Obviously, the research object of pure mathematics is abstract structure, while mathematics in theoretical physics is mainly complex arithmetic. As for which is more difficult, it should be pure mathematics according to the thinking inertia of ordinary people. It is precisely because of this that mathematical physics, a subject that develops mathematical structure with the help of physical images, has emerged. After all, a genius like Galois who can gain insight into abstract structures out of nothing is too scarce, and some images are better than rote memorization.
Secondly, I now think that the Lebesgue measure and integral of about 1900 are
Theory is much more difficult than quantum mechanics before 1930. Strangely, it was difficult for me to understand the special theory of relativity when I was an undergraduate, but now I am sure I can deduce the whole theory quite easily.
Come out. At that time, I had no physical intuition at all, so I thought it was better to study pure mathematics, which was actually not that good. I have never been there.
Yao is good at the rigor of mathematics, especially the rigor required by analysis. Mathematics pays more attention to thinking and the internal laws of matter and thinking. Mathematical theorems are general theorems that hope to see the big from the small.
So there are often more "useless" parts behind.
Mathematics starts from reality and is divorced from reality.
For other science and engineering disciplines, mathematics is more like a practical tool discipline. The branches of species are extremely complex, which leads to many solutions to the same problem, and then the upper limit is extremely high, which also leads to the extremely difficult research frontier, which is basically difficult for decades.
His main interests are algebraic calculation and analysis, function prediction and analysis, geometry, probability theory, automata and so on.
Thirdly, it can be seen that the essence of mathematics is the calculation method, not the calculation itself, and it is a discipline that attaches importance to thought. The ultimate of mathematics is enlightenment and transcendental. Biophysical chemistry is an experimental subject, and biochemistry is more like a liberal arts covered with experimental skin. The above is my full recognition of science.
I know that physics is still at the level of more than 80 in high school physics, and it is not necessarily good to learn mathematics well in physics. But reality-based science
All can be verified by reality, there are always solutions, and the methods should be traced. And mathematics can't be true. number
Yes On the other hand, those abstruse and beautiful mathematics can always find a place in physics and other fields, such as Lamanukin module form in string theory.
It is very useful. His seemingly strange mathematical formula not only inspired a lot of profound modern mathematics, but also existed in things.
It is widely used in science, engineering, biomedicine and other fields. And the list goes on.
So modern mathematics and physics are actually intertwined, and mathematics and physics are the basis of science and technology. Now life is inseparable from these technologies. If you don't understand this, you can't understand the present.
Society.
Cutting-edge physics always lacks suitable mathematicians.
Use, so promoted the progress of mathematics. For example: calculus, Riemannian geometry, quantum logic. It is difficult for mathematics to rest on its laurels only by logical deduction. Where do new concepts and axioms come from? We must draw inspiration from the real world, and physics is one of the biggest sources of inspiration. ?
Fourth, theoretical physics is half mathematics and half philosophy. It's hard to define the standard. After all, two of the three mathematicians in history also
A great physicist, I think. I always thought I could study pure mathematics or theoretical physics.
Condescending, despising everything, mastering the laws of the universe (sorry, a little doge). A math student or worker.
Of course, mathematics is difficult, and physics is also difficult. Even great mathematicians and physicists expressed similar views. Many people count.
Learning is divorced from reality, so there is no physical difficulty. But you know, the details of many things in physics need mathematicians to deal with, and these are very
Many have developed into an independent branch of mathematics. I don't think it is easier to deal with details than with reality. Also, the difficulty of the work.
Degree and its importance cannot be completely equated. A problem can be too difficult to be solved at all, but it is of little significance. there are also some
This work seems simple, but in fact it is profound.
I think the greatness of a job lies in the originality of the way you solve this problem. We often don't think that mathematicians who have solved many difficult problems are better than mathematicians who have done pioneering work. Because the latter often realized the crux of the problem and invented mathematical tools to solve the problem, the rest of the work can be said to be relatively dull for people.
Every dog saved his life.
To be fair, there is still a chain of contempt for scientific research, but I often feel puzzled. Basic subject
It's really important, but it doesn't mean that work in other disciplines is easier. It seems that some jobs may be theoretically
It's a technical job, but even it's not easy. It requires a lot of people's input and some technical skills.
Clever support. Technical skills have been accumulated, summarized and become a theory. I think the importance of work is more important than the difficulty. There are many things defined in mathematics, which we think are more important. If one day we find something important, mathematicians will give it a definition, although we have never considered it before. Physics and mathematics are very rational, and rationality is different from wisdom. Physics and mathematics are inseparable. Throughout history, physics has always been one step ahead of mathematics.
And even original works are inevitable.
Summarize from examples. Therefore, I think the work of any discipline is equal, equally difficult and pioneering.
Outstanding people at work. It's easier to judge a subject. I don't think we have a thorough understanding of it.
It is said that the string theory of theoretical physics can no longer be studied
Go on, because all the existing mathematical tools are used, string theory is inconsistent with reality, has been significantly different, and has been wrong by statistical theory. Now everyone is developing a deeper theory of subdivision structure, which is the way out for theoretical physics, not a geometric square.
On the contrary, algebraic direction is the real frontier of theoretical physics towards geometry.