To the Editor:

Andrew Hacker really wants to sell his book *The Math Myth.* And given that the book is an error-filled rehash of old, discredited, simple-minded ideas, he’s going to need all the hype he can get. Pity that the media, who have lately showered him with attention, don’t bother to check his facts, let alone whether his ideas are sound or even new. Hence *The Chronicle Review* allowed him in essence a full-page advertisement for his book, with the provocative title of “The Math Mandarins” (March 25).

Hacker’s fantasy is that there is some group (“no more than 200"; I’d love to see a list) of “math mandarins” who somehow exert powerful control over the K-12 math curriculum. In reality, the academics who exert the most control over the K-12 math curriculum are professors of mathematics education, who are normally housed in education colleges and rarely in elite mathematics departments. Indeed, I would imagine that if Hacker actually asked any of those supposed mandarins whether they were satisfied with the state of K-12 math education in the United States, it is a safe bet that none would express any satisfaction at all. Now if these so-called mandarins are so powerful and influential, why aren’t our schools performing as they wish (and supposedly command)?

Hacker gripes about the light teaching loads of math professors, but had he actually done a little homework, he would have discovered that mathematics professors at research universities often teach more credit hours than professors in other STEM fields. At the same time, math departments (like English departments) handle enormous numbers of student credit hours. So yes, for economic reasons, most research universities do not hire dozens of math professors to teach lower-level math classes. However, any mathematics department would welcome the opportunity to quadruple its professorial size to help with that teaching. Ah, where are those powerful math mandarins when you need them?

Hacker’s numbers are wrong. He’s been told this before, most recently by Keith Devlin, but still he soldiers on. For example, according to the American Mathematical Society, the number of Ph.D.s in mathematical sciences awarded in 2013 is 1,843, not 730 as Hacker states in his article. Knowingly repeating falsehoods is called “lying” — unless of course you are a crusader in a fantasy land where powerful math mandarins lurk in the background, changing the data, trying to crush you with their numbers.

And Hacker’s ideas aren’t new. Twenty years ago, I wrote a review for *American Scientist* of an error-riddled book called *Humble Pi.* That book’s author, trying to back up a theme almost identical to Hacker’s, wrote: “We live in a world dominated by mathematicians” who believe in the “supremacy” of math and “may feel entitled to control whatever they can.” Sounds a lot like math mandarins to me!

Conrad Plaut

Department Head

Department of Mathematics

University of Tennessee at Knoxville

To the Editor:

When I was in high school 50 years ago, English was a required subject. We students were required to read books and write essays, and I think we learned to recognize less-reputable rhetorical devices such as the construction of straw men, and other forms of misdirection. I don’t think anyone had at that time managed to publish opinion pieces in *The **New York Times* asking whether English was a necessary subject, or whether high-school English should include such advanced topics as constructing an honest essay, in which the conclusions reached bore some relation to the evidence offered.

The overarching rhetorical conceit in Hacker’s essay is that the research elite in mathematics exerts a powerful and sinister influence over mathematics education at all levels. They “dominate much of our educational system and set priorities for the greater society. While their apparent target are students, their larger goal is to configure the coming generation of adults. This explains their emphasis on requiring advanced mathematics for everyone.”

Wow! Those three sentences do cover some ground, don’t they? For the uninformed, let’s note that Hacker’s notion of advanced mathematics is high-school algebra, and that the research elite has a rather different notion of advanced mathematics. It seems that (according to Hacker) the undue and sinister influence of the research elite is directed toward preserving the standard high-school curriculum as it has existed for at least 50 years, just as it is. That could be a good idea or a bad idea, but the influence that the elite would need to exert to advance that goal would be exactly nil.

Those three sentences contain the thesis of the essay, and according to what I learned in high school, we should now search the rest of the essay for supporting evidence, some actual examples of exertion of influence, perhaps some account of reform efforts suppressed by the intervention of the elite. Well, there is exactly one bit of evidence offered in the remainder of the essay, and here it is: In 2012 there was a report by a commission on scientific education which suggested that mathematics could also be taught at the university level by faculty from other departments that use mathematics, and the then-head of the American Mathematical Society’s committee on education objected. That’s it, one meager example of turf protection, upon which Hacker proceeds to his damning conclusion: “The mandarins’ perspective is that anyone lacking their imprimatur is incapable of teaching mathematics, from elementary grades up, as they conceive of and pursue it.”

Since the remainder of the essay doesn’t contribute to the main thesis, what does it contain? There are two points. The first is that the mathematical enterprise is dying for lack of interest from students. This is false.

At my university, the number of mathematics majors has increased by a factor of four over the last 25 years. As for the scientific future, the picture is grim, not because we (yes, we: I am a retired research mathematician, but not a member of the elite) can’t attract students, but because so many brilliant young mathematicians can’t find long-term academic employment.

Hacker’s second point is that elementary mathematics courses at the university level are not being taught by tenured research professors but by adjuncts and teaching assistants. This is in fact a complicated issue, and it is not at all unique to mathematics. Let me just mention that at my university there are 30 tenured or tenure-track faculty members in mathematics and 26,000 students. My colleagues have the responsibility for mathematics education from the remedial junior-high-school level to the Ph.D. level, and they are spread pretty thin.

I would like to continue to discuss the failings of school mathematics (including the first two years of university mathematics) and the history of reform efforts led by research mathematicians, but I have run out of time and energy.

Frederick Goodman

Professor Emeritus of Mathematics

University of Iowa

*Andrew Hacker responds:*

While I could say a lot more, I’ll focus on the most contentious parts of these letters.

1. Since Conrad Plaut accuses me of “lying,” I must be wary with my reply. I will presume that he has read my new book, as he calls it an “error-filled rehash.” Hence he must know that I cited the National Center for Education Statistics as my source for mathematics degrees to U.S. citizens.

2. For some reason, Plaut prefers to use 2013 figures from the American Mathematical Society. (Data for 2014 are readily available.) So let’s look at the 2013 AMS report. As Plaut will know, its 1,843 doctorates include 468 in statistics. Of those remaining, 678 went to noncitizens, leaving 697 mathematics doctorates to U.S. citizens. This is actually lower than my 730 figure. I attest that these numbers are truthful.

3. Frederick Goodman complains that I gave only one instance of mandarins’ “exertion of influence.” This is true, as my article abridged a much longer book chapter. There I cite many cases where research professors have sought to shape syllabuses, down to elementary grades. (If he wants a quick look, they’re in Chapter 7.)

4. That mathematics majors at the University of Iowa have “increased by a factor of four” since 1991 is cheering, as they’ve been plummeting in the country as a whole. (I’d only ask Goodman if his fourfold rise factors in the increase in Iowa enrollments.)

5. My article and book pose a simple question: How many mandarin professors ever take off a semester to teach a freshman section or seminar? (Just to catch a view from the trenches.) Another report put out by the AMS found that only 10 percent of introductory sections at doctoral-level schools are being taught by professorial faculty, most of them apt to be assistant professors.