CEIIINOSSSTTUV

CEIIINOSSSTTUV- Hooke's Law (more commonly expressed as  F = -kx) as I learned in this year's annual Charles Simonyi Lecture delivered by Timothy Gowers! (Incidentally Timothy Gowers claimed that he was the first mathematician to  deliver a Simonyi lecture.) The subject of his lecture was Open Source Mathematics and CEIIINOSSSTTUV was his example for Closed Source Mathematics! He explained that when Robert Hooke, who appears in the picture, had formulated his Law he did not want to  make it public immediately. 

But, wanting to lay a claim to the intellectual copyright before anyone else did, he created the anagram CEIIINOSSSTTUV  - Ut tensio, sic vis (as the extension, so the force) which he would be able to use were the primacy of his work to be disputed!

The thrust of Gowers's lecture was that the Web can now transform mathematical research from being a private cerebral activity to a collaborative activity of many minds. He described this in action working on the density Hales-Jewett theorem (DHJ). He led into the mathematics very gently starting with noughts and crosses so that anyone could follow. But   what struck me personally, not being a mathematician, over and above the efficacy of the collaborative method, were the following effects.

The first was the ethical effect, both personal and social, of this way of working, and the second the illuminating effect both  for the future researcher and for the historian of mathematics.

He began by discussing the concept of CREDIT.
He said that in order to obtain the credit for an intellectual achievement considerable importance was attached to finding the first correct solution and so work was carried out privately.

Striking examples of the above were the example of Robert Hooke quoted above, 

and more recently of Andrew Wiles (famous for proving Fermat's Last Theorem) who worked in secret for seven years, before announcing his solution at a conference in Cambridge.

Moreover the theorem when presented publicly in its polished form gave no insight into the thoughts, and the many paths that led nowhere on the way on the way to the solution. He considered that an account of the many tergiversations was extremely valuable for other researchers working in similar fields.

This was he claims the first time the full working record of the solution of a hard mathematical research problem has been made available. 

He published his work under the name of Polymath1 and not as by a single person or several people. Evaluation of the work for CREDIT could be carried out by referring to the blog accompanying the article which documented  everybody's contributions, whether fruitful or otherwise.

From the notes which he kindly sent  to me:

At the moment, if you have a good idea in connection with an unsolved problem, there is a strong incentive not to share it (unless you have completely solved the problem).

But what if a problem was tackled by many people, all collaborating, and working \out in the open"? The incentive structure completely changes:

now one should share one's ideas as quickly as possible.

February 1st: project launched. Proof outline suggested, modelled on proof of a related result.

February 6th: already 200 comments and well over a thousand \lurkers".

February 8th (approx): first idea emerged that clearly represented a signicant advance in understanding of the problem.

February 9th: technical simplication proposed that made calculations much easier.

February 12th: wiki set up as somewhere to put background material and more detailed explanations of ideas that arose in the blog discussion.

February 21st: dierent proof outline suggested, modelled on a dierent proof
 of the related result.

February 25th: major lemma proved, analogous to major step of proof of the related result.

February 28th: second major lemma proved.

March 6th: serious diculty emerges.

March 8th: proof of related result modied to make it an easier model to use.

March 9th: complete sketch of a solution to the problem written.

Solution generalizes straightforwardly to proof of the full DHJ theorem and not just the special case we started out trying to solve.