

A second experiment concerning mathematical writing - ot
http://gowers.wordpress.com/2013/04/02/a-second-experiment-concerning-mathematical-writing/

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Dn_Ab
Stop here if you haven't taken the poll. I think it is very readable but gives
itself away by favoring certain phrases which suggest a template. Phrases like
"we are done", "whenever", "therefore,[setting]". All the proofs are terse in
general but it tends to spell things out more carefully than humans who prefer
to string ideas using conjunctions and leave obvious basics as implicit.

Because it spells things out like a careful someone just learning (uses "so"
less, the mature person is also apart) it would be a good tool for exposition.
By that token I can also guess the grad student as the one who seems most
comfortable (and also for favoring "take" and for all style statements while
using "exist" and "since" least). This is most interesting for what it says
about teaching and how internalized understanding makes teaching hard:
expertise is an iceberg floating in a sea of unconscious reasoning. My
guesses:

========

 _grad student_ : b, c,a, b,a

 _bot_ : c, a, b,c,c

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pervycreeper
Great observation. I didn't make it past the first problem, but I chose (c) as
well. Reason being, that proof seems to have the least, shall we say, semantic
depth (I'm just making up terms here). It invokes the least amount of meaning
/ refers to the fewest concepts per statement. Interestingly, not only is this
a sign of having been produced automatically, it can often be a positive thing
in terms of mathematical style.

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captbaritone
I thought people in this thread might also be interested in a bit of software
my brother wrote: [Mathgen](<http://thatsmathematics.com/mathgen/>)

It randomly generates math papers, one of which was [accepted by a peer-
reviewed
journal]([http://science.slashdot.org/story/12/10/19/1256216/randomly-...](http://science.slashdot.org/story/12/10/19/1256216/randomly-
generated-math-article-accepted-by-open-access-journal))

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Gravityloss
When some of the journals are revealed to consist of just robot editors and
reviewers as well, the circle is finally closed.

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hexagonc
I'm not sure of any of my answers, but I guessed the computer generated proofs
are: 1c, 2a, 3b, 4c, and 5c. These proofs seem to be the most uniform in
language, especially the way they all end with "we are done". I was the least
certain about 4c since this option doesn't seem in the established style of
the computer (assuming my other guesses were correct).

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mertd
It would be nice to be rewarded for the effort. They should reveal who wrote
which proof after the user has answered all questions.

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alainbryden
Yep. When I got not result after carefully considering my first answer, I
quit.

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pohl
Same here. Which one did you pick? I chose (a) because it began so nicely by
stating the goal clearly, something that humans often omit.

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AimHere
I think it's not (a)

There's a line in that proof saying r=min{a,b}; normally I take that to mean r
is the minimum of a and b (which makes the proof wrong, since not all metric
spaces have obvious orderings on their elements. Spaces like the complex plane
or the 2d plane, with an appropriate metric, for instance.

I suppose it could mean r is the point in {a,b} such that the ball B_a(x) or
B_b(x) has the smallest radius - but that looks more like a human making a
notational mistake, particularly given that both 1b) and 1c) use min(,) in a
way that seems correct to me (since they're using min on the values of the
metric, not the elements of the metric space.

AFAICT, either the prover made a mistake in logic or a mistake with notation -
which I reckon makes him or her human.

Then again, it's been years and years since I thought about this stuff, and I
was prone to making mistakes all the time when I did, so everything above
might well be wrong. My neurons are getting all fuzzy these days.

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mturmon
"...which makes the proof wrong, since not all metric spaces have obvious
orderings on their elements..."

Your reasoning here is wrong. The "a" and "b" come from the range space of the
metric, which by definition associates a pair of points in the metric space
(unnamed, but call it X) with a nonnegative real number.

In short, "a" and "b" are in R, not in the original metric space X, so it's
legal to take the lesser of a and b.

~~~
AimHere
Oops yes. I see that now. I told you I was rusty!

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rsingel
I'd be interested in seeing the first post, but there's no link. One of the
_biggest_ advantages of writing online is the ability to link.

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endoself
Two posts previous: [https://gowers.wordpress.com/2013/03/25/an-experiment-
concer...](https://gowers.wordpress.com/2013/03/25/an-experiment-concerning-
mathematical-writing/)

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gyom
I answered three of those where I didn't have to think too hard to follow the
reasoning. It would be nice to have the answers eventually after the
experiment is over.

One of my theories so far is those computer-generated proofs don't use triple
equalities (e.g. "a = b = c") even though it makes a better explanation in
certain limited situations.

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fnbr
I only answered the first one, but it was my impression that 1c was generated
by the computer as it used weird greek letters; I have never seen eta used in
that setting before, and I doubt that a grad student or an undergrad would be
inclined to break convention.

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tome
I can assure you that many undergrads and grad students are happy to use the
symbol eta.

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stevenwu
not too long ago I attended a talk by Thomas Hales (proved the Honeycomb
conjecture and the Kepler conjecture) where he talked in detail about his
Flyspeck project, which he says has just a 400 line kernel that traces every
line of a proof down to the axioms, that will formalize his proof of the
Kepler conjecture and many questions in the Q&A after had to do with curiosity
of machines being able to do exactly this. very interesting

