Mathematics is the king of science. ——-Gauss
Mathematics is the science of infinity.——Herman Weyl
In the field of mathematics, The art of asking questions is more important than the art of answering them.——Cantor
The scientific level of a country can be measured by the mathematics it consumes.——Rao
The value of mathematical knowledge to us is not only because it is a powerful tool, but also because of the perfection of mathematics itself. In the internal or external unfolding of mathematics, we see the purest logical thinking activities and the most advanced aesthetic expression of intellectual vitality. --- Pringsheim, Alfred
The economic principle of thinking is highly developed in mathematics. Mathematics is the highest form of science reached by various sciences in their high development, and various natural disciplines frequently turn to it for help. ---Mach,E
Wherever there is number, there is beauty.---Proclus
Some beautiful theorems in mathematics have the following characteristics: they are easily generalized from facts came out, but the proof was extremely hidden.
Mathematics is advancing unfettered along its own path. This is not because it has any license to be exempt from legal constraints, but because Because mathematics inherently has a freedom determined by its nature and consistent with its existence.---Hankel, Hermann
Geometry, theoretical arithmetic and algebra, in addition to definitions and axioms, these subjects There is no other principle, no other proof process except deduction, but in this process, simplicity, complexity, rigor and generality have been integrated. This feature is not possessed by other disciplines. ---Whewell, W.
Mathematical knowledge has three main characteristics that are different from other knowledge: first, mathematical knowledge makes its results more truthful than other knowledge; second, mathematical knowledge is It is the necessary first step to obtain other correct knowledge; third, the acquisition of mathematical knowledge does not depend on other knowledge. ---Schubert, H.
Mathematicians pay no attention to statements or conjectures. They deduce everything based only on definitions and axioms, and use argument and reasoning. In fact, it is incorrect to call those theories established only by conjectures or hypotheses as science, because conjectures often resort to certain opinions or claims, and therefore they cannot produce knowledge from them. ---Reid, Thomas
No subject can illustrate the harmony of nature more clearly than mathematics. ---Carus, Paul
French mathematician Poincare (,) once said, 'Logic is a tool of proof, intuition is a tool of invention. "Logic can tell us to take this road or that road without encountering any obstacles, but it cannot tell us which road can lead us to our destination. To do this, we must look at the target from a distance, and what teaches us the ability to look is Intuition. Without intuition, a mathematician would be like a writer who writes poetry grammatically but without any thought.
D. Hilbert emphasized, 'Mathematical knowledge. After all, we must rely on some type of intuitive insight.
The famous mathematician Hua Luogeng said: One of the most precious spirits in studying science is the spirit of creation and the spirit of independently opening up the wilderness. The reason why science is achieved. Today, it is mostly due to this spirit that when there is no way out, outstanding scientists often find another way to create a state where there is a bright future.