Grad student lore

Writing

Clear writing is clear thinking.
Most of the effort of writing is rewriting. You have to get something down, but then you have to read it over and over and make improvements.
One way to get better at writing is by reading. If you want to be writing research papers, you have to be reading them.
It’s not enough to be right. You also have to be persuasive.

Spend 95% of your time working with familiar tools, and 5% trying new ones.
Any tool that makes it hard to do something essential isn’t the right one.
Corollary: Latex beamer is awful. You shouldn’t have to work so hard to use video, arrows, highlights, and so on.
For putting latex output into Powerpoint or anything else, you can use latexit (Mac) or KLatexFormula (Windows/Linux/Mac).
Use Detexify to search for a latex symbol by drawing it.
PDF simulates a piece of paper. It’s terrible for most things done on a computer screen.
Automate repetitive tasks. Doing so can be like growing a new arm—painful, but handy.
Use version control fanatically. Check in changes atomically, not in huge chunks. Use branches to try new ideas. I have relearned these lessons many times.
Learn to track and document all of your work as you go. Use a format based on plain text documents. Those are the only ones that are sure to still work in 20 years.

Numerical experimentation is more like a laboratory science than math. If you don’t develop a system of keeping meticulous track of what you have done, you will go in circles and make big mistakes.
Clarity in coding is more valuable than cleverness.
Math is often about the 0.1% of cases that don’t work. Computing should be about the 99.9% that do.
If you haven’t tested your package, then I don’t trust it.

When you encounter a new idea, start with the simplest example you can fully understand.
There’s no sense trying to solve a hard problem if you can’t first solve a simpler version of it.
Infinity can be incredibly useful, but in applied math, it can be an unwelcome distraction.