The class was discussing a problem on the board. A boy said that he does not know what to do. A girl explained how she solved it. The boy said, “But how do you do …?”. She said, “I used theorem …”. He replied, “Boy, are you smart!” She replied, “That feels good!”

 

Afterwards, I spoke with her, telling her that when she does well, she will feel good. This is an important tool that mathematicians use – listen to one’s emotions. When one understands something fully, as when one does a problem correctly, he/she will feel good. Conversely, if one feels bad, it usually means that you do not understand the material (study it more!) or that the problem may be wrong (recheck it!).

 

Feelings are very important in mathematics and science. When I go to a seminar, I often hear statements like “I do not feel good about this,” or ”I feel good about this.” You too should examine your feelings during class and when doing homework.

 

Why do mathematicians do mathematics? Yes, mathematics is crucial for science, for our understanding of the world. Yes, mathematics is crucial for modern technology. These are not the reasons why mathematicians do mathematics. The reason is they want the good feelings we get when we understand something or do something new.