A second experiment concerning mathematical writing

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

by ot • 13 years ago

77 25 13 years ago

gowers.wordpress.com

mertd• 13 years ago

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

alainbryden• 13 years ago

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

pohl• 13 years ago

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.

dhimes• 13 years ago

Perhaps they are collecting stats. We should check back later.

anonymouz• 13 years ago

From the post: "I would also be interested in comments about how you came to your judgments. All comments on both experiments and all votes in the polls will be kept private until I decide that it is time to finish the second experiment."

ubercow13• 13 years ago

A lot of people read Gower's blog as it has some really useful expositions of undergraduate maths, which he makes available for anybody who might find them useful. In that sense I think he is justified in not providing a reward; you don't have to do the test if you don't want to anyway. He will no doubt post later with the actual writers' identities.

gyom• 13 years ago

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.

hexagonc• 13 years ago

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).

captbaritone• 13 years ago

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-...)

Gravityloss• 13 years ago

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

Dn_Ab• 13 years ago

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

pervycreeper• 13 years ago

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.

fnbr2• 13 years ago

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.

fnbr2• 13 years ago

^^^Weird being defined to mean "not very common"

tome• 13 years ago

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

rsingel• 13 years ago

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.

endoself• 13 years ago

Two posts previous: https://gowers.wordpress.com/2013/03/25/an-experiment-concer...

stevenwu• 13 years ago

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

A second experiment concerning mathematical writing

Related Stories