Alberta, I will give a general echelon ranking according to my personal understanding of the history of mathematics, for reference only:
The first echelon [refers to veteran leaders]
Euler, Gauss, Newton, Riemann
These four mathematicians are all in the echelon of God, and their contributions are extremely important, not only in the field of mathematics, but also in the field of physics.
For example, Leibniz and Newton invented calculus at the same time, but Leibniz was not as famous as Newton. Although the calculus invented by Leibniz is more practical than Newton, its influence is not as good as Newton's.
However, Euler and Gauss have made unparalleled contributions in the field of basic mathematics, and they are almost equal. Nowadays, the contributions of Euler and Gaussian can be seen everywhere in the scientific field, such as Euler equation, Euler constant, Gaussian distribution, Gaussian law and so on.
Riemann's contribution in the field of advanced mathematics paved the way for many disciplines, such as Riemann geometry, which provided a mathematical basis for the theory of relativity; Concepts such as Riemannian integral, Riemannian manifold and Riemannian condition can be seen everywhere in the field of higher mathematics.
second echelon
Euclid, Archimedes, Poincare, Hilbert, Leibniz, Chen Shengshen, Cantor, Galois, Cauchy, Descartes, von Neumann, Lagrange and so on.
There are many mathematicians who can rank in the second echelon, among whom some have made pioneering contributions to basic mathematics, such as Euclid and Archimedes; Others have made extremely important contributions in their respective fields, such as Chen Shengshen, the father of differential geometry, and Galois, the pioneer of group theory; There are also many versatile figures, such as Poincare, von Neumann, Hilbert and Leibniz.
Mathematicians of the second echelon have made pioneering contributions in at least a certain field of mathematics, and it is difficult to select six of them for ranking. However, mathematicians with extremely important contributions like Euclid and Hilbert still sit firmly in the top ten.
In addition, there are some mathematicians who have made outstanding contributions to a certain point in mathematics and are also very famous, such as:
(1) andrew wiles, the prover of Fermat's last theorem;
(2) emmy noether, the greatest female mathematician, is known as "the mother of modern mathematics";
(3) Turing, the father of artificial intelligence, made great contributions to computers.
(4) Godel, whose achievements in modern logic are extraordinary, is an immortal milestone in mathematics;
..... and so on.