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pragmatist comments on Does anyone know any kid geniuses? - Less Wrong Discussion
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Here's the video: http://www.youtube.com/watch?v=hBW4S9xcTOk
He starts solving the problem at the 9:50 mark.
He's supposed to prove that a certain infinite series converges, and he applies the integral test for convergence. It is of course extremely impressive that a 12-year-old would even think of doing this, but the test is clearly not applicable in this case. The summand function is neither non-negative nor monotone decreasing, both of which are requirements for the applicability of the integral test.
To be fair to him, though, they (unintentionally?) gave him a trick question. He was asked to prove that the series converges, but it actually doesn't. Also, I'm sure if I was put on the spot in front of a TV camera there's a high probability I'd make silly mistakes.
It is quite possible that he's improved markedly since then, and if he's a university student and published in Phys. Rev. A then I would guess he has.
I am extremely worried to see him in the context of Glenn Beck pushing Christianity. As far as I know, his ideas to disprove the Big Bang have nothing to do with religion, and I sure hope he hasn't written the bottom line. And you're right about the integral test.
If I remember correctly, the Big Bang model was first proposed by a Catholic priest and was initially dismissed as an attempt to sneak religion back into cosmology. If he was engaging in motivated cognition to defend his faith, then wouldn't he not try to "disprove the Big Bang"?
The Catholic Church has enthusiastically supported the Big Bang model since the '50s. But there are strains of fundamentalist evangelical Christianity that don't think the theory is consistent with the Bible and so reject it. The Young Earth Creationist website "Answers in Genesis" is an example: http://www.answersingenesis.org/articles/nab2/does-big-bang-fit-with-bible
In America at least, if I knew a person was very religious, I would count that as evidence against the claim that they believe the Big Bang occurred. If I remember correctly, surveys show that a majority of Americans don't believe in the theory, and I suspect this is largely because they think it is in tension with their religious beliefs.
While the Big Bang may be a better fit for theism than the steady state model, it is a worse fit than the claim that the universe came into being a few thousand years ago with essentially the same physical structure it has now.
Christians don't have the criterion of making sense.
Some of them do. In any case, it seems clear to me that the Big Bang model is coherent with theism, but the steady state model is not (or, at least, is much less so).
I am not comfortable with this generalization - particularly when applied across all ages and the Christian being discussed was right.
Beck said "show us what you showed me in my office" implying that he'd been shown the problem before.
But it should be fairly obvious to any calculus student that that series doesn't converge since the limit as it goes to infinity isn't 0... It doesn't even exist. Sine and cosine functions are an immediate red flag to this, all you need to do to look at it is a simple order of magnitude analysis.
Nevertheless, I'm sure he's very smart. But I'm not sure he has much common sense if he didn't see that right away. I'll also echo Alex's sentiments below...
Well my instinctive feeling would've been - this won't converge. The problem with people educated by tests. The tests imply there is an answer. In real world when you do something new you don't have clues like 'it converges'. When i was studying stuff, we just had fairly hint-less questions.