1, Massachusetts Institute of Technology: MIT for short, is a research-oriented private university in the United States, located in Cambridge, Boston, Massachusetts, with its main campus built on the Charles River. It is a pioneer university in the field of high-tech and advanced research in the world and is known as "the best university of science and technology in the world".

2. Princeton University: Founded in 1746, it is a well-known research-oriented private university in the United States. The Department of Mathematics of this university and the Department of Mathematics of Princeton Institute for Advanced Studies are not only in the fields of topology, algebra and number theory, but also in the fields of computer theory, operational research and new game theory.

3. Harvard University: It is a private research university headquartered in Cambridge, Boston, Massachusetts, USA. It is one of the most difficult universities in the United States. The alumni of this school include eight American presidents, multinational leaders and political celebrities. It has also trained 62 wealthy entrepreneurs and 335 Rhodes scholars, the largest number in the United States. In addition, there are 152 Nobel Prize winners who have studied and worked at Harvard.