Just one year before Kurt G?del published his "Incompleteness Theorem", mathematicians from all over the world gathered in Ginsburg, Germany, to attend a heavyweight conference on mathematical logic. This meeting is also a farewell stage for retiring david hilbert. David hilbert read out his retirement declaration to the applause of all mathematicians attending the meeting. The final declamation of this declaration caused a sensation on the spot: "For mathematicians, there is nothing unknowable in the world; In my opinion, all natural sciences are like this. The reason why no one has ever successfully cited an unsolvable problem, in my opinion, is that there is no unsolvable problem in the world. Compared with those ignorant pedants who hold agnosticism, we mathematicians have the belief that we must know! We will know eventually! " This last sentence is very famous in mathematics-mathematicians regard it as Hilbert's declaration of faith; This sentence became the epitaph of Hilbert in the future; The original German text is as follows: Wirm? Sam Wesson! We will win! However, just over a year later, Hilbert's retirement declaration became the laughing stock of classical philosophers. The fatal blow of the incompleteness theorem made mathematicians realize modestly for the first time that1at the beginning of the 9th century, Russian mathematician Lobachevsky discovered that Euclid's "parallel axiom hypothesis" was actually a circular argument: a point outside a straight line and only one straight line did not intersect with the straight line could not be proved independently! It is only human intuition to think that two parallel lines will continue to intersect indefinitely! Lobachevsky tried to prove the "parallel postulate" by reducing to absurdity, that is, assuming that more than one straight line is parallel to the straight line outside the straight line, and then tried to find out the huge contradiction in geometry. But Lobachevsky was surprised to find that such a starting point, which is contrary to Euclid's "parallel postulate", can still derive an axiomatic system which is different from Euclid's geometry but equally perfect, namely Roche's non-Euclid geometry, which is now well known! Ironically, Lobachevsky's new discoveries have not won the high respect of the scientific community, just as most great discoveries in the history of human civilization have been treated. Most scholars think that this challenge to Euclidean geometry is "obviously not in line with human experience and cognition", so it must be wrong! Mathematicians don't emphasize the "objective perfection and transcendence" of mathematical rationality at this moment when they discover the new continent! AugustusdeMorgan, a British mathematician who has never read Lobachevsky's paper, even "represents the whole mathematical world" and gives the final conclusion: "I believe that there will never be another geometry that is essentially different from Euclid's geometry." This confident assertion sounds familiar. It is similar to the criticism of Heliocentrism by the Inquisition which doesn't understand science, or the fierce attack of "supernatural existence" by the so-called objective scientists who have a fundamental understanding of spiritual research. Directly denying what you don't know seems to be the most prominent and obvious feature of extreme religious people and scientists, and they are proud of it. However, the tide of history will always relentlessly fade away those ignorant prejudices, crush the narrowest die-hards into endless gravel, and reflect the truth beyond the times. Humans have glimpsed the tip of the iceberg from non-Euclidean geometry. Not only Euclid's principle, but almost all knowledge systems that provide a rational basis for modern science are based on some unprovable assumption. Newton's Mathematical Principles of Natural Philosophy has eight definitions and three laws at the beginning, and these definitions and Newton's laws, which people think are impeccable, are the products of cognitive experience rather than mathematical logic. No one has the ability to provide even a complete proof of inertia, acceleration and reaction with mathematical logic. Although starting from these unprovable things, scientists can confidently list a whole physical knowledge structure map full of "because" and "so", which can be described as "rationality". However, this so-called "real science" comes entirely from the field of experience. Without Newton's three laws, which cannot be verified by reason, physics will be useless! This means that science itself comes from experience. Science is based on experience, and its development needs the help of rational construction. It is rationality that extends the cognitive tentacles of scientists, but whether it contains rationality is not the standard to judge whether a science should belong to science! Rationality is only a good environment to help science grow, and it is by no means the essential reason for the initial emergence of science! Unfortunately, however, many so-called scientists don't want to think so (perhaps because they lack philosophical self-restraint). Their view has always been that a lot of folk "pure empirical knowledge", including Chinese medicine, is by no means science! Their belief in positivism even surpassed the Crusaders' obsession with the Roman church, but they never had the courage to question whether the set of physics they were crazy about also came from empirical knowledge. Interestingly, these scientists hold high the philosophical banner of positivism, but never investigate the fact that Chinese medicine is far superior to modern medicine in specific clinical efficacy, what's more, they simply don't understand that there is a profound and complete theoretical system beyond cognitive experience behind Chinese medicine-no so-called scientific person who is used to criticizing Chinese medicine knows that Chinese medicine is actually an ancient science based on the Yijing theory rather than clinical treatment experience! Of course, the situation of Chinese medicine is far from ironic. Anecdotes in the scientific system can better illustrate the double standards of scientists. The most famous Schrodinger equation (Schr? DingerEquation) is a good example. So far, no theoretical physicist dares to claim that he has read the Schrodinger equation. Because this set of equations is purely an "empirical formula" based on experimental data. Even Heisenberg, who likes to solve physical problems with mathematical thinking, is not satisfied with Schrodinger equation. In a letter to WolfgangPauli, he said, "The more I think about the physical meaning of Schrodinger's theory, the more disgusting I feel. Schrodinger's intuitive description of his theory is meaningless. In other words, it's bullshit! Niels bohr Mister, the godfather of quantum mechanics, talked about the Schrodinger equation. But his attitude is more open-minded. Bohr believes that this equation itself is trying to describe many "uncertain" things, so as an empirical formula, as long as it is convenient, practical and can provide reliable data. In the field of physics, Schrodinger equation is "convenient and practical" but has no physical meaning at all, and many equations can't even be solved by mathematicians. One of the most popular is the famous Naville-Stokes equation (Naville? Stokes equation) and Yang Zhenning-Mills equation (Yang? Mills equation). The uniqueness of these two equations lies in that they are pure empirical formulas summarized by theoretical physicists based on experimental data; As for the theoretical significance of these two formulas, lovely scientists don't care at all! Even mathematicians do not guarantee that these two equations have solutions! In the summer of the Millennium, edward witten, the "father of the ultimate superstring theory", once said: "The understanding of natural science in history has always been an important source of mathematical inspiration. Therefore, at the beginning of the new century, the main framework used by physicists to describe the laws of nature cannot be dealt with mathematically, which is really very frustrating. Finding the general solution of Yang Zhenning-Mills equation will mean that human beings really understand the standard model of quantum physics, which will be a milestone for 2 1 century mathematics to catch up with theoretical physics in the 20th century. "Nowadays, this double standard held by scientists requires strict rational deduction for all' unscientific things', but it is blatantly' doing something special' in the' private plots'. As long as what is included in "orthodox science" is "rational mixed experience", the rest is "irrational empiricism"! It is no wonder that Irving Gingrich, who is both a religious believer and a master of astronomy, sends out his heartfelt feelings: scientific research.