..then a basketball break,
in which a friend of mine broke his arm on the pavement,
and we stopped playing..
but then dinner, and more LaTeX.
"so what's the point?" you ask, "things are going. what's the big deal?"
"ah," i'd reply, "but i didn't tell you what i was writing, did i?"
there's an idea, which has been bugging me. it's related to the error i recently discovered in my work.
[see this previous post for details]
since that error, i haven't really trusted my own math or any of the few proofs that i've written. in fact, when working on new ideas, often i'm relieved to find several errors, because
if i made such a grievous error,
and if it cost me that many theorems and corollaries,
then i have to become better at finding those errors.
you see, i wasn't the one who found the error in my proof. someone else did, but it's not embarrassment that bothers me.
what bothers me is that by missing that error, i demonstrated that after all these years, i might not know what is a proof and what isn't, what is good math and what is bad.
if you can't tell what is good math, then how are you supposed to do good math?
"so, you're a fraidy-cat neurotic," you'd say, "so what?"
that's the thing, and that's where the aforementioned idea comes in. it doesn't fix the error, but if it's correct, then it proves some of my previous conclusions and corollaries.
those conclusions were based on an error-prone idea, but what i'm saying is that i found another way around, another method of proof. it's simpler and the method is more concrete than my last idea, but ..
.. i don't trust it.
the adviser is out of town ..essentially indefinitely.. so i'm on my own on this one. fool that i've been: i should have given a study seminar talk on the background of my research, last semester or before. i could then bug someone to troubleshoot my proof, and finally find that elusive error.
i've been wrong before and it could well be wrong: that's life, and that's math. not everything works out, and as the saying goes,
if all your ideas are working,
then you're not getting enough ideas.
i feel silly for saying it, but i just don't want to lose my conclusions for a second time. the first time was hard enough.
[1] i meant that i was off & on, not the screen. trust me: my laptop isn't that dependable!
2 comments:
That is tough, but at least you don't have a broken arm. So there's an upside.
Are you going to Helsinki this month?
that's true. for the record, i learned today that my friend has a compound fracture, but at least it was his non-dominant arm. he's fine, otherwise.
i'll be in helsinki .. and i notice that you're slated to talk, L. i look forward to it.
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