Why is it generally believed that mathematicians can't make first-class achievements after 40 years old?
Throughout his life, Gauss has a strong ability of innovation. So did Newton, but his interest in his later years turned to alchemy, theology and chronology. But one thing happened in his later years, which can prove that his mathematical talent is still based on the top mathematicians in Europe, that is, Bernoulli and others put forward the problem of the steepest descent line. It was not easy to solve this problem at that time. At that time, although many of the best mathematicians solved the problem, it should not take three to five days. What about Newton? As you know, it took more than half a night to finish. This is a variational problem, and it is easy for college students who have studied functional analysis and simple variational basis to solve it. However, if we don't think about the problem based on a specific era, we can't appreciate the greatness of God-like people in that era. Newton actually used the basic idea of variational method when solving the problem of fluid optimization. If he takes this kind of problem as his important research topic, I'm afraid the Euler-Lagrange equation will be changed into Newton equation. Euler also exists as a god. I was blind in my later years, and my writing ability was enhanced. My thoughts led the overall progress of mathematics in the18th century.