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The Lagrange syndrome and the paradox of scientific progress

Imagine yourself as a theoretical scientist figuring out all on your own something really really neat, presenting it to the expert public, grinding it through the highly critical and sometimes savage anonymous peer review, polishing it in page proofs, and finally seeing it in print... only to be horrified soon afterwards by the FACT that the result had already been published before.

If this scientific deja vu ever happened to you, you are not alone. In fact, this happens so often in scholarly publications that one wonders how any progress is ever achieved in physics. I could easily pick 10 examples from publications of this year alone, but that wouldn't be fair, plus it would make me unpopular. I could mention examples of my own record, but that would be silly. The only thing to do is pick examples from the record of illustrious scientists of the past.

You (as I) may take some solace in the fact that this phenomenon has been documented in physics since as early as 1754. This is the year that Joseph-Louis Lagrange published his first mathematical paper (an analogy between the binomial formula and the derivatives of the product of two functions). Soon after the paper appeared, he found that the analogy had already been discussed in correspondence (namely, IN PRINT) between Johann Bernoulli and Leibniz. Naturally, Lagrange was greatly upset, as he feared to be accused of plagiarism. Isn't it interesting though? I mean, how many other "natural philosophers" could you have had before Lagrange, for crying out loud! And how many journals would you have needed to read in order to keep current? (Proceedings of the Royal Astronomical Society and what else?) Still, the scientific record found a way to humiliate a great beginner.

Nowadays, there are so many publications that it is just impossible to keep up. There are so many scientific meetings that it is just impossible to get any work done if you attend. It stands to reason that almost anything I write has either been published already, or will be published again by somebody else. Which is NOT to say that the material is known, as, most likely, nobody is reading my papers nor those of anyone else that is not a prominent scholar at a prestigious institution.

What's one to do? Just keep up the good work. So long as you continue to feel humiliated every time you inadvertently reproduce a "known" result: You are just experiencing a natural reaction out of your scientific integrity. But listen, as soon as you notice that you lost that healthy feeling, please do us all a favor and drop out of science ipso-facto.

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Lagrange's story and plenty others are much better told by the Mac Tutor History of Mathematics Archive

Posted on November 18, 2005.