Finding a special case and putting forward a universal statement about mathematical theorems are completely different. Secondly, the proposition is an inequality theorem. Finally, a useful conjecture can be proved logically before it becomes a theorem.

There are three differences between studying mathematics and natural science:

1. The difference between measurement and logical reasoning

In natural science, we get quantitative conclusions based on measurement and observation. However, the conclusions in mathematics can only be drawn from definitions and axioms, using logic and strict proof, and cannot be summarized by experience.

2. The difference between factual proof and logical proof

Although the laws and theories of natural science have been confirmed by experiments, in fact, the confidence of experiments can't be 100%, and the possibility of being overturned is very small. But in mathematics, it is absolutely not allowed to verify whether a hypothesis (guess) is correct through experiments. Only logically, through induction or deduction. It is either completely correct, without exception; Either it will be completely denied because of an exception, and there is no roughly correct statement.

3. The difference between the relativity of scientific conclusions and the absoluteness of mathematical conclusions.

Because every theorem in mathematics is a cornerstone, there will be new cornerstones on this basis. For example, trigonometry, analytic identities and calculus can be established through Pythagorean theorem.

Irrational number is the inference of Pythagoras theorem, but it also brings a great leap in mathematical thought, which shows that human understanding of logarithm is still limited and needs new ideas and theories.

Adam Rice and others found that the mass of the universe is negative through calculation, so they decided that there must be something in the universe that we can't see or understand, that is, the so-called dark energy, and Rice and others won the 20 1 1 Nobel Prize in physics.

Mathematical thinking is based on unchangeable facts, using logic to find out contradictions, find problems and then try to solve them. An unchangeable fact, for example, the number of elementary particles in the universe is limited, and no economic growth can be doubled for a long time. Specifically, in finance, any compound interest growth based on castles in the air is unsustainable, such as Ponzi scheme.

The most valuable part of learning mathematics is to receive a logical training, form the habit of rational thinking, be good at finding contradictions and problems in life, and then find answers and take actions by logical methods.

The golden section (1: 0.6 18 or 1.6 18: 1) is a bridge between mathematics and aesthetics. The shape of the typhoon and even the switch of the Milky Way are golden proportions, reflecting a constant of the universe itself. Including the designers of the Parthenon, Leonardo da Vinci and Eiffel, all knew the golden section and deliberately used this ratio.

We can use two-point and multi-point perspective in artistic creation. Art needs not only mathematics but also optics. One of the characteristics of impressionist painting is to make good use of the progress of human understanding of color and brightness in physics at that time.

The optimization method has two meanings: first, it can find the optimal solution of practical problems; Secondly, it emphasizes that the method of finding the optimal solution itself should be the simplest, or optimal.

The principle of the optimization method is based on the golden section, which is also called "0.6 18 method" by Mr. Hua. Mr. Hua's outstanding point is that he has found a mathematical method that is easy for front-line workers to master and use, which is the level of a real master.

Apply mathematical principles to life.

For example, when taking a photo, the protagonist in the photo will be placed at the golden section, and the picture will appear balanced and smart.

In terms of investment ratio, it is suggested to put about 62% of assets in the stock market, which has high returns and relatively high risks. Of the remaining 38% assets, about 24% are placed in relatively safe bonds, which is about 38% of the golden section. Finally, more than 10% of assets are all kinds of complex portfolio investments.

When making a travel plan, if you have 10 days, you can collect information in the first 6 days and make a comparison, and then make a decision on the seventh day. At this time, the decision will be optimal to a large extent.