“Rigorous reasoning is crucial in mathematics, and insight plays an important secondary role these days. In the natural sciences, I would say that the order of these two virtues is reversed. Rigor is, of course, very important. But the most important value is insight—insight into the workings of the world. It may be because there is another guarantor of correctness in the sciences, namely, the empirical evidence from observation and experiments.”
--Kannan Jagannathan, Professor of Physics, Amherst College
- I agree with the quote above, that both rigor and insight are important roles in mathematics, and that insight is actually more important than rigor despite the fact that rigor is very important. Why is insight more important than rigor? This is because when people need insight in order to look into the workings of the world. And this can best be seen in one of the most important and fundamental processes of science: the scientific method. This method asks a person to first think of a question that he or she is curious about and wants to know about. This is insight, because it helps us find the questions that we want to solve. Without the questions, there will be no scientific process. Only after the question is voiced can the rigorous reasoning take place when the person is trying to create a reasonable experiment to test their his or her hypothesis.
- I believe that that insight is also important to solve problems. A sudden insight may help a person solve problems that he or she has been working on for a long time, such as a puzzle.
- Generally, to get the empirical evidence from observation and experiments (which is also known as the "rigorous reasoning", one must have insight. Insight provides the basis of science because it is the first step of the scientific process.
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