Advice is what we ask for when we already know the answer but wish we didn’t. (Erica Jong)
The latest few words of advice on research for graduate students I read have been penned down by Fan Chung. She addresses mostly combinatorialists, but what she says applies equally well to theoretical computer scientists at large. I like the fact that she stresses the collaborative nature of the research enterprise, and that she embraces one of my favourite hobby horses, viz. the Hardy-Littlewood rule: authors are alphabetically ordered and everyone gets an equal share of credit. She adds:
The one who has worked the most has learned the most and is therefore in the best position to write more papers on the topic.
(I had never thought in these terms myself, but yes that's true.) She also writes:
If you have any bad feeling about sharing the work or the credit, don't collaborate. In mathematics, it is quite okay to do your research independently. (Unlike other areas, you are not obliged to include the person who fund your research.) If the collaboration already has started, the Hardy-Littlewood rule says that it stays a joint work even if the contribution is not of the same proportion. You have a choice of not to collaborate the next time. (If you have many ideas, one paper doesn't matter. If you don't have many ideas, then it really doesn't matter.) You might miss the opportunity for collaboration which can enhance your research and enrich your life. Such opportunity is actually not so easy to cultivate but worth all the efforts involved.
I could not agree more. I will add Fan Chung's advice to the list of links I suggest to all my students and colleagues. Maybe you'd like to do so too.