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 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,, 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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