Is a theorem trivial because the proof is trivial?

Xiao-Gang Wen (MIT), Hao Zheng (PKU) and I finished a paper on the boundary-bulk relation for topological orders in any dimensions http://arxiv.org/abs/1502.01690. The proof is almost trivial with the tool we have introduced. But we think that the idea is quite interesting. We will submit it somewhere for publication.

I remember that some years ago, I proved an important result, which was first proved by somebody else. Their proof appeared a few days before I got my proof independently.  Their proof is over 70 pages long. But my proof is almost trivial and not worth publishing. I don’t know how to dress it up as a paper because the proof is too short. I took me another year to add many other results before submitting it for publication. It seems that how to publish something interesting but trivial to prove is a non-trivial question.

In the article “The origins of Alexander Grothendieck’s `Pursuing Stacks’ wrote byRonnie Brown, http://pages.bangor.ac.uk/~mas010/pstacks.htm, I found the following paragraph that is very entertaining. 

“He (Grothendieck) had a strong interest in detail and small things. He was against `le snobisme‘, and so was delighted with a comment of Henry Whitehead: `It is the snobbishness of the young to suppose that a theorem is trivial because the proof is trivial.’ He wrote that mathematics was held up for centuries for lack of the `trivial’ concept of zero. One of his striking phrases was `the difficulty of bringing new concepts out of the dark’. He thought speculation to be an essential creative activity.”

All my mathematical results obtained so far are quite trivial. I lack the technical power to prove anything “non-trivial”, such as those long-standing and famous problems. My only hope is that they are not un-interesting to some readers.

About kongliang

I am a mathematician interested in quantum field theory.
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