The Ph.D. program in Mathematics comprises two years of courses followed by a third year of personal research work, under the guidance of an advisor, to produce a dissertation, also called a thesis.
Ph.D. stands for "Philosophy Doctor". It is the generic name of the doctorate degree in all the sciences (maths, physics, computer science, etc.) and the humanities (literature, languages, history, etc.), with the exception of law. In medicine, it is M.D.; and in law it has yet another name.
At the end of the first two years, students must pass qualification examinations -- the Quals -- to be allowed to pursue toward the diploma.
François's professors were all outstanding, not only because of their impeccable academic credentials but some of them because of their background or non academic activities as well.
Thomas, the professor in charge of Advanced hypothesis testing, drove a yellow Lotus sports car and was barred from all United States casinos.
With some friends, he had designed a method to observe extremely accurately the gestures of the croupier and the behavior of the roulette wheel, and transformed quite legally the game into a vacuum cleaner of money for them.
Morris was one of those friends. Still a young associate professor, teaching Introductory probability, he had been in a previous life a professional magician who performed on stages all over the world amongst chorus girls, acrobats and lion tamers.
He kept from his past trade a peculiar way to produce the expected results at the end of long calculations.
Often students would ask Morris to perform a trick, but he almost invariably declined.
Once though, he came to the office of Vicky, Fay and François, who were working late at night. They asked him to do a trick, and he accepted.
From his pocket he pulled a deck of cards, and with one hand opened it into a fan, like the tail of a peacock. Without seeing the cards, he asked Vicky to pick one, show it to Fay and François, and put it back into the deck.
He asked François to shuffle it and hand it back to him. Then he put the cards on a table face up and spread them. The three students could see that the card Vicky had picked wasn't there.
Morris said: Fay, would you please check under your notepad. She did and there was Vicky's card.
Fay: And you know which one it is too?
Morris: Sure, said Morris with his high-pitched voice and an impish smile, it's the one missing from the deck... Vicky chose the Queen of Hearts.
François and his fellow students were nearly all teaching and research assistants in the department which in return took charge of their tuitions and paid them a small stipend for living expenditures.
The work of T.A. (teaching assistant) consisted in correcting papers of undergraduate and master's students, and helping them with their studies.
François was also the R.A. (research assistant) of Morris. He would meet with him almost every day, in late afternoon, in Morris's little office crammed with science books on shelves and in piles on the floor. On one shelf there was also a basketball.
François read over papers, checked proofs and results, sometimes simplified final mathematical expressions.
That, in addition to his own studies, was a heavy load. But he enjoyed this life, which still left him some time to spend with his friends, most of them, like him, enrolled in doctorate programs.
They were all gradually leaving the world of students to that of academics.
The autumn following the Quals, Morris was away for the year, on leave to another university.
One day François was talking to Saul, a tenured professor both in Applied Maths and in Geology, who suggested to him a problem that would be suitable for a doctorate. He accepted and Saul became his advisor.
The following months, François worked on the problem, seeing his advisor every two or three days. In March, Saul told him that he had enough results and was ready for the thesis.
During the spring François wrote his dissertation, while now and then travelling to give lectures on his work at several universities on the East Coast and West Coast.
François received his diploma in June.
Soon afterwards came an offer from the Massachusetts Institute of Technology, in Cambridge, near Boston, as instructor in the maths department for the following two years.
During the month of July, he taught his first course at Stanford in the Summer program, and then got ready to move.
The Californian period of his life was over. It would continue on the East Coast of the United States.
He was twenty-five.
He knew what the next two years would be.
But, beyond that, like for any young man, the future was vast, open and unknown.