There are essential differences between mathematics and physics in controlling the application of mathematical knowledge. Some concepts and knowledge that work in mathematics may not work in physics. Therefore, when applying mathematical knowledge in physics, we must combine the actual situation of the problem and adopt scientific solutions to different problems in order to get the most reasonable answer. +Take a physical problem as an example: "A car is traveling at a speed of 20+m/s, and when it encounters an emergency, the driver stops at an acceleration of 4+m/s and asks what the displacement is after braking for 6+s." For this kind of problem, although the displacement after 6+s is a problem, the car stops after 5+s, and finally 1+s is still the same. Therefore, mathematics must be mastered in combination with the actual situation when dealing with problems.

Allen Berg and McClane developed categorization in1940s, and Grothendieck developed algebraic geometry on this basis in1960s.

Some mathematicians, led by attiya, believe that the essence of physics is geometry. However, physicists will not accept this judgment, and mathematicians cannot accept that mathematics is a scientific tool. Practice shows that mathematics and physics are indispensable for understanding the world, just like people's left and right legs. Which is more important?