
The Beauty of Bounded Gaps (2013) - cyang08
http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html
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aisofteng
This is from 2013.

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pmalynin
Yup, I've been taught the result in first year calculus and the resulting
corollaries, which was over 2 years ago now.

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JadeNB
> Yup, I've been taught the result in first year calculus and the resulting
> corollaries, which was over 2 years ago now.

Are you joking? This is not calculus, and it's certainly not first-year
material.

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williamstein
I think he means that he stated the result in a calc class, not that he proved
it. It would be very reasonable (and cool!) to state without proof in a calc
class.

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JadeNB
I certainly won't presume to tell Will Stein about number theory, but it seems
strange to me to include in a calculus class (even without proof). Far be it
from me to suggest ever excluding interesting mathematical content, but I'd be
suspicious of an ordinary calculus class appreciating the significance of this
result. On the other hand, maybe such prophecies are self fulfilling, and the
enthusiasm of the teacher engenders the enthusiasm of his or her students,
whatever the material.

(I am curious what "the resulting corollaries" are, though.)

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pmalynin
Hmm, well you can read for yourself, my prof is nice enough to have posted all
of the lecture notes online; These are the lectures from the second class
where the result is covered on the third page:

[https://www.math.ualberta.ca/~xinweiyu/117-118.14-15/2014090...](https://www.math.ualberta.ca/~xinweiyu/117-118.14-15/20140904.pdf)

And then the homework (Q3):
[https://www.math.ualberta.ca/~xinweiyu/117-118.14-15/2014090...](https://www.math.ualberta.ca/~xinweiyu/117-118.14-15/20140904HW1.pdf)

Where the corollary follows.

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JadeNB
To be clear, I didn't mean "Are you joking?" as in "You are obviously lying or
mistaken"; I really meant, exactly and only, "Are you joking?", because I
found it incredible. Well, obviously you are not; and I would have taken you
at your word without proof, but thank you for the careful documentation.

I still would be hesitant to talk about this in my own calculus courses, but,
given the impression that this made on you and Will Stein's endorsement
([https://news.ycombinator.com/item?id=12886751](https://news.ycombinator.com/item?id=12886751)),
it sounds like that's just undue timidity on my part.

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JadeNB
If you're a fan of "How not to be wrong" ([http://www.jordanellenberg.com/how-
not-to-be-wrong](http://www.jordanellenberg.com/how-not-to-be-wrong) )—and, if
you're not, then go read it and you probably will be—then it may be worth
noting that this article is by the same author. It is an excellent and
accessible exposition that doesn't shy away from pointing to more technical
resources for those who are interested.

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duerrp
There's a nice documentary on Zhang (and the progress his work triggered)
here:

[https://www.youtube.com/watch?v=XIIyKWxGhEA](https://www.youtube.com/watch?v=XIIyKWxGhEA)

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kazinator
> _Quite the opposite—we take [primes] as immutable features of the universe,
> and carve them on the golden records we shoot out into interstellar space to
> prove to the ETs that we’re no dopes._

That sentence itself is golden!

