*Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and—to go a step further—*

our mathematicians do not know mathematics.

In April 1958, the theoretical physicist J. Robert Oppenheimer presented a talk to the International Press Institute in Washington, D.C.; six months later, the full text of the speech was published in an article in *Harper’s Magazine*, “The Tree of Knowledge.” In this article, Oppenheimer talked about the nature of scientific knowledge and the way it had changed over the centuries:

There are enormous differences between our world of learning today—our Tree of Knowledge—and those of Athens, or the Enlightenment, or the dawn of science in fifteenth- and sixteenth-century Europe [Oppenheimer 1958, p. 55].

Oppenheimer discussed the growing number of scientists and the spread of scientific knowledge, the relationships and differences between “pure” and “practical” science, and the consequences of scientific progress. He concluded the speech by arguing that the continuing growth of science would inevitably pose difficulties in achieving the goal of nuclear disarmament.

Photograph of Oppenheimer, ca 1944.

Public domain, U.S. National Archives and Records Administration.

It was only in the introduction of the speech that Oppenheimer talked specifically about mathematics. In order to show how much knowledge had changed over the centuries, Oppenheimer offered an example from ancient Greece:

You can get some suggestion of how shattering these changes have been if you remember that Plato, when he tried to think about human salvation and government, recommended mathematics as one of the ways to learn to know the truth, to discriminate good from evil and the wise from the foolish. Plato was not a creative mathematician, but students confirm that he knew the mathematics of his day, and understood it, and derived much from it [Oppenheimer 1958, p. 55].

It was at this point that the subject quotation of this column appears. When shown out of context, the quotation could be taken to mean that today’s mathematicians do not know *any* mathematics; however, Oppenheimer only argued that, in contrast to Plato’s day, it was no longer possible for any one person to comprehend *all* of mathematics:

Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and—to go a step further—our mathematicians do not know mathematics. Each of them knows a branch of the subject and they listen to each other with a fraternal and honest respect; and here and there you find a knitting together of the different fields of mathematical specialization [Oppenheimer 1958, p. 55].

While Plato’s *Republic* may have argued that an ideal ruler should be well versed in mathematical knowledge, Oppenheimer concluded the introduction to his speech by stating that, while the continued study of mathematics was undeniably well and flourishing, “it is not likely today that our most learned advisers—the men who write in the press and tell us what we may think—would suggest that the next President of the United States be able to understand the mathematics of the day” [Oppenheimer 1958, p. 55].

##### References

Oppenheimer, J. Robert. 1958, October. “The Tree of Knowledge.” *Harper’s Magazine* 217(1301): 55–60.

“Quotations in Context” is a regular column written by Michael Molinsky that has appeared in the *CSHPM/SCHPM Bulletin* of the Canadian Society for History and Philosophy of Mathematics since 2006 (this installment was first published in May 2012). In the modern world, quotations by mathematicians or about mathematics frequently appear in works written for a general audience, but often these quotations are provided without listing a primary source or providing any information about the surrounding context in which the quotation appeared. These columns provide interesting information on selected statements related to mathematics, but more importantly, the columns highlight the fact that students today can do the same legwork, using online databases of original sources to track down and examine quotations in their original context.