Mathematics is an infinite science. Herman Weil
In the field of mathematics, the art of asking questions is more important than the art of answering questions. -Cantor
The scientific level of a country can be measured by the mathematics it consumes. -Rao
For us, the value of mathematical knowledge is not only that it is a powerful tool, but also that mathematics itself is perfect. In the internal or external development of mathematics, we have seen the purest logical thinking activities and the most advanced aesthetic embodiment of wisdom and vitality. Alfred Pringsheim
The economic principle of thinking has been highly exerted in mathematics. Mathematics is the highest form of science achieved by various sciences in its high development, and all natural disciplines frequently turn to it for help. Mach, e
Where there are numbers, there is beauty. Proklos
One of the characteristics of some beautiful theorems in mathematics is that they can be easily summarized from facts, but their proofs are extremely hidden.
Mathematics is moving forward freely along its own path, not because it has any license that is not bound by law, but because mathematics has a freedom that is determined by its essence and consistent with its existence. -Herman hankel.
Geometry, theoretical arithmetic and algebra have no other principles except definition and axiom, and there is no other proof process except deduction, but in this process, simplicity, complexity, rigor and generality have been integrated, which is not available in other disciplines. - Whewell，w
Mathematical knowledge has three main characteristics different from other knowledge: first, mathematical knowledge makes its results more real than other knowledge; Secondly, mathematical knowledge is the first step to acquire other correct knowledge. Third, the acquisition of mathematical knowledge does not depend on other knowledge. Schubert
Mathematicians don't care about statements or guesses. They just explain everything according to definitions and axioms, using argumentation and reasoning. In fact, it is not correct to call those theories established only by guessing or supposing as scientific things now, because guessing often relies on some viewpoints or opinions, so knowledge cannot be generated from them. -Reid, Thomas
No subject can clarify the harmony of nature more clearly than mathematics. Paul carus
The French mathematician Poincare once said,' Logic is the tool of proof, and intuition is the tool of invention. "Logic can tell us to go this way or that way without any obstacles, but it can't tell us which way can lead us to our destination. Therefore, we must look at the target from a distance, and intuition has taught us the skills of looking at the target. Without intuition, mathematicians would be writers like this. He can only write poems according to grammar, but he has no thoughts.
D Hilbert emphasized that' mathematical knowledge ultimately depends on some intuitive insight.
Hua, a famous mathematician, said: in scientific research, one of the most precious spirits is the spirit of creation, that is, the spirit of independent land reclamation. Science is what it is today, mostly because of this spirit. When there is no way out, outstanding scientists often find another way to create the realm of "a village with a bright future".