while I created it to serve Tarsnap’s needs, it would be a stretch to place such a general-purpose open-source tool under the narrow umbrella of “working on backups.” In short, academic institutions systemically promote exactly the sort of short-term optimization of which, ironically, the private sector is often accused. Is entrepreneurship a trap? No; right now, it's one of the only ways to avoid being trapped.

maybe we should allow people to say they’re just not a math person, and maybe we should find ways they can still support and appreciate math without feeling like they need a Ph.D.

Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind. ​ The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere.

You will have the opportunity for unparalleled focus on whatever your research question is. ​ Those who have recently obtained a PhD can outwork virtually any of their peers in terms of duration and efficiency ​ To undertake this vow of poverty voluntarily, while doing work that is more intellectually challenging than most of your peers that are earning average salaries shows superhuman commitment to seeing something through to completion ​ This criticism will either get to you, and you’ll bail out of the program, or you’ll learn to separate the valid criticism from the invalid criticism, a skill that will serve you well in any profession, in any discipline ​ If you work on your degree alone, you’re doing it wrong. Have a side job. ​ Stick to your schedule. Be humble. Don’t expect to get more than 3 hours of high-order intellectual work done per day

For the rest of her life, my grandmother told this story to pretty much everyone she met. When I visited her at the assisted living facility for the next decade—where she loved living as it gave her independence—even the janitors would greet me as the granddaughter who had gone to the United States to get a doctorate, and whose committee had applauded my grandmother. She told this story to people she sat next to in the ferry; she told this to anyone who asked her about her life.

Slowly, gradually, it dawned on me that what I enjoyed was mathematics. The mathematical aspects of CS were what got me excited and kept me up at night working on projects. ​ The Summer after I graduated, I decided I had too much awesome stuff in my head that nobody wanted to hear me talk about at parties, so I started a blog called Math Intersect Programming ​ If someone offered me this deal to write about math and CS, I would take it in a heartbeat. I would never want to retire.