## What’s the Matter with Hertz Foundation?

Imagine you have plenty of money and dozens of volunteers. You decide to award one or two fellowships a year to the best of the best of the best in math sciences. Easy, right? Then how do you repeatedly fail at this, without anyone notice? Let me tell you how. It’s an interesting story, so bear with me.

**A small warning**. Although it may seem I am criticizing Hertz Foundation, my intention is to show its weakness so it can improve.

#### What *is* the Hertz Foundation?

Yesterday I wrote a recommendation letter to the Hertz Foundation. Although a Fellow myself, I never particularly cared for the foundation, mostly because it changed so little in my life (I received it only for two out of five years of eligibility). But I became rather curious as to what usually happens to Hertz Fellows. I compiled the data, and found the results quite disheartening. While perhaps excellent in other fields, I came to believe that Hertz does barely a mediocre job awarding fellowships in mathematics. And now that I think about it, this was all completely predictable.

First, a bit of history. John Hertz was the Yellow Cab founder and car rental entrepreneur (thus the namesake company), and he left a lot of money dedicated for education in “applied physical sciences”, now understood to include applied mathematics. What exactly* is* “applied mathematics” is rather contentious, so the foundation wisely decided that “it is up to each fellowship applicant to advocate to us his or her specific field of interest as an ‘applied physical science’.”

In practice, according to the website, about 600 applicants in all areas of science and engineering apply for a fellowship. Applications are allowed only either in the senior year of college or 1st year of grad school. The fellowships are generous and include both the stipend and the tuition; between 15 and 20 students are awarded every year. Only US citizen and permanent residents are eligible, and the fellowship can be used only in one of the 47 “tenable schools” (more on this below). The Foundation sorts the applications, and volunteers interview some of them in the first round. In the second round, pretty much only one person interviews all that advanced, and the decision is made. Historically, only one or two fellowships in mathematical sciences are awarded each year (this includes pure math, applied math, and occasionally theoretical CS or statistics).

#### Forty years of Math Hertz Fellowships in numbers

The Hertz Foundation website has a data on all past fellows. I compiled the data in Hertz-list which spanned 40 years (1971-2010), listed by the year the fellowship ended, which usually but not always coincided with graduation. There were 67 awardees in mathematics, which makes it about 1.7 fellowships a year. The Foundation states that it awarded “over 1000 fellowships” so I guess about 5-6% went into maths (perhaps, fewer in recent years). Here is who gets them.

**1)** **Which schools are awarded?** Well, only 44 US graduate programs are allowed to administer the fellowships. The reasons (other than logistical) are unclear to me. Of those programs that are “in”, you have University of Rochester (which nearly lost its graduate program), and UC Santa Cruz (where rumors say a similar move had been considered). Those which are “out” include graduate programs at Brown, UPenn, Rutgers, UNC Chapel Hill, etc. The real distribution is much more skewed, of course. Here is a complete list of awards per institution:

MIT – 14

Harvard, Princeton – 8

Caltech, NYU – 7

Berkeley, Stanford – 5

UCLA – 3

CMU, Cornell, U Chicago – 2

GA Tech, JHU, RPI, Rice – 1

In summary, only 15 universities had at least one award (34%), and just 7 universities were awarded 54 fellowships (*i.e.* 16% of universities received 81% of all fellowships). There is nothing wrong with this *per se*, just a variation on the 80-20 rule you might argue. But wait! Hertz Foundation is a non-profit institution and the fellowship itself comes with a “moral commitment“. Even if you need to interfere with “free marketplace” of acceptance decisions (see P.S. below), wouldn’t it be in the spirit of John Hertz’s original goal, to make a special effort to distribute the awards more widely? For example, Simons Foundation is not shy about awarding fellowship to institutions many of which are not even on Hertz’s list.

**2)** ** Where are they now?** After two hours of googling, I located almost all former fellows and determined their current affiliations (see the Hertz-list). I found that of the 67 fellows:

University mathematicians – 27 (40%)

Of these, work at Hertz eligible universities – 14, or about 21% of the total (excluding 3 overseas)

At least 10 who did not receive a Ph.D. – 15%

At least 13 are in non-academic research – 19% (probably more)

At least 8 in Software Development and Finance – 12% (probably more)

Now, there is certainly nothing wrong with directing corporate research, writing software, selling derivatives, designing museum exhibits, and even playing symphony orchestra or heading real estate company, as some of the awardees do now. Many of these are highly desirable vocations. But really, was this what Hertz had in mind when dedicating the money? In the foundation’s language, “benefit us all” they don’t.

I should mention that the list of Hertz Fellows in Mathematics does include a number of great academic success stories, but that’s not actually surprising. Every US cohort has dozens of excellent mathematicians. But the 60% drop out rate from academia is very unfortunate, only 21% working in “tenable universities” is dismaying, and the 15% drop out rate from graduate programs is simply miserable. Couldn’t they have done better?

#### A bit of analysis

Every year, US universities award over 1,600 Ph.D.’s in mathematical sciences, of which over a half go to US citizen (more if you include permanent residents, but stats is not easily available). So they are choosing 1.7 out of over 800 eligible students. Ok, because of their “tenable schools” restriction this is probably more like 300-400. Therefore, less than half of one percent of potential applicants are awarded! For comparison, Harvard college acceptance rate is 10 times that.

Let me repeat: in mathematics, Hertz fellows drop out from their Ph.D. programs at a rate of 15%. If you look into the raw 2006 NRC data for graduation rates, you will see that many of the top universities have over 90% graduation rate in the math programs (say, Harvard has over 91%). Does that mean that Harvard on average does a better job selecting 10-15 grad students every year, while Hertz can’t choose one?

Yes, I think it does. And the gap is further considering that Hertz has virtually no competition (NSF Fellowships are less generous in every respect). You see, people at Harvard (or Princeton, MIT, UCLA, etc.) who read graduate applications, know what they are doing. They are professionals who are looking for the most talented mathematicians from a large pool of applicants. They know which letters need to be taken seriously, and which with a grain of salt. They know which undergraduate research experience is solid and which is worthless. They just know how things are done.

Now, a vast majority of Hertz interviewers are themselves former fellows, and thus about 95% of them have no idea about the mathematics research (they just assume it’s no different from the research they are accustomed to). Nor does the one final interviewer, who is an applied physicist. As a result, they are to some extend, flipping coins and rolling dies, in hope things will work out. You can’t really blame them – they simply don’t know *how to choose*. I still remember my own two interviews. Both interviewers were nice, professional, highly experienced and well intentioned, but looking back I can see that neither had much experience with mathematical research.

You can also see this lack of understanding of mathematics culture is creeping up in other activities of the foundation, such as the thesis prize award (where are mathematicians?), etc. Of course a private foundation can award anyone it pleases, but it seems to me it would do much more good if only some special care is applied.

**A** modest** proposal**

There is of course, a radical way to change the review of mathematics applicants – subcontract it to the AMS (or IMA, MSRI, IPAM – all have the required infrastructure). For a modest fee, the AMS will organize a panel of mathematicians who will review and rank the applicants without interviewing them. The panel will be taking into consideration only students’ research potential, not the university prestige, etc. The Hertz people can then interview the top ranked and make a decision at the last stage, but the first round will be by far superior to current methods. Even the NSA trusts AMS, so shouldn’t you?

Hertz might even save some money it currently spends on travel and lodging reimbursements. The 13% operating budget is about average, but there is some room for improvement. Subcontracting will probably lead to an increase in applications, as AMS really knows how to advertise to its members (I bet you currently receive only about 40 mathematics applications, out of a potential 400+ pool). To summarize: *really*, Hertz Foundation, think about doing that!

**P.S.** It is not surprising that the 7 top universities get a large number of the fellowships. One might be tempted to assume that clueless interviewers are perhaps somewhat biased towards famous school names in the hope that these schools already made a good decision accepting these applicants, but this is not the whole story. The described bias can only work for the 1st year grad applicants, but for undergraduate applicants a different process seems to hold. Once a graduate school learns that an applicant received Hertz Fellowship (or NSF for that matter), it has every incentive to accept the student, as the tuition and the stipend are paid by the outside sources now.

**P.P.S.** Of course, mathematicians’ review can also fail. Even the super prestigious AIM Fellowship has at least one recipient who left academia for bigger and better things.

**UPDATE** (April 15, 2019). Over the years since this blog post, I have been contacted by people from the Hertz Foundation board. I have also followed up on the story and the recent fellowship recipients. I am happy to say that the foundation implemented various important changes vis-à-vis math interviews, to the visible effect. At the moment, the numbers are too small to report statistics and the changes I know are not a public information. I concluded that my criticism no longer applies, a happy ending to the story. I encourage now everyone to support the foundation financially as well as recommend your best students to apply.

I came across this after I found my name (Joel Miller) on your list of Hertz Mathematics awardees. https://igorpak.files.wordpress.com/2012/10/hertz-list.pdf

I want to make a few comments.

First, your list has errors. Although you have me as not receiving a PhD, I do have one. I declined the Hertz Fellowship to get my PhD at Cambridge.

Second, you’re missing much of the point of the Hertz fellowship. You are measuring success in large part by whether people go academia. That is simply not the goal of the Hertz foundation.

1) Sure. Thank you for bringing this up. The post is from awhile ago. Hertz website had no additional info on you and searching for the right Joel Miller was not easy.

2) What IS the goal then? And unless you are involved with their activities and board discussions, how exactly do you know that I am “missing much of the point”?

The website only says “We look to support the graduate education of America’s most promising technical talent, the PhD-directed effort of the young men and women who can be expected to have the greatest impact on the application of the physical sciences to human problems during the next half-century.” This might mean something in fields like Biochemistry where the distance to ‘human problems” is shorter. But when it comes to Mathematics this can be interpreted in 100 different ways from “excellence in teaching” to “excellence in applied math research”, to “having a popular blog on the subject”. The interpretation I chose is the one which allows quantitative analysis. I would be very interested to see if you can show that Hertz fellows are statistically “better” than a random choice of say Harvard Ph.D. students in maths, by any quantitative measure.

P.S. At some point after the post I was contacted by the Hertz Foundation board members who were worried about their process. I trust they are aware of the issue and have made changes for the better, but I am not privy to specifics.