Validating Originality in Mathematical Proofs: A Guide for Researchers

[matt grime]

Finally got my brain in gear (which is odd given it's not even 10:30), and see what I was misreading yesterday.

 

[Jimmy Snyder]

If you can't get on there i could send it to you.

Thanks. I can't speak for anyone else but I had no trouble getting in. You just need to register, and it's free. The article gives a fascinating insight into how theorems come to be.

 

[honestrosewater]

What a coincidence- I just happened upon a http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1039293064?abstract= in a logic journal that says:

There is nothing original in it [this paper], beyond the easy observation that Lyndon's theorem gives the distribution laws. I wrote it up for publication because I became aware that the facts have not reached print. In fact they haven't even reached the grapevine. Recently I came across a team whose research project revolved around answering the question which Lyndon's theorem has already answered.

The author wasn't unknown (I'm actually reading one of his books now), but I don't imagine that's the reason they published the paper.

 

[mathwonk]

jimmy, that interview was with Raoul Bott. I have a personal story concerning him. Over 30 years ago I was a temporary instructor at a small college, struggling to learn as much math as possible by teaching as many new courses every year as they would allow, and volunteering to teach others as overloads.

Desiring to make my explanations clear, I tried to understand the material, and began constructing new proofs as you are doing. In an attempt to discern what in the world the green/stokes theorems were good for, I noticed with glee that they could be used to prove that the circle does not deform away from the origin, and hence one deduces the fundamental theorem of algebra, and brouwer's (smooth) fixed point theorem.

In summer, I persuaded my college to fund my attendance at a differential topology course for graduate students in Mexico, where Bott was lecturer. One day walking outside I told him my proof. Putting his arm kindly around my shoulders, he asked "Isn't that the usual proof?" I don't know, I said with subdued excitement, I made it up myself. What a privilege to be in his company for a few minutes.

I felt inspired by the whole meeting because the students there were not much stronger I thought than me. Moreover the hard work I had done at understanding differential methods made it clear to me what the points were that some of the lecturers were making. I could see that I had achieved the same view of some elementary things as they seemed to have. I stretched myself to take in the new ideas they spoke of, like characteristic classes for foliations, and as obstructions to embeddings of manifolds.


Within 5 more years I had a PhD (in a different area), and in a few more years I was an academic visitor at Harvard where I saw Bott again, feeling almost like a colleague. He did not remember me but I did not mind, being in heaven.

Now I am a tenured professor of mathematics at a university.

If you keep pushing your curiosity, it will lead you further, in some way.

best wishes

 

[Jimmy Snyder]

I published myself.

Thanks to everyone who helped me with this question. Here is a link to my web page where I have written up the theorem for all the world to see. If anyone has comments or suggestions for improvement, I would be most gratified to hear of them.

http://www.jimmyrules.com/operator.pdf

I just got finished reading Professor Kubrusly's "Elements of Operator Theory". I found a lot of typos and other errata in the book and sent them to him. Like so many authors of math and physics texts, he is very approachable and expressed his gratitude for the information I sent him. I also sent him the link above but he has not gotten back to me about it. His book, like most others in the field, has a proof of the second theorem in my paper that relies on the polarization identity.

 

[Jimmy Snyder]

Follow up:

The essential features of my proof were published by Martin Schechter in the book "Operator Methods in Quantum Mechanics", in 1981. His statement of the theorem is in Lemma 1.5.1 on page 8. His proof on page 10 scoops me by 24 years. I don't know if this reference is the original or the repetition of a proof that is even older.

I came across this book by accident. I chose it practically at random to better understand QM.

 

[mathwonk]

one of my first attempts at a thesis turned out to be due to,hurwitz in the 1800's.