deodands

Perpetual student

[My friend RL is nearly at the end of a pureish maths degree and is considering a physics one and an applied maths MSc]

There is something to be said for acquiring lots of human knowledge by doing degree after degree. But not that much.

Acquire one degree and you demonstrate (partly to others but mostly to yourself) that you have all the skills and talent to find, judge, and use for your purposes the kinds of knowledge that you need to solve problems and follow your interests. While there are big, big, cultural differences, a pure maths degree is your self-certification that you can potentially learn all the undergraduate maths, physics, compsci and actually quite a lot of other sciences if you ever need to. Of course learning more and more of them through a formal degree is great (just wait till you get to molecular biology, which blows the rest away...) but there are some opportunity costs.

One cost is that an extra cognate degree adds practically no market value to you. Going off and doing a law degree or a psychology one or English or something would do, and certainly gives you a whole different set of skills which I have learned to value through their absence.

But the biggest opportunity cost is that learning anything is not the same as doing it. For some people that matters because they love the doing of it, and those people certainly report such a high from that doing that it is worth a try. As for me, I never really inhaled. What I loved about becoming an academic was the extra insight it gives you into what human academic knowledge means. I had some papers I was proud of but I think I was most proud of the fact I could ask sensible questions about other people's papers. The trade of getting a PhD written, papers out, and then getting and delivering grants gives you a critical, tired eye for the mass of dullness people will claim your attention for. And that makes your appreciation of the little nuggets of wonderfulness about the human potential for understanding, like the solved extracellular structure of the EGF receptor or PageRank or vector spaces, all the keener.

Find an area you love and dive into a PhD. You'll end up despising most of what you thought you loved, but unlike most human relationships that makes what's left over all the sweeter, and unlike all human relationships it is guaranteed to stay with you until death.