The weather on the weekend is very good, the late spring season is the most suitable time to play, the flowers and fruit dew, the greenery is getting thicker, the warm sun shines on the body warmly, couples strolling through the streets of Paris in twos and threes, not only a kind of fun, but also a different kind of scenery.

At the home of Marin Mason at the University of Paris, more than a dozen scholars came one after another, including old men in their sixties and young men in their teens and less than twenty, all of whom were invited guests by Galileo and Marin Mason, and who were also famous scholars of this era in Europe, belonging to the elite of an era, and who created the spring of science.

They received few gifts, just a delicate telescope, a thin European translation of "Nine Chapters of Arithmetic", and a bag of black tea. But this kind of tasteful gift is just right for their appetite, and for scholars, it is a very pleasant thing to collect a classic book and have a refreshing cup of strong tea when they are thinking about learning.

Xu Xiake and his entourage must have brought more than these gifts, there are more surprising things that have not yet been taken out, the things that have been taken out are the most ordinary, he plans to wait until these scholars start to discuss academic issues, in giving them a surprise, although Zhu Youxiao is to let them come with a learning attitude, but psychologically speaking, they are still very proud, these people are the academic elite of the Ming Dynasty, and they also have their own areas of expertise, the focus of research, and they also want to show their excellent aspects.

Li Ciyu studied the most classical "Nine Chapters of Arithmetic", and Gu Yanwu, Huang Zongxi, Chen Zilong They were deeply influenced by Zhu Youxiao, and studied the mathematical works of the Song Dynasty more deeply, but they still have some problems with the research methods, which is also an important reason why Zhu Youxiao asked them to come together, in-depth exchange and learning methods are a shortcut to improve research ability, Zhu Youxiao does not understand such professional problems, after all, he is only a secondary school graduate in later generations, The mathematical research of these majors is still rude, and the real research ability is not worth mentioning compared with the mathematicians of the current era.

The study of classical Chinese mathematics reached its peak during the Song Dynasty, which was also the peak period of the development of China's commodity economy. The political climate of the Song Dynasty was very open, and with the exception of Cheng Zhu Lixue, which brought the study of Confucianism to its peak, and even somewhat distorted, the study of mathematics showed a tendency to study logical reasoning, that is, purely theoretical mathematics. It is a pity that at this peak period was interrupted by the iron hooves of the Mongol army, even many classic research works were lost, even in the Ming Dynasty, more than 200 years of development, mathematical research did not reach a higher level, but began to lag behind the development of mathematics in Europe.

When Zhu Youxiao saw the Ming Dynasty Xu Guangqi's translation of "Geometric Originals", he found that this was not its true face, but a fragment, and it was very good that Xu Guangqi, who was not a specialist in mathematics, was able to do this, laying the foundation of modern Chinese mathematics. But for Zhu Youxiao, this is still a lot worse, and the research foundation of all modern science and engineering disciplines in the history of mathematics must be given the highest priority.

When he discovered Gu Yanwu, Huang Zongxi, Chen Zilong, and other famous scholars in the late Ming Dynasty, he began to change their research direction, searched all the books and classics in the palace, and let them combine Chinese classical mathematics with the "Geometric Originals" to study, but with little success, which is the reason why the traditional research model is somewhat rigid, and also the reason for the lack of basic research.

Under the introduction of Galileo and Marin Mason, the scholars or students of the Ming Dynasty sat down with the famous European scholars of this era, because each of them had a copy of the Nine Chapters of Arithmetic, so they began to discuss the problems in this book. Li Ciyu explained to them the research methods and experiences of the Ming scholars, and then asked them in an inquiring tone about their views on the study of European scholars.

Among these people, the most famous mathematician was Johann Kepler, who was once the chief mathematician of the Prussian royal family, followed by Descartes. Johann Kepler was the oldest and therefore the most authoritative mathematician of them. After Li Ciyu introduced "Nine Chapters of Arithmetic", he explained his research views, not only the calculation process is rigorous, but also the logical thinking and proof methods are refreshing to Li Ciyu, even Gu Yanwu and them, they also feel that John Kepler has opened another door to research for them, and there is a feeling of enlightenment.

As the seminar continued, Gu Yanwu put forward some research experiences on the Geometric Primitives, and humbly asked Descartes whether it was correct. Because Gu Yanwu only saw part of Euclidean geometry, it can be said that the research is very superficial, and he does not have many opinions of his own, but seeing that he can use an abacus to calculate some problems in geometry, he modestly proposed to him that he can discuss some problems that combine the two, and see if there is another academic method.

Gu Yanwu, Huang Zongxi, and Chen Zilong have deep attainments in the study of the Song Dynasty's "Ten Techniques of Arithmetic" and Shen Kuo's "Limiting Volume" and "Drawing Circles", mathematician Jia Xian's "Huang Chapter 9 Algorithm Fine Grass", and mathematician Yang Hui's "Multiplication and Division".

As the topics discussed by Descartes and Gu Yanwu deepened, the follow-up questions of Euclidean geometry gradually became clear. When "confinite plot", "circle drawing", and equation analysis gradually entered the discussion, Johann Kepler and other mathematicians also joined the discussion, gradually combining geometric problems with algebraic problems, and entered a new field of Cartesian research.

Algebra is a different name for arithmetic in Europe and the Ming Dynasty, but there are also differences, fortunately, Gu Yanwu and they are proficient in mathematical problems, and they quickly understood the name of algebra, and understood that they set up unknown numbers X, Y, Z, A, B, C and other theories that represent numbers, and algebra replaced the arithmetic concepts in their mouths, so that the research will be deepened and the topic will be more extensive.

The new field of Descartes' research is analytic geometry, turning geometric problems into algebraic problems to study, or expressing algebraic problems in geometric form, which produces a coordinate system, which is a completely new thing, with Descartes' current mathematical attainments, he has not yet written "Fang *", analytic geometry is still a hazy thing, but after this in-depth exchange with Ming scholars, under the joint research and discussion, the new topic of analytic geometry is about to emerge.

In addition to these problems, European scientists are also very interested in the telescopes brought by Xu Xiake, Galileo discovered the subtlety of telescopes and made telescopes, but now European telescopes are generally very rough, and it is very rare to bring such exquisite telescopes to Daming, and they want to understand how Daming made them.

This question is very embarrassing, because although Zhu Youxiao made this telescope, he himself does not understand the theory of the system, even if it is the microscope of the Daming Academy of Sciences, it is also imitated according to the telescope, little by little by hand, slowly put together, as for the principle, no one knows, just according to the formulated template and the prescribed scale, as for the imaging principle, no one knows.

This may also be a reason, the telescope was first made by Zhu Youxiao, maybe it belongs to the sage products, everyone is afraid of taboos, no one dares to study in depth in this area, in case it is made farther than the emperor made to see, and it is clearer, it seems to be guilty of deception, so the telescope has not been greatly improved in the past few years, but it is only more sophisticated, this is the only change.