Peng's quality, so he naturally had the idea of pulling him into his team.

And the second person he values is naturally Wei Dong, who is second only to him in the mathematics department and has a deep foundation in mathematics. So when Wei Dong came to him to ask some questions, Junxin also took the opportunity to pull him into the established mathematics seminar class.

With three people, the prototype of the seminar has been successfully established, with Wei Donglai, a person who has been exposed to foreign education and has contacts and contacts with the outside world, to provide the latest research progress abroad; Hao Peng, a person who has studied and done research in China, pays attention to the domestic dynamics and the latest research results; Junxin is in the middle of the scheduling, always paying attention to the latest developments, and providing research directions with what he has learned. With the cooperation of the three people, the discussion group has initially formed a scale.

The next thing Junxin needs to do is to improve the research direction of the discussion group, which is relatively simple. For Junxin, who understands the development of mathematics, there are many ideas, and they all have a certain operability. For example, his research on Hao Peng is a study of the Poincaré conjecture, and the direction he gives is some of the research results of Professor William Thurston. These results were provided by Wei Donglai, and Junxin supplemented them on the side. The research direction for Wei Donglai is selected as mathematical physics, mainly in string theory.

As for other research, Junxin has not started for the time being, although Fermat's theorem himself knows the results of the proof, but Junxin is not ready to prove it independently, he hopes to precipitate for a period of time after the publication of the conjecture named after his name, and systematically learn the knowledge of elliptic lines, and then start. Therefore, he plans to devote his energy to the study of elliptical lines in the near future, but he finds that there is very little information about this in China, and there is no information to provide reference, so he can only continue to study number theory.

On the other hand, Junxin agreed to participate in the New Year's Day performance because he owed the counselor a favor. Later, the class leader informed him that the school had prepared a piano for him to play.

After hearing this, Gu Mengxue asked him curiously how he could play the piano. As a result, Junxin started a general education course on the connection between mathematics and music.

"I've never seen you talk about the piano, you really know how to play the piano?"

"Mengxue, piano is mathematics, I don't know the piano, but there is no problem with mathematics!"

"How?"

"Let's talk about the relationship between music and mathematics first!" Jun Xin paused and said, "There are countless mathematicians in the mathematical community who have discussed the relationship between music and mathematics, and the two most famous mathematicians are Pythagoras in ancient Greece and Fourier in ancient Greece. ”

Pythagoras believed that all were more or less influenced by "the whole universe as harmony and number." For thousands of years, the study of the relationship between music and mathematics has been a hot topic in the West, from the ancient Greek Pythagoreans to modern cosmologists and computer scientists, all of whom have been influenced by this concept to a greater or lesser extent, Kepler, Galileo, Euler, Fourier, Hardy and others have devoted themselves to studying the relationship between music and mathematics. ”

"From a musician's point of view, modern composers such as Bartók, Schoenberg, Cage and others have all made bold experiments with the combination of music and mathematics. The Greek composer Xenakis created "algorithmic music", which replaces musical thinking with mathematical methods, and the creative process is also the calculation process, and the title of the work is similar to a mathematical formula, such as "S+/10-1.080262" for 10 musical instruments, which was calculated on February 8, 1962. Makahair developed Stockhausen's idea of "graphic music" (music for reading and seeing) to make "geometric music" in the form of a rotation of geometric figures

"What does that have to do with being able to play the piano?" Gu Mengxue obviously heard of what Junxin said for the first time, so although she thought it was very novel, she couldn't stop her curiosity about Junxin's piano skills.

"Hehe, won't you know when you perform on stage?" Jun Xin smiled but didn't answer, which really made Gu Mengxue quite depressed.

"I really don't know how to play the piano!" Jun Xin said with a somewhat serious face, "But I have seen a series of research results on sound by Fourier. The results of these studies can be summarized into a mathematical problem called the Fourier transform. It is just a number that any song or a piece of music is the result of a Fourier transformation in my eyes. ”

"In fact, the shape and structure of many musical instruments are related to various mathematical concepts. Whether stringed instruments or wind instruments emitted by columns of air, their structure reflects the shape of an exponential curve. If all sounds can be described mathematically, which can be the sum of simple periodic sinusoidal functions, and the three properties of sound, pitch, volume, and sound quality can be clearly represented graphically, and the pitch is related to the frequency of the curve, and the volume and sound quality are related to the amplitude and shape of the periodic function, respectively, then why can't music be composed by composing by composing music by composing it compositively? Perhaps, relatively speaking, we mathematicians have the ability to calculate a piece, so maybe one day in the future, if I can't find a job, I can consider becoming a composer. ”

"At first, I agreed to come down to the show because of the class leader's invitation and the recommendation of the instructor, but recently I found something very interesting after studying the mathematics of the piano. You say, if I represent all chords as something mathematically concrete, let's say latitude. So, is it possible that chords can be reduced to the specific characteristics of notes by studying the properties of latitude in detail? ”

"Uh..."Gu Mengxue said that she couldn't keep up with Junxin's rhythm at all. Although he has made up a lot of mathematical knowledge during this time, he is still very inferior to the math madman in front of him.

The idea came from Timodeko's theory, which Timoteko believed that the space in which the chords existed was a bizarre, multidimensional space, which Timoteko called "orbital folding", where the chains formed by musical notes were twisted and connected like the Mobiusstrip (the two ends of a loop are pulled and turned 180 degrees and then glued). Timoteko's research proved that the simplest chord containing only two notes has the form of a Mebius band; A three-note chord resembles a prism; More complex chord forms are difficult to express in the shapes we are familiar with.

Timoteko was a well-known composer at Princeton University, and it was at a party that he met the maestro and learned about this highly suggestive theory of music and mathematics after listening to his introduction. And once there was a lot of research on this, naturally I thought of more.

However, Gu Mengxue was obviously not interested in these, and just weakly repeated her words next to Junxin: "I just want to know what kind of music you played at the performance." ”