When Statistics Was 'Not Good Mathematics'

Today, I decided to translate one of my older posts from my Telegram channel (Myths and Facts About Science and Scientists) about John Tukey (1915–2000), whom many consider the father of data science. When discussing his contributions, people often mention that he introduced the concept of the "bit," developed the Fast Fourier Transform algorithm, and invented box plots—among many other things. However, rather than detailing his entire biography, I was particularly intrigued by a small but significant part of it: how, after earning a master’s degree in chemistry from Brown University in 1937, he ended up at Princeton and, within a short period, obtained both a master’s (1938) and a PhD in mathematics (1939).

I came across an interesting interview with Tukey and mathematician Albert Tucker (who, by the way, had Nobel laureate John Nash as one of his PhD students). In this interview, they reminisced about Princeton in the 1930s–1950s, a time when the university did not yet have a dedicated statistics department, and statistics was not even considered a distinct scientific discipline.

At one point, Tukey remarked:

“The best thing about being a statistician is that you get to play in everyone’s backyard.”

I love this quote because it perfectly captures the role of statistics in the world. For Princeton (and nearly any other university) in the mid-20th century, this was true. However, at the time, this was less of an advantage and more of a necessity—mathematicians did not consider statistics a branch of mathematics. Tucker recalled that he struggled to persuade the dean of the mathematics department to allocate funding for statistical projects. When asked about the reasons for this attitude, they responded in the interview:

Tucker: Statistics was not mathematics.

Tukey: It was not good mathematics…

Tukey went on to explain that, back then, it was a widespread belief that statisticians were either subpar mathematicians or just bad mathematicians. Moreover, he recalled that some statisticians themselves held this view. He was particularly shocked when a well-known British statistician once remarked that one could be a good mathematical statistician without being either a good mathematician or a good statistician.

He also pointed out that, in the 1930s, statistics was often pursued outside of mathematics departments in many universities. People became statisticians after earning degrees in biology, chemistry, or physiology—but rarely in mathematics.

For instance, they recalled that Frank Yates, a renowned British statistician who worked with R. A. Fisher and later led the Rothamsted Experimental Station in 1933, had previously worked as a surveyor in Africa (I plan to write a post about him later). Florence Nightingale, who contributed to statistical methods in the 19th century, is better known for revolutionizing nursing than for her statistical work. Charlie Winsor, later famous as a biostatistician, had a degree in physiology, while Joseph Berkson—best known for the statistical paradox named after him (Berkson's paradox, Berkson's bias, or Berkson's fallacy)—held a master’s in medicine and a doctorate in physiology.

Princeton finally established a statistics department in 1965, with Tukey as its dean.

Tukey was also known for several striking quotes about statistics. For example, according to his students, he once gave them a book of crossword puzzles. Later, they discovered that he had removed the answer page and replaced it with his own note, which read something like:

“Doing statistics is like doing crosswords, except that one cannot know for sure whether one has found the solution.”

However, my favorite Tukey quotes concern the importance of asking the right questions—something that is often more crucial than using advanced analytical methods:

“Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise.”

And another one, about the limitations of statistics when dealing with poor data:

“The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.”

It would be great if today’s statisticians (and data scientists) remembered the words of their "intellectual father".