Mathematicians discover new way for spheres to 'kiss'

The interesting ta for me:

> Had she been one of his graduate students, he would have tried harder to convince her to work on something else. “If they work on something hopeless, it’ll be bad for their career,” he said.

A small anecdote: my dad is a mathematician. For a significant portion of his postdoc/early career (in the 80's/90's) he worked on proving a particular conjecture. Eventually he abandoned it and went to be much more successful in other areas.

A few years ago someone found a counterexample. He was quite depressed for a few weeks at the thought of how much of his strongest research years had been devoted to something impossible.

Choosing a "good first problem" in math is quite difficult. It needs to be "novel," somewhat accessible, and possible to solve (which is an unknown when you're starting out)!

Thanks that is a good anecdote. Did he get over it and how?

To me such a career is useful for (a) the greater good: you can't make discoveries without dead ends and (b) the maths created along the way! Or if not shares then the skills developed.