The statistician in the library: Stephen Stigler’s four decades crossing disciplinary lines

Pioneering scholar talks Stigler’s Law, French lotteries and statistical history

Editor’s note: This story is part of ‘Meet a UChicagoan,’ a regular series focusing on the people who make UChicago a distinct intellectual community. Read about the others here.

At any university, statisticians aren’t usually at the top of the list of library visitors. But when Prof. Emeritus Stephen Stigler was a visiting associate professor of statistics at the University of Chicago in the early 1970s, he found himself drawn to the libraries and their archives of math publications.

He was surprised to find, in an issue of the American Journal of Mathematics from the 1920s, some principles related to his doctoral thesis that had been stated four decades before—but apparently lost in the literature. Then he found another example—an article written in 1816-1818 by French mathematician Pierre-Simon Laplace that included a mathematical result that was unknown at the time of Stigler's reading.

"I realized there is a tendency to read recent literature but not to look back too far," said Stigler, the Ernest DeWitt Burton Distinguished Service Professor Emeritus, who retired this past fall after over 40 years at the University of Chicago. "It showed that people back at that time were doing interesting things and asking modern questions—just not with the framework we have today."

Stigler's interest in history had already been sown as an undergraduate when he minored in the subject, but that moment in UChicago's Eckhart Library sparked a long career investigating the history of the development of mathematics and statistical methods, in relation to problems in many fields—from astronomy to medicine to social sciences and psychology.

Stigler’s Law of Eponymy

Stigler earned a doctorate in statistics from the University of California, Berkeley in 1967, and then joined the faculty at the University of Wisconsin–Madison, where he worked for 12 years. He also spent a year as a fellow at the Center for Advanced Study in the Behavioral Sciences at Stanford University, where he developed research connections with anthropologists, psychologists and other social scientists.

In 1979, the year Stigler began his full-time appointment at UChicago, he was invited to contribute an article to a Festschrift in honor of sociologist Robert K. Merton. Earlier, Merton had written a paper about how and why so many scientific discoveries have been found in different places and times ("multiple discoveries")—similar to examples Stigler had found in the UChicago libraries a few years before. Stigler decided to pen an article entitled "Stigler's Law of Eponymy," which stated that no scientific discovery is named after its original discoverer.

In the article, Stigler cited examples of misapplied eponymies including the Pythagorean Theorem—the theorem relating the three sides of a right triangle, written as a² + b² = c², where c represents the length of the hypotenuse—which arose much earlier in China.

"I'm not saying that everything has been done before, but that everything is related to things we've done before, and understanding how things have changed is the challenge before us," Stigler said.

The name, Stigler's Law, was itself a nod to the fact that Stigler was building upon Merton's work.

“It was typical Steve to write a tongue-in-cheek paper about a law that he quite unabashedly and ironically named after himself,” said longtime colleague Peter McCullagh, the John D. MacArthur Distinguished Service Professor Emeritus of Statistics.

‘A huge milestone for me’

Stigler’s interest in history, however, was everything but typical in the field.

“There is a small cadre of people across the world who make it their calling to study the history of their science,” said McCullagh. “But Steve is not one to follow paths.”

Stigler began to collect early editions of mathematical texts. He wrote many articles on the history of statistical concepts, and in 1986, published The History of Statistics: The Measurement of Uncertainty before 1900, which he'd begun writing seven years before starting at the Center for Advanced Study in the Behavioral Sciences. The book garnered positive attention from The New York Times.

"It was different from anything I'd done before and a huge milestone for me," Stigler said. He went on to write other books, including Statistics on the Table: The History of Statistical Concepts and Methods and The Seven Pillars of Statistical Wisdom.

Despite his retirement this past September, Stigler's work to document the history of statistics continues. He now has a book on the history of the French lottery out for consideration with a publisher.

Casanova’s lottery

His curiosity about the subject began in 1994, when he bought a small book that included data about all the numbers drawn in the lottery over an 80-year period. Stigler soon began to acquire other texts, including French law books about how the lottery was carried out, decrees from the king, and advice for gamblers.

"The French lottery is a unique example of a big state affair that was based on statistical principles—the law of large numbers," Stigler said. "Nowadays there are all sorts of safeguards and anti-risk protections, but this lottery didn't have those. The king ran the risk of losing a huge amount of money at any given time. The only thing protecting him was mathematical theory that says it's an unlikely possibility."

The book, preliminarily titled Casanova’s Lottery, reveals that Casanova (yes, that Casanova) sold the idea of the lottery to the resistant French ministers. The lottery became hugely popular, accounting for 4% of the income of the French nation, and the idea quickly spread to Germany and Italy. Many modern lotteries are very similar to the early French version, down to the wheel filled with numbers.

“Steve strives to get to the unusual and unexpected side of things,” said McCullagh. “We’d never think of Casanova as a mathematician, but it turns out he understood the principles and ran lotteries.”

Stigler’s passion for the history of statistics extends to the ancient. Recently, he was working with the Oriental Institute at UChicago to analyze what appears to be contingency tables and statistical tabulations on a set of clay tablets from Mesopotamia 5,000 years ago. The tablets seem to be a record of crops over a time period with marginal totals.

"At the dawn of writing, people were doing statistics," Stigler said. "They believed they could learn something from aggregates of data."

Stigler has espoused that same belief throughout his career, earning a slew of honors—including memberships and fellowships in the American Philosophical Society, the Royal Academy of Science, Letters and Fine Arts of Belgium and the American Academy of Arts and Sciences. He is also the former president of both the International Statistical Institute and the Institute of Mathematical Statistics, and a recipient of the Quantrell Award for Excellence in Undergraduate Teaching.

In his retirement, Stigler said he will continue to research a few "odds and ends" in modern and ancient history. He also hopes to travel, when conditions allow it.

—A version of this story was first published by the Physical Sciences Division.