Hardy's peculiarities
Godfrey Harold Hardy (1877-1947) was a very influential mathematician of the 20th century. Part of his work focused on number theory where he made many important
contributions, the famous "circle method" being one of them. He is also credited with the discovery of one of the greatest mathematical
talents of all times: Srinivasa Ramanujan. Ramanujan had written to several mathematicians but it was only Hardy who took him seriously and
invited him to England.
Hardy's life is full of anecdotes and remarkable quotes. Being a number theorist, Hardy was obsessed with the Riemann hypothesis. Once he was
asked what would be the first thing that he would do, should he come back to life 100 years after his death. "Find out whether the
Riemann hypothesis has been proven or not" was his quick answer. He was known to be an atheist but he used to say that God was mad at him.
He would still find a way to take advantage of this. Here is how: he was very afraid of travelling by boat. Whenever he had to take a long
trip he would send somebody a letter stating that he had just proven the Riemann hypothesis and that he would publlish his proof after the
trip. If this does not make sense, consider this: Do you think that God would ever let his boat sink and thus grant Hardy the reputation
that he had solved the big problem but perished in the sea? That was Hardy's way to travel safely...
Around the end of his life, he is said to have wondered whether his mathematical career had contributed anything to the world. "I have
never done anything useful. "No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the
least difference to the amenity of the world." He even went as far as publishing a, now famous, book titled: "A mathematician's apology".
Since then, generations of mathematicians have, of course, thought differently of his contributions.
It should be appropriate to close this brief account of Hardy with another quote of his:
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that...
Lecture Objectives:
- Diagonalization of a matrix
- Defective matrices
- Inner products on complex vector spaces
- Hermitian matrices
- Unitary matrices
Homework:
1-7 from 6.3
1-4 from 6.4
Reading:
Sections 6.3, 6.4
