There are a set of math problems out there that are part of a thing called the “Millennium Prize.” It is basically a handful of exceptionally difficult math questions that each carry a $1 million prize for solving. In theory, a mathematician could wander into a college with a yellowed notebook and a solution to the problem and walk out (after many weeks of deliberation and a final agreement by the mathematics community) as a millionaire. Math has been done this way for a long, long time. Mathematicians would peddle their craft for cash and patronage since the time of Archimedes, the Greek math-man who solved a gold density problem using his bathtub and ran about the streets of Athens naked shrieking “eureka”. Kings would pay good money to have a man (pretty much only men did math for most of history) who would count and calculate for them, both for economic purposes and for curiosity’s sake.
Lookit that guy, he’s so cute when he’s excited to figure out that mass displaces water.
Towards the 1500s, algebra (from the Arabic word for “bringing together”, al-jabr) was beginning to be taught commercially and to the public. This meant that there were mathematicians who built careers teaching math to the public and required more students. One of the best ways to prove that you were a great mathematician was to hold a public contest of calculations with other mathematicians. Each person would be given a list of equations and a third party would hold the prize money, the mathematicians would scurry off and solve as many as they could and come back to claim the prize if they solved more equations or solved the equations faster. In their work, Robber Barons and Politicians in Mathematics: A Conflict Model of Science, Sociologists Randall Collins and Sal Restivo took to calling the Prize-Fighting mathematicians “Robber Barons” because the climate of contested solutions encouraged secrecy and theft. A mathematician’s formula would be his most prized possession because of the prize money and the prestige that it could bring. A winning solver would have money to burn and students lining up at their doors. Mathematicians who published their theories would no longer have an edge over other mathematicians in the contests, and would lose revenue and teaching income for it. This encouraged some shady business at times, and discouraged the publishing of math books. Two illustrative examples of the problems with “Robber Baron” math:
Fermat’s Last Theorem: in the margin of one of his Arithmetica books, the mathematician Pierre de Fermat wrote that he had solved one of the unsolvable questions of math! But that it was too large to fit in the margin. Then he died. Without writing it down. For the next three hundred and sixty years, mathematicians strained and failed their way to solving Fermat’s problem until we were able to solve it in 1994.
This is Pierre de Fermat, and he trolled the Math world from the grave.
Tartaglia and Cardano: A mathematician with a wicked stutter in the mid 1500s named Niccolo Fontana Tartaglia (thought to be the first person to create the science of ballistics by applying math to cannonball trajectory) discovered a formula for cubic equations and set about absolutely crushing every math contest in Milan. When a down-and-out ex-physician named Girolamo Cardano heard about the winning Tartaglia, he dressed up as an aristocrat and offered patronage to Tartaglia. After what amounts to blackmail and threat of violence, Cardano was given the formula under the oath that he not tell anyone. Cardano happily galumphed about Italy using the formula to win contests until he ran into another mathematician named Annabale della Nave, who claimed to have come up with Tartaglia’s solution in the early 1500s. Cardano took that claim as justification to break his promise and published a book with Tartaglia’s life work in it. Cardano gave some credit to Tartaglia, but took the book’s profit for himself. Tartaglia rapidly produced a scathing counter to the book that tried to stake a claim in his own discovery, but was largely ignored.
Coming soon to a theater near you: A gritty crime thriller about the dark, pulsing underworld of Milan’s bean counters
There are a handful of other examples of the math competitions going on throughout history, perhaps most notably Newton and Leibniz, but those stories are for another time. It should also be noted that competitions like those of the Renaissance did spur a great deal of innovation. Mathematicians would fall over themselves to find solutions to some of the greatest questions ever posed in their era. By the same key however, the limited incentive to share meant that theoreticians would be constantly weighing the lasting use of their theories with the single burst of cash that publishing a new book of theories would produce. In the end, many mathematicians would pass their theories along to students or publish a compendium of their work on their deathbed, so barring obvious examples like Fermat, the actual impact of laissez-faire math on progress is disputable.
Randall Collins and Sal Restivo, Robber Barons and Politicians in Mathematics: A conflict Model of Science, (The Canadian Journal of Sociology / Cahiers canadiens de sociologie, Vol.8, No.2, Spring 1983), published by Canadian Journal of Sociology.
S.T.S. Historic Contests in Mathematics, (Mathematics News Letter, Vol.8, No.3, Dec. 1933), published by Mathematical Association of America.
Tartaglia – The Stammerer, (The Mathematics Teacher, Vol. 23, No. 6, October 1930) published by National Council of Teachers of Mathematics.
David Bergamini and the Editors of LIFE, LIFE Science Library: Mathematics (Time Inc., 1963).