Advice to a Beginning Graduate Student or What is Research? Or The 4 R's of Graduate School: Reading, Rithmetic, Research, and Writing. Outline of the talk: READING, STUDYING, THINKING, STARTING OFF on the Ph D, DEEP in the MIDDLE of the Ph D, WRITING it all up.

READING: Books are not scrolls. Scrolls must be read like the Torah from one end to the other. Books are random access -- a great innovation over scrolls. Do NOT feel obliged to read a book from beginning to end. Permit yourself to open a book and start reading from anywhere. In the case of mathematics or physics or anything especially hard, try to find something anything that you can understand. Read what you can. Write in the margins. Next time you come back to that book, you'll be able to read more. Consider writing what you read as you read it. I remember a professor of Mathematics at MIT, name of BERTRAM KOSTANT, who would keep his door open whenever he was in his office, and he would always be at his desk writing.

STUDYING: You are all computer scientists. You know what FINITE AUTOMATA can do. You know what TURING MACHINES can do. Finite Automata can add but not multiply. Turing Machines can compute any computable function. Turing machines are incredibly more powerful than Finite Automata. Yet the only difference between a FA and a TM is that the TM, unlike the FA, has paper and pencil. Without writing, you are reduced to a finite automaton. With writing you have the extraordinary power of a Turing machine.

THINKING: CLAUDE SHANNON once told me that as a kid, he remembered being stuck on a jigsaw puzzle. His brother said to him: "You know: I could tell you something." I advise you, when you're stuck, to imagine a little birdie or an older version of yourself whispering "... I could tell you something..." I once asked UMESH VAZIRANI how he was able, as an undergraduate at MIT, to take 6 courses each semester. He said he had to find a shortcut. Umesh understood that problems often have short clever solutions. When you work on a problem long and hard but unsuccessfully, and then learn that someone else found a solution, see it as a great opportunity. Ask yourself: "How SHOULD I have been thinking to solve that problem?" Danny Sleator tells me that BOB FLOYD independently recommended exactly this exercise. When you succeed but find someone else already published, roughly 50% of the time it is NOT at all the same as what you did. 25% of the time, it is the same but not as good. 25% of the time it is better. This means that 50% of the time or more, you can still publish.