the next generation, part 3*: possibilities.

you know, today's meeting was pretty fun.

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the student, having had a few days to think about a few concrete aspects of the problem, was a lot more comfortable showing me things that he thought about, telling me claims that he suspects are lemmas .. and why he thinks so.

what really helped, i think, is that it became clear to us that there was plenty we could learn, just by computing explicit configurations.

the student seemed to feel both awed and excited, that these were strange, interesting, yet accessible things for him. i think he realised today some scope of what was possible for him, that he started to believe in himself.

this isn't to say that i didn't guide the discussion, but i felt like the back &-forth today is suggestive, and this laissez faire style might actually work.

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* .. and no, you didn't miss part 2; i haven't posted it yet.

training the next generation (a first post in a potential thread)

so i finally have something ready to write about [1]: i'm advising a former calculus student of mine on a summer (undergraduate) research project .. and (for me, anyway) it's a scary thing.

many of my colleagues are old hands at this, i know;
so if i seem naive, it's because this is the first go and i don't know any better.

i worry, for good reason: he's studying a topic i know little to nothing about. in particular, it's not clear to me how easy or hard the problems i pose to him really are .. and as a result, i don't know how much frustration i'm throwing his way.

it depends, of course, how much the student is willing to work. if i give him a badly-posed problem, then a good work ethick can actually be bad .. in the sense that, by working with abandon for too long a time, he burns out and gets turned off by pure maths in the future.

in case it's not clear, i'm encouraging the student to make his own conjectures;
of the established theorems whose proofs he can easily understand,
i'm suggesting him to try his own variants.

in other words .. and for better or worse ..
i'm insisting that i don't give him orders;
he'll have to train himself to think like a pure mathematician,
but i'll be there if he needs advice or guidance.

i was worried about his technical chops before .. until i realise that if his proof-writing skills require work, then this is potentially the best way that he can practice them: by working with a topic that interests him.

let's hope these aren't another example of famous last words ..!

[1] as you can see at the end of this post, i'll be tagging these thoughts with the handle "Σ:nextgeneration" .. and the usual disclaimer follows: unlike other maths blogs out there, i'm not out to train or educate maths-inclined people out there, at least not directly. instead, i'm going to show you, through my mistakes, what not to do.