Mathematics has developed to the present, and countless excellent mathematicians have emerged, and some of them are even more famous in history, and no one knows, such as Gauss, the prince of mathematics, and Newton, the discoverer of gravity. If I really want to rank these gods, I don't think I have the ability to rank them, because most of their contributions are immeasurable. For example, the gods in the picture below, we can only give them a rough grade, if newton, Gauss, Archimedes as the highest grade, followed by Euler, Cauchy, Poincaré and so on. I think the top four are irrefutable, and the rankings in the back depend on what the officials like. The great gods included in this list are: Riemann, Canto, Hamilton, Eisenstein, Pascal, Abel, Hilbert, Klein, Leibniz, Descartes, Galois, Möbius, Jacob Bernoulli, John Bernoulli and Daniel Bernoulli, Dilickré, Fermat, Pythagoras, Laplace, Lagrange, Cronek, Jacobi, Poljo, Robachevsky, Nottle, Germain, Euclid, Lejender.

Math Gods Leaderboard
In addition, there is a very popular ranking abroad: the rankings are 1 Newton, 2 Archimedes, 3 Gauss, 4 Euler, 5 Riemann, 6 Euclid, 7 Poincaré, 8 Lagrange, 9 Hilbert, 10 Leibniz. Rankings are more convincing based on the breadth and depth of mathematical research and its impact on future generations.
These 10 people correspond exactly to 5 pairs of relationships in 5 eras:
Newton – Leibniz: Rival
Hilbert – Poincaré: Rival
Euclid – Archimedes: Master and apprentice
Euler - Lagrange: Master-apprentice
Gauss-Riemann: Master-apprentice
Master-apprentice relationship diagram of some famous mathematicians
Of the two pairs, Newton-Leibniz is arguably the most famous pair in the history of world science, because the priority of inventing calculus is debated; Poincaré-Hilbert, although the two do not have the direct argument of the previous pair, Poincaré belongs to intuitionism, Hilbert belongs to formalism, Poincaré is the mathematical leader in Paris, France, Hilbert is the mathematical leader in Göttingen, Germany, Poincaré opposes set theory and Hilbert strongly supports set theory, and it is not wrong to call the two opponents.
Of the three pairs, Gauss was directly Riemann's mentor at Göttingen, and Riemann later took over Gauss's position at the Göttingen Observatory; Euler and Lagrange were not formally nominal mentors, but Lagrange began to communicate academically to Euler, who was then at the Berlin Academy of Sciences, and Lagrange later took over Euler's position at the Berlin Academy of Sciences at the recommendation of Euler, so historians generally regard Euler as Lagrange's mentor; Euclid and Archimedes' teacher-student relationship is not so precise. Because of their age, many sources are unknown, but both studied mathematics in Alexandria, Egypt, the center of mathematics in the world at that time, and it is generally believed that Archimedes was a student or apprentice of Euclid students. In this way, the master-apprentice relationship between these three pairs is also justified.
From the perspective of specific work, there is also a clear inheritance relationship between the three pairs of master-apprentice research areas:
Euclid – Archimedes: Geometry, Euclidean geometry is confined to the plane, and Archimedes derives the volume of the spherical surface of the three-dimensional, the volume of the cone, and so on, and also pioneered the exhaustion method.
Euler-Lagrange: Variational method, Lagrange expanded the variational method pioneered by Euler, solved the problem of isoclideanity, and established the famous Euler-Lagrange equation in the variational method.
Gauss-Riemann: Complex analysis, differential geometry, Riemann's doctoral dissertation was on complex functions, and it was Gauss who was examining it at the time; Riemann's famous inaugural speech "On Assumptions in geometric foundations" was also the topic that Gauss chose for him from three alternative topics.
And the 2 pairs of opponents can be said to focus on opposing areas and belong to different types:
Newton – Leibniz: Newton was essentially a physicist, while Leibniz was essentially a philosopher; so both established calculus theories one from kinematics and the other from the tangents and areas of curves. But because of the difference in the nature of the two, the two have always been a bit out of place.
Hilbert - Poincaré: Hilbert pays more attention to form and logic, and the 23 problems he put forward are also related to the logical basis of mathematics and axiomatic systems, while Poincaré pays more attention to spatial intuition and has made outstanding contributions in the fields of topology and chaos theory. The contradiction between the two is most evident in the set theory established by Canto: Hilbert praised it as one of the greatest achievements in the history of mathematics, while Poincaré was strongly opposed to the infinite and to set theory.
From the perspective of the times, these 5 pairs of masters also just created 5 key eras in the history of mathematics:
Euclid – Archimedes: The Age of Logical Enlightenment. The epoch-making symbol of this era is Euclid's "Geometric Origin", which marks the real formation of the axiomatic system and mathematical reasoning proof, euclid used 5 axioms to build the entire European geometric building, leaving endless treasures for future generations. Archimedes further enriched mathematical tools on his basis, and can be said to have pioneered applied mathematics, discovered the buoyancy principle, the lever theorem, and manufactured a large number of construction machinery.
Newton– Leibniz: The Age of Scientific Analysis. Similarly, the establishment of calculus and the Mathematical Principles of Natural Philosophy were epoch-making achievements. Calculus provided the most powerful tool for mathematical analysis, and the Principia built the entire edifice of classical mechanics, and the subsequent Industrial Revolution in the West can be said to have built on these achievements. It is worth mentioning that Leibniz also pioneered mathematical logic and binary, but this was too advanced at the time, and people did not complete his work until the age of computer information in the 20th century.
Euler- Lagrange: The Age of Application and Popularization. It can be said that the work of the two inherited the legacy of Newton-Leibniz, applying the analytical tools of calculus to various fields of mathematics and physics, such as the two pioneered the variational method, Euler pioneered topology and graph theory, Lagrange pioneered analytical mechanics, and the work of the two also promoted the mathematical and physical fields that existed almost at that time, such as number theory, differential equations, fluid mechanics, celestial mechanics, and so on. In addition, the higher mathematics of the Newton-Leibniz era was still a book of heaven that ordinary people could not understand at all, and Euler's "Introduction to Infinite Analysis" and other works, invented mathematical symbols such as f(x), sin, cos, e, i, π, Lagrange's invention of f', f'' and so on, made mathematics more understandable and popularized the teaching of mathematics.
Gauss-Riemann: The Age of Strictness and Maturity. Gauss was considered to be the first strictist, and mathematicians before him often did not pay attention to the rigor of the proof, even the concept of limits, the strict definition of integrals. The fundamental theorem of algebra has long been proposed, and the quadratic reciprocal law has long been proposed by Euler, but no one has rigorously proved it, and Gauss finally completed the proof of the theorem. This not only means that future generations can directly use conclusions, but also means that mathematics has a more rigorous foundation. Later definitions of Riemannian integrals also solved the problem of how integrals are defined, and mathematics became more mature. Of course, the mathematical foresight of the two men is also amazing, and the establishment of differential geometry and complex analysis is epoch-making.
Poincaré – Hilbert: Modern Mathematics. The characteristics of this era are that the branches of mathematics are more and more divided, the more and more detailed, the intersection and combination between various disciplines are becoming more and more frequent, the entire mathematical building is becoming more and more large and complex, and the application of mathematics in computer science, quantum mechanics and other fields has also promoted the development of mathematical skills, and various new concepts have also emerged to impact the foundation of mathematics. Poincaré's pioneering algebraic topology, chaos theory, Hilbert's research in functional analysis, and the formulation of 23 problems are all hallmarks of this era. Of course, the mathematics of this era is already very complex, no single doctrine dominates the entire field of mathematics, the formulation of set theory and Gödel's incompleteness theorem have impacted people's understanding of mathematics, and Poincaré and Hilbert are only two of the most representative of many trends in this era.
It can be said that these 5 pairs represent the highest level of mathematics in the world in the BC, 17th century, 18th century, 19th century and 20th century. From this point of view, it also makes sense to rank them in the top 10. The existence of these 5 pairs of master-apprentice and opponent relationships also shows from the side that mathematics is constantly developing in the continuous inheritance and deepening and confrontation collision, and also reflects the profundity and mystery of the discipline of mathematics.