Edna St Vincent Millay's sonnet "Euclid alone has looked on beauty bare" evokes the ethereal, otherworldly quality of mathematics. Scandalous behaviour is not usually associated with the discipline, but mathematicians are human: pride, overblown ego and thirst for fame have led to skulduggery, plagiarism and even murder. Some of the more egregious scandals are reviewed here.
Cover-ups usually involve politicians but are not exclusive to them. One of the most notorious examples in mathematics involved the murder of Hippasus of Mesapontum. The Pythagoreans, a mysterious and secretive group, believed that mathematics was the key to the universe, as reflected in their motto “All is Number”.
Then Hippasus stumbled upon an amazing fact: the diagonal of a square with unit side cannot be expressed as a ratio of whole numbers. This shattering discovery fatally undermined their philosophy and the Pythagoreans tried to suppress it. According to legend, when Hippasus let the cat out of the bag they threw him overboard from a ship, drowning him.
Equations of the first and second order could be solved by the Babylonians. In 1539, Niccoló Tartaglia discovered a way of solving third order, or cubic, equations. Such knowledge was precious and could determine entire careers. Girolamo Cardano, anxious for the secret, cajoled and flattered Tartaglia, begging him to reveal his method and swearing a sacred oath not to divulge it.
In 1543, finding a similar solution in writings of Scipione del Ferro that predated Tartaglia's discovery, Cardano felt free to reveal the method in his "Ars Magna". Tartaglia was furious at this betrayal and denounced Cardano as a scoundrel. There is no record of any reconciliation between the two men.
Plagiarism
Sad to say, plagiarism abounds in the sciences as well as the arts. The Marquis de l'Hospital (1661-1704), a wealthy nobleman and gifted amateur, yearned for fame as a creative mathematician. He was tutored by the genius Johann Bernoulli, who introduced him to the intricate new ideas of calculus.
The marquis persuaded Johann to sign an agreement handing over first rights to all his mathematical discoveries. Johann had just married and needed financial support. But then l’Hospital published a book on mathematical analysis, presenting as his own many results discovered by Bernoulli. In particular, the book contained a theorem about evaluating expressions of the form 0/0 which, to this day, is called l’Hospital’s Rule.
Évariste Galois lay bleeding on the duelling field. Not yet 21, he would soon be dead. The facts are murky, but he may have been tricked by a political opponent into a duel. A staunch republican, Galois was imprisoned for six months for his political activities. The night before the duel, reputedly over a young lady, Galois feverishly wrote down some of his most original and ground-breaking mathematical ideas. He perished in obscurity, and it would be another 15 years before the brilliance of his work was recognised.
Georg Cantor invented, or discovered, a rich hierarchy of infinite quantities. But along with infinity invariably comes paradox. Conservative mathematicians strenuously resisted Cantor's new ideas, launching ad hominem attacks against him.
The most virulent criticism came from Leopold Kronecker, who blocked Cantor's publications and obstructed him from obtaining a position in Berlin. Kronecker's vindictiveness over a 10-year period contributed to Cantor's nervous collapse. In 1918, Cantor died in a mental institution.
Prolonged dispute
One of the most bitter and prolonged disputes – the “calculus wars” – was the conflict between Newton and Leibniz, each claiming priority and charging the other with plagiarism. Neither was willing to share the glory of making the greatest mathematical advance since ancient Greek days.
In Brexit-like fashion, the British claimed credit for Newton while the Germans maintained that Leibniz invented calculus. A Royal Society report found in Newton's favour. Quelle surprise: Newton oversaw the investigation and wrote the report. The dispute caused a rift that inhibited mathematical development in Britain for a century.
Peter Lynch is emeritus professor at UCD school of mathematics & statistics, University College Dublin. He blogs at thatsmaths.com