Who needs math?

According to a study by sociologist Michael Handel, summarised here by Jordan Weissman, 75% of American workers never use any mathematics more complicated than fractions in their work. (It goes without saying that most partake of recreational calculus, at least on weekends…) Writing in the NY Times last year, Andrew Hacker argued that most schoolchildren are wasting their time learning mathematics: They’ll never understand it, and they won’t be any the worse off for it. As for scientists, the great entomologist E. O. Wilson has recently taken to the pages of the Wall Street Journal to argue that

 exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory.

For that matter, even Albert Einstein famously remarked to a schoolgirl correspondent

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

But that was after he’d mostly decamped from physics for sagecraft.

Wilson goes on to portray mathematical biologists as technicians, armed with useful tools and useless ideas. And if you need them, you just hire them. (It’s not like they have anything important to do with their time.) So what’s going on? Are mathematicians scamming the public, teaching algebra and other unnecessaries to justify their existence? I would suggest that there are several important issues that these wise men are ignoring or underplaying:

  • It may be true (as Hacker argues) that only a tiny techno-elite actually needs to know how a computer works, or how to compute the trajectory of a spacecraft, or how to program a Bayesian network. But when they’re 11 years old you don’t know who will have the interest or aptitude to join that elite. If you start sieving the children out early because they don’t seem like a likely candidate for that track — and let’s be honest, a lot of the tracking is going to be based on parental status and educational attainment — most of them will have no way to change tracks later on, because of the cumulative nature of mathematical understanding. Worth noting, in this context, is Handel’s observation (cited above) that skilled blue collar jobs are actually slightly more likely to require “advanced maths” (algebra and beyond) than skilled white collar jobs. So you can’t decide who needs the advanced maths based on the kinds of work they’re going into. Those without the education are simply more likely to be stuck at the lower rungs of whatever trade or profession they go into. (On the other hand, a larger fraction of white collar workers are in Handel’s “upper” (skilled) category, so an average blue collar worker probably needs less maths than an average white collar worker.)
  • Mathematics is a language. And what is discussed in that language is, as Hacker recognises, crucial to the fate of everyone in the world. Those who have not learned at least the rudiments of the language are excluded from the conversation. I am reminded of a friend who dismissed the value of learning to speak French, with the argument that “Everyone in France speaks English.” Now, France might have been a bad choice for his claim, but even if it were true, it puts you at a significant disadvantage to be surrounded by people who speak your language, while you can’t decipher their language to understand what it is they’re saying to each other.
  • Think about that Einstein quote: Everyone finds mathematics difficult when they’re pushing beyond their current knowledge. If we’re going to drop mathematics training when it becomes challenging, we might as well stop counting when we run out of fingers and toesies.
  • I would suggest that Wilson may be using more sophisticated mathematics in his work than he is aware. To paraphrase J M Keynes, practical biologists who believe their work to be quite exempt from any need for mathematics, are usually the slaves of some defunct mathematician. Modern biologists of bench and field are often quite attached to some mathematical and statistical machinery that happens to be some years old, and seemed impossibly abstruse when it first seeped in from the pure mathematics or theoretical statistics world. Many of the attempts to apply mathematical techniques in biology (or sociology or economics or whatever) will prove more clever than enlightening, but some will stick, and become part of the basic toolkit that the biologists who think they don’t need any sophisticated math do use. Wilson’s arrogant posture really reflects the fact that there are far more trained mathematicians who are intellectually flexible enough to try and figure out what the biologists are doing, and what the connections might be to their own field, than trained biologists willing to work in the other direction.

The Long Room: An academic allegory

Richard Tames’s A Traveller’s History of Oxford describes the “Long Room” of New College, a range of first-floor latrines built over a huge cesspit. Robert Plot, first superintendent of the Ashmolean Museum rhapsodised in the late 17th century that it was

stupendous… so large and deep that it has never been emptied since the foundation of the College, which was above three hundred years since, nor is it ever likely to want it.

The book also notes that this historical appraisal was in fact erroneous, as the pit had in fact, according to College records, been emptied in 1485.

The author does not make clear whether this description is intended as an allegory of academic productivity.

Mutually Assured Logical Destruction

or, What Dr. Tortoise said to Prof. Achilles

I remember reading a biologist — I’ve forgotten who it was — remarking that, in comparison to some other fields, arguments in biology rarely turn venomous, because no matter how certain you may be, based on current knowledge, you can expect that within a few years the question will be definitively resolved one way or the other. If you are indeed correct, science will not suffer for your having indulgent your colleague’s error, and neither will your reputation. And you might be wrong. It’s very difficult to hold to absolute confidence in your own beliefs when they concern a matter of fact, and the fact will be revealed. It is a bit like the logic of keeping the peace through nuclear deterrence.

This was most trenchantly put by the great German mathematician David Hilbert, who famously commented on Galileo’s “cowardly” recantation in the face of the Inquisition:

He was not an idiot. Only an idiot could believe that scientific truth needs martyrdom — that may be necessary in religion, but scientific results prove themselves in time.

Continue reading “Mutually Assured Logical Destruction”

What’s the Matter with Economics?

One of the most politically important economics results of recent years has been the paper by Reinhart and Rogoff on the link between high sovereign debt and low GDP growth. This work is something I’d been following for a while, as R&R’s book was one that I’d admired greatly. Their work claimed to show a strong negative correlation between sovereign debt/GDP ratio and ensuing GDP growth, and was reported as saying that 90% debt/GDP ratio marks a cliff that an economy falls off, killing future growth. This was seized upon by proponents of austerity as proof that budget cuts can’t wait.

As reported here and here by Paul Krugman, and here and here by Matt Yglesias, it now turns out that the result isn’t just theoretically misguided, it’s bogus. Economists who struggled to reproduce the results finally isolated a whole raft of errors and dubious hidden assumptions that completely undermine the conclusion. Only the most blatantly ridiculous fault was an error in their Excel spreadsheet formula that caused them to exclude important sections of the data from their computation. You’d think that this couldn’t get any worse, but instead of apologising abjectly, R&R have tried to argue that none of this was really essential to their real point, whatever that was.

My main thoughts:

  1. Do economists really do their analysis with Excel? I find this kind of shocking, like if I found out that some surgeons like to make their incisions with flint knives, or if airline pilots were calculating their flightpaths with slide rules. Once you accept that premise, it’s not surprising that they made a blunder like this. I’m not a snob about technology. Spreadsheets are great for doing payrolls, and for getting a look at tables of numbers, and doing some quick calculations. But they’re so opaque, they’re not appropriate to academic work, and they’re so inflexible that it’s inconceivable to me that someone who analyses data on a more or less regular basis would choose to use them. Continue reading “What’s the Matter with Economics?”

Total Impact: Wakefield edition

So it seems Andrew Wakefield is back in the news. As Phil Plait has described well, the man who has done more to undermine public health than any physician since Martini and Rodenwaldt has been given space in The Independent to accuse the British government of inadequate measles prevention. Because his rantings scared lots of parents off the MMR vaccine, and the NHS didn’t want to provide separate measles vaccines instead.

The pathological self-promoters you will have with you always, so there’s no real surprise there. But it got me to thinking about his future in British medical research. Because some denizens of less enlightened lands may not know how IMPACTFUL British research has become: The prime directive for state-sponsored research under the current government (though I think it started already under Labour) is “impact”, defined as

an effect on, change or benefit to the economy, society, culture, public policy or services, health, the environment or quality of life, beyond academia

because academia is just a province of Faerie, not an actual part of the society or economy. In addition to impact being a crucial part of every grant proposal, and the postmortem on every grant after it’s completed, this definition will guide 20% of the scoring on the Research Excellence Framework (REF) just now getting underway, replacing the Research Assessment Exercise (RAE) last conducted six years ago, because now instead of research being assessed, we agree that it’s all excellent but needs to be frameworked, or something.

So anyway, it’s noteworthy that BENEFIT is only one acceptable form of impact. Any change or effect gets you points for impact, rather in the way the bibliometric citation counting that prevails in many academic fields doesn’t distinguish between citations for your paper providing key insights that inspired follow-on research, and citations that point out yet another bone-headed mistake in the paper that has been confusing researchers and holding back the progress of the field.

What’s more, it’s not clear how anyone would evaluate whether those who benefit from the research are themselves providing a net benefit or harm to society. (Sorry, I mean, to the taxpayer. There’s no such thing as society.) Presumably no one will provide a support letter from bioterrorists, explaining how their headline-generating work would have been impossible without the groundbreaking research of Professor X, but someone like David Li could show evidence that his work formed the industry-wide basis for the multi-billion pound market in mortgage backed securities which (you may have heard) helped to crash the world economy. The fact that he might himself agree that his formula never should have been applied, that the bankers “misinterpreted and misused it“, and that “Very few people understand the essence of the model“, doesn’t detract from the benefit that derived to some people, at least in the short term, and even the worst recession in 75 years certainly counts as a “change in the economy”, demonstrating the IMPACT of the research.

With that in mind, I reveal the hitherto secret Wakefield Impact Case Study, titled “Royal Free Hospital School of Medicine characterisation of risk factors for Autism and Vaccination Policy”. We are confident that the massively impactful Wakefield will quickly be hired by a major research institution and showered with research grants. Continue reading “Total Impact: Wakefield edition”

Daniel Kahneman, Social Psychology, and Finance

I’ve been a booster of the Tversky-Kahneman cognitive-bias revolution since I read their article in Scientific American as a high school student. (To be honest, I’d always lazily thought of it as Tversky’s work, but Daniel Kahneman has had the good sense not to die prematurely, and to collect a Nobel memorial prize.) And I’ve greatly enjoyed Kahneman’s new popular book on his collected lessons from many decades of research on cognitive biases.

Putting that together with my longstanding contempt for the finance profession (expressed at greatest length here, but more generally listed here), I was particularly delighted to start in on the chapter titled “The Illusion of Validity”, where Kahneman lays into the self-serving illusions of finance professionals. It turns out, though, that this chapter is an intellectual trainwreck, with oversimplifications piling up on crude distortions, while the whistle of self-satisfied self-promotion shrills incessantly in the background. It’s both insufferable and so poorly reasoned that it begins to call the reliability of the rest of the book into question. Kahneman doesn’t claim to be free of the cognitive biases he analyses in others, but you might expect more self-awareness.

Continue reading “Daniel Kahneman, Social Psychology, and Finance”

Universities and charity

 

Here’s a weird, but hardly novel, controversy: Charity tax row: Oxbridge joins revolt.

The Oxford and Cambridge vice-chancellors wrote privately to Chancellor George Osborne saying his plans risked undermining the culture of university philanthropy. UK universities, which raised some £560m from charitable gifts last year, want him to rethink. Ministers want to stop tax avoidance. Mr Osborne says he is shocked by thescale of legal tax avoidance by multi-millionaires. Under current rules, higher-rate taxpayers can donate unlimited amounts of money to charity and offset it against their tax bill to effectively bring the amount of tax they pay down, sometimes to zero. But from 2013, uncapped tax reliefs – including those on charitable donations – are to be capped at £50,000 or 25% of a person’s income, whichever is higher… An Oxford University spokeswoman said that the government’s own policy emphasised the role of private and philanthropic investment, rather than the public purse. “A step that penalises the government’s own approach seems ill-considered.”

Hmmm. How about this alternative statement:

The university’s own justification depends on its promoting self-consistent argument, rather than specious self-serving sophistry. “An argument that contradicts the university’s own raison d’etre seems ill-considered.”

Continue reading “Universities and charity”

On the downgrade

Further reflections on non-transitive folk probability

Continuing my thoughts about zero-one probability from here, I come to the recent decision of Standard & Poor’s to lower their rating of US treasury debt. There are plenty of reasons to doubt their judgement,  both because they’ve been absurdly wrong in the past (subprime mortgage backed securities were AAA, but treasury bills are risky?), because they can’t read budget estimates or can’t do basic arithmetic, because they are trying to project political trends, which they surely know even less about than about arithmetic, or because the people who work there are generally known to be pretty dim. But from a probabilist’s point of view what’s strange is the timing. Whatever you may think of the recent deal to avoid the US defaulting on its debt, it did avoid defaulting on its debt. Surely the likelihood of a default went down after the deal was passed. So why is the credit rating lower this week than it was last week? Now, this is all perfectly consistent with the view that S&P is not actually making a prediction of future default probability, but simply seeking the best opportunity to promote its wares. Certainly, the way they operate is not the like someone trying to give what will be perceived as neutral advice; they act more like central bankers, timing their announcements to try to move markets and (above all) seem relevant. They’re reminiscent of the folktale of the rooster who threatens to withhold his crowing, which inevitably will forestall the sun rise. The other animals plead with him to relent, but it’s a threat that only works as long as the rooster is modest enough to recognise that he can’t hold out forever. In the case of the US treasury bonds, S&P held out, and still the sun rose.

But there is something about their approach that seems to make sense to intelligent people, and not purely idiosyncratic. I’m reminded of Tversky’s famous conjunction fallacy, with studies seeming to show that people’s everyday probability intuitions don’t necessary satisfy the apparently inevitable law of conjunction: The probability of A or B must be bigger than the probability of A and the probability of B. Here we see intuitions of probability that don’t seem to satisfy the law of total expectation: If  are possible future states of the world, and is the probability of event A conditional on  happening, then the probability of event A now must be some kind of average of these conditional probabilities.

downgrade

Where the money is…

Mathematical finance as an accessory to crime

Not long after I finished my PhD in probability theory, a significant fraction of the field was devoured by the financial mathematics moloch. Particularly in Europe, probability theory positions disappeared, to be replaced by openings in financial mathematics, which either went unfilled or cycled among a very few senior researchers and a few quick-change opportunists (and, gradually, their fledgeling academic progeny).

Everyone felt they had to get in on the action, and of course there was a certain amount of positive feedback. When many jobs chase few graduates, it generates huge demand among students for training in such a demonstrably burgeoning field. Obviously, the academic feedback was limited by the fact that most of the eager young ‘uns were seeking employment in banks, not in academia — but the banks were hiring as well. Anyway, just about 10 years ago, a Dutch colleague asked me if I might be interested in joining his own institute’s planned financial mathematics group, for which they were proposing to create TEN new positions. My reply was that finance did not interest me as a topic of research, but I added that there was something unseemly — bordering on unethical — in mathematicians’ headlong chase after banking lucre. The current generation of mathematicians is the trustee of a vast and powerful system of analysis, whose creators were supported, honoured, and financed by public institutions. What is it but a crime, when we abscond with the fruits of this scholarship, and sell it off (cheaply) to banks, who will use it to extract billions of dollars from financial markets? Continue reading “Where the money is…”

Oxford admissions

One of the genuinely unique features of Oxbridge is the admissions procedure. To judge by the news reporting, there is no issue in education that interests the British as much as admission to the “Ancient Universities”. The only countries with comparable concerns (that I am aware of) are the US, France, and Japan. I know almost nothing about Japanese university admissions. France, famously, has a parallel system of Grandes Écoles of fairly modern (mostly post-Revolution) vintage, while the traditional universities are completely unselective in admissions, though of course some courses ruthlessly prune students through mid-course exams. The Grandes Écoles are a broad pallette of fairly small and specialised institutions, relying on special preparatory classes and rigid admissions exams. While the ENS in Paris as the primus inter pares for academic subjects, the specialisation means that aspiring business or political or civil-engineering leaders have their own, equally exclusive institutions.

An American trying to understand the significance of Oxbridge admissions should imagine the frenzy over Ivy League and comparable universities, reduced to two elite universities, of which students are permitted to apply to only one. For all the frenzy in the US over getting children into Harvard, it is well understood that there are fine gradations of quality and prestige, and at least half a dozen institutions whose diplomas will do you exactly as much good in climbing the socioeconomic ladder, as well as several dozen more that will count you among the elite.

The UK is blessed with a large number of truly excellent universities, world-class in research and truly dedicated to teaching their students. But why should anyone care how brilliant your instructors were (unless you are one of the small minority who go on to a research career, and even then, only if the brilliant instructor has worked closely enough with you to be able to make a meaningful recommendation, and that brilliant instructor is one of that small subset who are not only brilliant themselves, but capable and willing to recognise brilliance in others)? University admissions in a stratified educational system is as much about exclusion as education. The “return” that universities provide to most of their undergraduates, from the coarse economic perspective, is largely conditioned on exclusivity. It’s rather like a hyper-expensive resort that provides reasonable comfort, but offers above all the opportunity to be secluded with other phenomenally wealthy vacationers. The price becomes part of the service, rather than being a trade-off. Universities don’t exclude by wealth primarily (particularly not in the UK), but by academic performance. There is a widespread perception that a certain amount of academic brilliance is the right qualification for many of the most desireable jobs in the modern economy, enough to make a place among the academic elite seem immensely desireable. Bankers pay £20,000 a year or more to send their children to “independent schools” (or “public schools”), the primary measure of whose success (it would be unfair to say it is their overriding educational goal) is the number of students they place in Oxford and Cambridge.

The universities could probably do more to exclude the striving sons and daughters of the haute-bourgeois, in favour of the enthusiastic poor or not-so-poor scholars, but then society at large would stop caring about us, and would stop supporting us in the style to which we have become accustomed. On the other hand, if the moneyed classes were too  It’s a delicate balance, which recurs in many aspects of the university. For instance, there is considerable pressure to put business people onto boards of universities, to align the universities more closely with business interests. But of course, if the business community knew how to achieve their interests in selection, training, and research, they wouldn’t be mucking about with universities at all. They want to bend the universities more to their interests, but too much capitalist gleichschaltung leaves universities like the internal research departments that they already have too much of. Academics are a bit like yeast, going about our own metabolic processes, whose effluvium (in this case intellectually sharp employees, leaders, and future captains of industry — no offense intended) turns out to be of great value to others, for reasons that we tiny yeast cells can no more than dimly recognise, while we are mainly striving to reproduce ourselves (in the academic sense, by seducing the rare brilliant student into a life of cogitation). As a machine for selecting and training the upper class, universities seem obviously inefficient, since they are intentionally pursuing quite different goals. Like the brewer’s yeast, though, academics work cheap (by the standards of private industry); furthermore, the system is entrenched and well tested, and the rigour with which academics enforce intellectual standards and is far enough superior (or, at least, complementary) to the soft-soap appraisals of business and government to compensate for the frequent disjunctions and not infrequent contradictions between them. Even if universities were supposed to serve no other purposes than those of business, for business leaders to streamline the university in their own image would be like trying to augment honey production by steam-cleaning the beehive.

On what basis are some individuals judged “worthy” of an Oxford education? The obvious answer is, those who are most talented, and have the most potential to learn and achieve notable scholarship, in their chosen fields. But why? There is some feeling that the brightest students will make the best use of an excellent education. And yet, this is far from the usual principles for allocating scarce resources. We do not insist that the finest automobiles go to the best drivers, nor do we insist on providing top-notch kitchen utensils to good chefs. (There is some effort to match exceptional music instruments to exceptional musicians, though.) When the market solution is rejected, it is typically for egalitarian reasons. But on an egalitarian basis, one might argue for providing the best post-secondary education to the most ignorant students, to balance things out. For an alternative justification, we might jump to the argument that the education at an elite university differs not in quality but in kind. This is especially true in the UK, where Oxford and Cambridge rely largely on the tutorial system. By leaving students very much to their own devices, but providing close contact and frequent interaction with leading senior scholars, this puts a premium on students’ ability to organise and motivate their studies, and to ask probing questions. For someone incapable of this (or simply uninterested), a place at Oxford would not be a gift. Then there is the problem of competition and mutual assistance among fellow students: Clearly students all benefit from a certain amount of stratification by ability, simply to allow lectures to be targetted at a common pace.

Oxbridge discrimination, elite schools, and the Sutton Trust report

The public is clearly of two minds. It is opposed to “elitism” on principle, but wants to be respected in the world for its elites. There seems to be less hostility than in the US toward pointy-headed academics, but they want class distinctions to be erased in the allocation of resources. As long as genius blows whereThe fact that well-heeled parents are buying not only a posh accent with their school fees, but sharper minds, genuinely better prepared for a top university, cuts uncomfortably across these lines. To put it bluntly, while everyone could benefit from an Oxford degree, not everyone would benefit from an Oxford education. This discrepancy is what drives the headlines, though, since one feels that the valuable Oxford degrees, being partly funded by the taxpayers, should be spread around more broadly. In particular, there is the sense, expressed in articles such as this one, that  This article describes the Sutton Trust report, which found that out of about 3700 schools in the UK, there are 100 — 78 of them private — which provides Oxbridge with about 1/3 of their matriculants. What does that mean? It sounds to many like an indictment of the fairness of the admissions process. Some schools are receiving more than their “fair share” of Oxbridge places. Or are they? In principle, this pattern could be explained if the 100 top schools had twenty times as many pupils as the rest, on average. Of course, they do not, but the idea does not seem so absurd when we replace “pupils” by “highly motivated pupils with highly motivated families”. Wealth is a factor, that is, but so is the importance placed upon education. Furthermore, as long as there is a perception that elite schools are the necessary springboard to Oxbridge, those families who yearn for Oxbridge will, if at all possible, scrape together the money to send their little ones to an independent school. The less motivated — perhaps because they do not care about education, perhaps because they find Oxbridge pretensions insufferable — will be less well prepared for Oxbridge (though perhaps better prepared for something else), and may not even apply. Indeed, if we look at application statistics, we see that the state school pupils are drastically underrepresented among the Oxford applicants as well. Only 57.5% of Oxford applicants in 2005-7 came from state schools. Those who did apply did fairly well, as we see that 53.2% of the places went to applicants from state schools. (Worcester received only 46.4% of its applications from state schools, but 48.7% of those accepted were from this group.)

Even if we accepted the soundness of the statistical inference — some schools are unfairly (or, at least, unreasonably) advantaged in placing their graduates in elite universities — the logical conclusion is being twisted to a political agenda. Consider that we believe ourselves to have strong empirical evidence for the proposition:
1) Graduates of elite universities are more likely to get good jobs and be economically successful in their lives.
The socially conscious concludes that therefore
2) We need to widen access to this important Oxbridge benefit.
We are then confronted with strong empirical evidence for the proposition:
3) Graduates of elite schools are more likely to be admitted to elite universities, and be economically successful in their lives.
The same pattern of reasoning then would lead us to
4) We need to widen access to this important elite school benefit.
One might widen access by helping more children from a variety of backgrounds to be able to afford to attend the best schools. Or, one might widen access by improving the education provided in the state schools, copying the methods and the funding levels of the independent schools. But no, that is not feasible. You see, that would demand higher taxes, and the British public does not believe in being taxed the way other Europeans are. But then, it is hard to see why, if they believe that the wealthy should be allowed by right to keep the money they earn, they are surprised when the wealthy want to use the money to buy something valuable, like a good education. And yet, this is not the conclusion drawn by some newspaper columnists and government ministers. (with some notable exceptions such as this journalist and this anodyne ministerial comment)

The report clouds the issue by multiplying the meaningless statistics: Quite promininent is the information that “The proportion of university entrants going to Oxbridge from the top performing 30 independent schools was nearly twice that of the top performing 30 grammar schools — despite having very similar average A-level scores.” That sounds rather damning, unless you know that  Oxford is choosing only from the students who have the maximum possible score of three A grades in their A-level exams. These comprise fully 10% of all school leavers, while less than 1% will be able to find a place at Oxford or Cambridge. Thus, comparing average A-level grades would not be expected necessarily to have much relevance in predicting Oxbridge acceptance rates. It is rather as though one were to infer invidious discrimination from observing that the Royal Philharmonic was far more likely to hire graduates of a leading conservatory than university graduates in music pedagogy, despite the fact that both groups on average had learned to play the same number of scales.

While the UK gives students only one shot at the “elite”, at the very least the message of rejection is somewhat limited by the admissions criteria. Whereas UK universities seek out the students most capable for the particular course of study that they aspire to study, US universities nourish the fiction that they evaluate the whole person. So when Harvard or Yale or Stanford rejects you, it is not just your academic qualifications that they are judging inadequate. It is your life.

My own experience as a student going through the US university admissions mill certainly colours my experience. Being quite naive about the process, I applied only to four universities: Harvard, MIT, Yale, and Johns Hopkins (the last only because my brother was there). I had admissions interviews at the first two, and was accepted at the last two. As someone who has gone on to be a quite competent research mathematician, I find the rejection by MIT back then particularly telling. I was a top student in high school, winning a fair share of local and national prizes in mathematics. I have gone on to become a fairly successful research mathematician. And yet I was rejected by MIT, which is focused almost entirely on natural sciences, and accepted by Yale, with much broader interests and a football team to squeeze in. Why? I can only guess that, as a shy and introverted, math-obsessed and relatively young school pupil, I did not perform very well in an interview that had almost no academic content.

Discrimination, Legacies, and Development Cases

US universities are rather infamous for the many different ways they discriminate for or against certain applicants. The most notorious are the legacies — preference for childre, or occasionally other relatives, of alumni — and the “development cases”, a euphemism for children of the great and the good, whose patronage may be expected. For an excellent discussion of the open scandals of US university admissions, see Daniel Golden’s The Price of Admission. Oxford explicitly rejects the principle of considering family connections as a factor in admissions.

I was interested to notice that even stuffy, old, rich Trinity College rejected Euan Blair, son of the Prime Minister, despite the fact that the warden (head of the college) is himself a notoriously wealthy and nonacademic alumnus of the college, and apparently a friend of the Blair family. Given the public attention that his case received, it’s easy to suppose that they were making a show of scrupulousness in admissions, but even then, it is notable that they felt it to be important to show that they would not play favourites with the son of a prime minister. Certainly US universities feel no compunctions about competing for the children of the wealthy, famous, and powerful, vaulting them ahead of more conventionally qualified applicants. Blair would hardly have been a disastrous student here: He did receive a conditional acceptance, but failed to make the required A-level grades — apparently his school predicted two A’s and a B, and he in fact received a C in French — and went on to study ancient history successfully at Bristol. (It is hardly a unique case. A classics tutor in Worcester told me of having rejected the son of a wealthy alumnus who they had ranked sixth among their applicants, when there were only five places. )

Of course, this is an often overlooked reason to be worried about the wealth-differential between colleges

Mathematics admissions at Worcester College

I presume that mathematics admissions are similar in most of the colleges, although the mechanics surely differ between those colleges with large numbers of applicants, and those with only a few. For some years now Worcester College has received the largest number of applications for mathematics and connected subjects, and in fact, the largest number of applications overall. Consequently, we had to interview from early morning to late evening on two consecutive days. Each applicant was interviewed twice, once on a sheet of questions that they had already seen, once on unseen questions. As I mentioned above, the school grades were all at the maximum. They had taken a mathematics exam specifically for Oxford admission, which has some influence on decisions.

In the end, I was quite impressed with how much one could see in a half-hour interview to distinguish the student with a superficial test-taking expertise from the student with the seeds of real mathematical vision and sharp problem-solving intelligence. At the same time, there are obvious dangers. The interview is extremely convincing, because it is something you have seen with your own eyes, and it does tend to wipe out all other considerations — particularly since, as I have remarked, the school system fails to provide the exceptional pupils with very many possibilities to differentiate themselves from the mass of merely adequate contemporaries. And while the interviews seem to be a very good tool for finding the prospective students likely to thrive in the tutorial system, it is hard to escape the suspicion that there are the rare young people whose minds are profound but not necessarily quick, who would benefit greatly from this university, and contribute greatly as well, who never manage to show their true mettle in a half-hour interview. We give two interviews, and then a third if there is disagreement, but it’s clear that a real genius might be missed.

On the other hand, I think that the interviews (at least as applied in mathematics) are well crafted to avoid the obvious inequities that concern many people. In discussions of admissions I never heard anyone suggest any criterion for admission other than mathematical ability, or rather, mathematical potential. Peripheral factors — in particular, quality of a candidate’s school, or national origin and language difficulties — were discussed only to the extent that they would help in translating the ability shown in the interview into potential. The principle, of course, is that the seed that sprouted well on stony ground has more potential than the seed that has already shown what it can do in rich loam. A candidate who seemed exceptionally nervous, or who was struggling a bit with conversational English, might deserve another look if his or her performance at the interview seemed otherwise not quite at the level of another without these handicaps. In the end, though, as sedulous as we tried to be in adjusting our expectations for the obvious distortions of personality and background, there is no question that a bright young person would be best served by the training of an excellent school, which would allow his or her ability to be directly demonstrated in the interview, rather than relying on the hit or miss possibility of some interviewer descrying great potential as through a glass darkly.

It might seem that students should calculate to apply to the less popular colleges, to compete against a weaker field. The advantage to be gained from such a strategy is marginal, though, and it could be counterproductive. There is a pretty thorough system for making sure that colleges with too many excellent applicants pass some on to the colleges with too few. My own impression is that there were a few rejected applicants, but not a large number, who probably ought to have found a place somewhere in the university had resources been unlimited.