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The Mozart of mathematics

After more than a hundred years, the publication of the collected works of Leonhard Euler is finally nearing completion. But the archives of this great mathematician from Basel still have much more to offer.

Leonhard Euler
Image: Wellcome

(From "Horizons" no. 109 June 2016)​​​

"It's simply a huge amount of material", says Martin Mattmüller. On the bookshelf behind him stand the 75 volumes of the Euler Complete Edition published thus far. "It's barely possible for a single human being to get to grips with all of it". And even more astonishing that a single man was able to write it all.

Mattmüller is himself also a mathematician from Basel, and he's the Secretary of the Euler Commission. This Commission works under the auspices of the Swiss Academy of Natural Sciences (SCNAT) and is responsible for publishing the collected works of Euler. "Two volumes about astronomy are still to appear", he says. He's 58 now, and the edition should be finished by the time he's 60. "In two years they should be done". This means that all of Euler's publications will have appeared in a modern edition. The edition of his letters should also be finished in the foreseeable future – the last four volumes are currently being edited.

Originals in Saint Petersburg

Leonhard Euler (1707–1783) is regarded as the most prolific mathematician ever to have lived. He wrote two dozen books and almost 900 essays. He was born and educated in Basel, but spent the rest of his life at the Russian Academy of Sciences in Saint Petersburg and in Berlin. Besides making a major contribution to the whole field of mathematics and to physics, he also engaged with technological problems – such as trying to improve turbines and telescopes. His famous formula e=-1 has been chosen by his fellow mathematicians as the most beautiful equation of all time. And he even invented a precursor of Sudoku.

At the time of the celebrations for Euler's 200th birthday in 1907, the Swiss Society of the Natural Sciences (today's SCNAT) founded the Euler Commission and gave it the task of publishing the complete works. This project, 'Opera omnia', began with a lot of enthusiasm, and the first volumes were published in rapid succession from 1911 onwards.

But the project came to a halt several times. The Commission lost some of its assets in the 1930s when a bank went bust. And Euler's manuscripts, which had been lent to Basel from St. Petersburg, had to be sent back to their permanent home. The Commission would gladly have kept them for good in Switzerland, but the Soviet Union even refused an exchange deal that would have involved Swiss archives giving up letters by Lenin in return. Since then, the researchers in Basel have worked with photos and copies wherever necessary.

Unrecognised genius

After the Second World War, the project started up again. But it began to drag once more in recent years. The editors were often retired professors. So whenever one died, the project slowed down again. And the manner of working has also changed over the decades. The first volumes were edited by physicists and mathematicians and had few footnotes and only brief introductions. But since the publication of Euler's correspondence began, his material has been edited with a greater attention to historical, critical principles. Euler's original works had ceased to be available in print, so the aim of the earlier editors was simply to make them accessible once again to mathematicians and to historical researchers. This problem doesn't exist today because most of his publications can be found on the Internet.

However, there are still many letters, notebooks and other unpublished manuscripts that have not found a place in the Opera omnia. "From today's perspective, we would probably give priority to editing this material, some of which has never been analysed at all", says Martin Mattmüller. There are plans to publish all of it after the printed volumes have appeared. This would again be a mammoth project – only this time it would be digital.

It would be worthwhile in any case because Euler was a truly unique figure, believes Mattmüller. "Switzerland didn't have a Goethe or a Mozart. But we had Euler – a man of absolute global significance. People here are far too little aware of this".

By Matthias Plüss, science journalist. He writes chiefly for Das Magazin.