In mathematics, some things seem to be just "human works", and it is more appropriate to use "invention". For example, in the process of proving some results, mathematicians find it necessary to introduce some ingenious but not unique ideas to get some special results. However, in other cases, the word "discovery" is indeed much more appropriate than "invention". Such as the plural. When it was introduced, people got much more from its structure than what was put in advance. People can think that in this case, mathematicians and "God's masterpiece" met. In other words, the essence of complex numbers and complex numbers exists objectively, neither invented by anyone nor intentionally designed by any group of mathematicians. This is not an invention of human thinking: this is a discovery! Mathematicians just "rediscovered" them! Mathematicians actually find ready-made truths, and the existence of these truths is completely independent of the activities of mathematicians. Mathematical object is an independent and objective existence independent of human thinking.

We can quote the views of two great mathematicians.

Archimedes believes that the objective existence of mathematical relations has nothing to do with whether human beings can explain it.

Newton said, "I don't know what the world thinks of me." I just feel like a child playing by the sea. Sometimes I am happy to find a smooth stone or a beautiful shell, but the ocean of truth has not been discovered before me. " It can be seen that no matter how great a mathematician is, he is only the lucky one who can catch a glimpse of some eternal truths.

Of course, the connection between mathematics and objective reality is not always so close and powerful. For example, the introduction of quaternions and various hypercomplex numbers are examples put forward by those who oppose this connection. The introduction of quaternion has a physical background, but for other hypercomplex numbers, even this background is lost. They seem to be the free creation of mathematicians. This phenomenon is not uncommon in mathematics. The first abstraction of mathematical concepts is often closely related to the outside world. But once these concepts are introduced into mathematics, they are often further abstracted. When this abstraction reaches a certain level, it seems that it loses contact with the outside world. There are not a few mathematicians who only gallop in the internal logic of mathematics and don't care about the connection between mathematics and the outside, but they have made important contributions to mathematics. With the increasing abstraction of mathematics, especially the prevalence of mathematical axiomatic thinking, the view of denying the connection between mathematics and the outside world is quite common among mathematicians for a period of time.

But as poincare pointed out in the report of the first international congress of mathematicians in Zurich in 1897: "... if I am allowed to continue to compare these beautiful arts, mathematicians who leave the outside world behind are like painters who know how to combine colors and forms harmoniously but have no models, their creativity will soon dry up." The history of mathematics development proves that he is very insightful. Eighty years after he made this image metaphor, an international academic seminar was held in Denmark to discuss the relationship between mathematics and the real world. More mathematicians believe that mathematics is closely related to the real world, and mathematics reflects the real world and has been developed in practical application.