What's a Mathematician to do?

That's right: not with his math. The math he talks about in his book has been around for at least 200 years.

I don't and will never pretend that when you're a mathematician you're forbidden to help others -- that would be meaningless and ridiculous. I react to the "feel good" sentiment that the motivation to do maths should be found in a desire to better the world.

Math is an end in itself; if you want to help the world that should be on your own time.

Ellenberg's book is great.

    "You keep on learning and learning, and pretty soon
    you learn something no one has learned before."

Ramanujan wrote to Hardy: "I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university of from the government."

Returning to our world, a tenured university position could provide stability, while a contractual appointment to teach Linear Algebra I & II might end next year - and a journey by stagecoach to the next temporary appointment. In such a situation it may be simpler to write code for a living, while one 'dreamed a dream' on weekends.

The way it normally works, one figures out these answers during the M.A level itself. The trouble starts if one does not & keeps plodding on.

I apologize if this sounds dull & dreary, but I recently gave this advice to a nephew who wanted to study maths after an undergrad degree - he is now safely writing code for a salary & his parents are relieved. Have I stymied the next Ramanujan, perhaps out of a sense of sour grapes at my own inability to prove the Riemann Hypothesis? Both are possible, but unlikely.

I'm in my 6th year of my PhD as a theoretical physicist. I have been rejected for ever prestigious fellowship and tenure track position I have applied for, my academic career is dead. As I finish my PhD I'll start applying for national lab and industry positions and likely end up right next to your nephew writing code somewhere. I will never contribute in any significant way to the world of theoretical physics.

Do I regret it? Hell no! At least I tried! I loved so much of my graduate school experience and I got to try my hand at real research, teach huge classes of undergrads about my favorite topics and travel all over the country giving talks at conferences.

I imagine going to graduate school is a lot like starting up your own business, its a high risk/reward situation. And if you do succeed you get huge grants, a tenure track position, and wonderful students to work with. Failure means going back to industry with the everyone else (is that so bad?).

If I had skipped grad school and moved straight to industry (I've had multiple internships in the valley) I would certainly be much further ahead, both financially and in terms of job security. But I would have missed out on an important life experience and more importantly I never would have made my attempt to contribute to math/science.