“… IN THE PREVIOUS LESSONS, WE FOCUSED ON THE APPLICATION OF MATHEMATICS TO PHYSICS AND CHEMISTRY, SO WHO HAS READ MY ARTICLE ON QUASICRYSTALS PUBLISHED IN NATURE LAST YEAR? As the time approached, the course, which was not offered until the middle of the semester, was now approaching the end, but Junxin continued to take the class at his own set pace as if he didn't realize it.

After hearing Junxin's question, many students in the audience raised their hands. The discovery of quasicrystals is an incredible legend in the world of chemistry. This experiment is very simple to repeat, but the result is so subversive, so, after Junxin, a large number of researchers have emerged, and the subsequent research results on quasicrystals are also more and more. When people are looking for quasicrystals, they will always subconsciously look for the person who discovers the structure of this substance, and they can always contact the person on the podium who is talking.

But what people talk about the most is that the discovery of this substance of quasicrystals was completely discovered by two people outside the chemical world, one is a professional mathematician, and the other is a literary scholar who is not even a natural science. This makes the discovery of quasicrystals a kind of legend, and the spread speed in the industry is correspondingly faster and farther.

"Carter, tell me what role mathematics played in the discovery of quasicrystals?" Randomly looking for a person's name on the roll call, Junxin looked up and asked, in fact, the name reminded him of the fallen basketball superstar Vince Carter.

"Sir, I think that the role of mathematics is crucial in the discovery of quasicrystals. ACCORDING TO YOUR PAPER IN NATURE, YOU FIRST MATHEMATICALLY DEDUCED THE FACT OF THE MATHEMATICAL EXISTENCE OF QUASICRYSTALS, THEN DESIGNED CORRESPONDING EXPERIMENTS BASED ON THIS INFERENCE, AND FINALLY COMPLETED THE PROOF IN THE LABORATORY, THUS FINDING EVIDENCE FOR THE EXISTENCE OF QUASICRYSTALLINE SUBSTANCES. ”

From this logical analysis, quasicrystals, a substance, in fact, represent the delay of mathematical analysis to other related disciplines, and the role it plays is still immeasurable. I have reason to believe that without mathematics perhaps by chance, people might be able to stumble upon quasicrystals, but they wouldn't be as efficient and accurate as you are. Therefore, in the process of discovering quasicrystals, mathematics plays not only an analytical role, but also a key guiding role. ”

Junxin nodded with satisfaction, but did not comment on Carter's words, but continued: "The discovery of quasicrystals came from a mathematics student who went to the wrong classroom and came to the classroom of a chemistry professor, and was asked about relevant concepts, and finally used what he learned to find loopholes in the foundation, which may be a very interesting story." Maybe you'll be the next person to go down the wrong track, but I sincerely hope you'll make the same discoveries as I did, and this course is designed to lay the groundwork for your discovery, and trust me, I know what I'm talking about. ”

There was a burst of chuckle from the audience, and Jun Xin also smiled and continued: "The discovery of quasicrystals is actually completely mathematical thinking at work, from a mathematical point of view, because of the existence of the Penrose puzzle, then from the perspective of a mathematician, the two-dimensional Penrose puzzle is delayed to three measurements, which is completely theoretically possible." This is related to the current crystallography theory, so the entry point for this problem is mathematically, and this is perfectly fine. ”

"The first thing I did when I thought about this was to delay the Penrose structure of the three measurements, which at least theoretically proved that my idea was not problematic. Then the next experimental verification will require a little bit of luck. There was another chuckle from the audience. In fact, when Professor Thurston informed Junxin that these teachings would be recorded as teaching materials, Junxin changed the atmosphere of the classroom a little, and at least became a little more lively.

"So, how to verify that the three measurements of the Penrose puzzle correspond to the crystal structure requires a little skill." After the foreshadowing was completed, Junxin began to introduce his thoughts when thinking about this problem, as well as the simple calculation of the three measurements of the Penrose puzzle.

The people in this class are not considered students of the mathematics department, but if you want to enter this class, you must have a superior mathematical foundation, which is also the requirement of Junxin, because the discussion of any problem in it must involve mathematical operations. People who don't have a foundation in mathematics can't keep up with the pace and pace of the course at all.

For Junxin's question, everyone in the audience listened very carefully, this is indeed a very fascinating question, not only this discovery is legendary, but also the person who made this discovery now personally explained the idea of making this discovery, which is a very rare opportunity for this group of students who are still blank, which is equivalent to you and the discoverer making this discovery together.

Junxin's explanation is very detailed, but many of the things that have been published are passed by, because this is something that everyone knows. There is no need to spend too much time. In addition, in the previous course, Junxin mentioned more theoretical things, but rarely gave practical examples to illustrate these theories, and at most made some analogies to increase the interest.

Now is the first complete example given by Junxin. Others don't know that Junxin's theory courses are all copied from the theory courses of the Princeton public courses in later generations, and they think that these things are edited by Junxin alone. Therefore, they believe that these theories were also created by Junxin, and today's examples happen to be a huge supplement and explanation of these theories.

"To sum up, from Penrose's three-circumference theory, we can see that there is a mathematical connection between the lattice structure of the crystal and the elements of the puzzle, but the structure of the Penrose puzzle is not as closely related as the crystal structure, but more of a long-range order but does not have the symmetry of the property."

"However, the theoretical conflict between the structure of the crystal tells us that the crystal is a long-range ordered and spatially regular structural substance with a symmetrical structure, which makes me doubt the definition of crystal structure." Junxin concluded, "You don't have to believe it, because in the end, I am a mathematician, not a chemist, and I naturally believe that mathematics is my characteristic, which is also the origin of the later verification experiments, because the chemical definition is wrong, which was also verified at the International Crystallography Congress last year, and the current definition of crystallography has been revised after that meeting, and the detailed things should be explained in your current textbook, so I won't go into details, is there any problem?" ”