Where in the world is science developing most actively at the moment?

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In the USA, first of all, of course. There are a lot of universities there, and many of them are research universities, which, of course, greatly stimulates the development of science. There is a lot of competition when writing articles for authoritative journals. It is not easy to get published in a good journal. In Russia, there are several serious journals on physics and mathematics left, where good articles are published. But there are many journals where publication does not give much in terms of international fame.

In general, in the current conditions, Russian science is sliding down to the provincial level. Therefore, we must strive to publish in international journals, and this is very difficult. Plus, a large number of scientists from China have created a special situation.

The thing is that if you, as an employee of a Chinese university, wrote an article that is published by a good international journal, then your salary doubles or triples. Therefore, the Chinese simply flood all the journals with their articles, this is a well-known fact. China now spends a lot of money on its science, which cannot be said about our country.

— Are there any serious discoveries taking place specifically in usa mobile phone numbers database the field of mathematics? Is mathematics now the driver of the development of natural sciences? Or is its role now limited to the function of a satellite science?
Pure mathematics does not need any external stimulation and develops according to its own internal laws. However, it often happens that, despite its abstract nature, the results of abstract mathematical research are successfully applied in solving specific practical problems. On the other hand, the emergence of new problems in physics, chemistry and biology stimulates the development of new directions in mathematics. Modeling of biological systems has led to an in-depth study of nonlinear systems of differential equations, etc. I am not even talking about probability theory, which is used everywhere, from sports to astrophysics.