Sunday, March 7, 2010

The Tripos and us

The Tripos was a venerable Cambridge institution -- an exam that mathematics students took to get their degrees and perhaps earn a scholarship.

It was impossibly arduous. Four days of problem solving, a break and another four more days of backbreaking labour that even future exceptional mathematicians found impossibly difficult. Most of the time the problems required a certain quickness in ability and the use of tricks to solve within the given time period. Mere aptitude in mathematics was not enough. It was and perhaps still is considered amongst the most difficult math exams in the world. (Some of us in the Indian system have a faint notion of the kind of problems that were set - what we called the S. L. Loney type - a sphere spinning on a needle that is balanced on an ellipsoid that is dangling from a pendulum or some such absurdity).

There was a certain caste system amongst those who succeeded. In the first class, the topper was the Senior Wrangler, followed by Second Wrangler, Third Wrangler and so on. The second class were the Senior Optimes followed by the Third Class, the Junior Optimes (yes, this is sounding more and more like Asterix). The last of the Junior Optimes was called a Wooden Spoon because tradition dictated that he (yes, always a he then) be given, by his friends a wooden spoon (actually a huge malting shovel lavishly decorated and inscribed in Greek) which the poor fellow was expected to take, hoist on his shoulder and carry it and himself out of the hall.

Senior Wranglers were God-like figures with all the attendant myth and mythology that would spring up around them. However they were not necessarily the best mathematicians, but, it was believed, would become the most influential one. After all, the Tripos stressed a certain knack in in solving problems fast rather than mathematical aptitude. Most future famous physicists and mathematicians were not Senior Wranglers (J. E. Littlewood was one notable exception). James Clerk Maxwell, J. J. Thomson, William Thomson (later Lord Kelvin) were all Second Wranglers. G. H. Hardy was, to his great consternation a Fourth Wrangler, Bertrand Russell a Seventh Wrangler.

Since the Tripos was impossible to 'max' without adequate practice, a whole alternate system of education cropped up around it. These were the coaching classes. Private coaches, for handsome fees, would coach you, not in the subtleties of mathematics but in how to take the Tripos. They would pour over old exams, make useful notes for solving problems, give you hours of practice all for the single minded purpose of taking the Tripos -- what someone called codifying mathematical knowledge into neat bundles. (Yes, yes, I know, it's familiar, but do bear with me, dear reader). The workload for students who took these mind numbing coaching classes was prodigious. For them, attending their usual lectures was a luxury they could ill afford. According to the famous mathematician J. E. Littlewood, himself a Senior Wrangler, one had to spend two thirds of the time practising solving difficult problems against time. Students frequently ignored the course material, in order to concentrate on the Tripos and hence the coaching classes. Hardy himself was coached by the legendary R. R. Webb, a 'producer' of many Senior Wranglers.

G. H. Hardy's aim was to eventually change this whole mind numbing examination system. His famous statement was that examinations (any examination, not just the Tripos) were necessary but only as an absolute minimum standard to get a degree. "An examination can do little harm as long as its standard is low", was his credo, instead of students and their tutors exhausting themselves to turn a comfortable second to a marginal first.

Hardy, despite his influence, succeeded in only marginally changing the system. On his pushing, a degree candidate still took the Tripos but was ranked only as Wrangler, Senior or Junior Optime, reducing somewhat the merciless pressure that the exam had created. The system had clearly more inertia than Hardy had bargained for, and he finally gave it to these minor changes.

The Indian analogy is obvious. The JEE is perhaps as stultifying, as mechanical as the Tripos (is or was). It stresses little knowledge of or ability in the subject, mainly a quickness of intellect and an ability to be able to use tricks to solve problems in the given time period. That is where coaching classes come in. It has today reached a stage where even the smartest students would not clear the JEE with a high rank without the knowledge of certain mathematical tricks in their kitty. Eventually all problems, even JEE problems can be solved without such tricks, but the race against time precludes a slow and methodical approach to any problem.

The Tripos system did produce some great scientists though few from amongst the toppers. Can the JEE boast of that? The numbers here are negligible and the names that spring to mind (for obvious reasons I don't wish to enter into a controversy about contemporary names who could be considered 'great') are hardly in the world class category of the Tripos toppers. More often than not, they end up in management, becoming CEOs or VPs of companies and only rarely a distinguished academic. The JEE is not a passport to greatness, not even as much as the admittedly flawed Tripos system. It's perhaps time for a significant change in the approach to this examination system -- though something tells me that that is not going to happen anytime soon. (It's also not in the interest of the coaching class companies to see it change). Like the British system which we inherited, the inertia in our system is large enough to neutralise even the most dedicated revolutionary.

Acknowledgement: As a product of the Indian and American education systems, I have little or no direct knowledge of the British Tripos system. Most of the stuff above is based on reading the literature, mainly the beautiful and fascinating account of the system in Robert Kanigel's masterful biography of Srinivasa Ramanujan.


N. Sukumar said...

More generally, I have often heard it said (mostly by physics professors in the US whose students could not get jobs in the field) that physics education is all about teaching problem-solving skills. While a recitation TA at Stony Brook, it was expected that most of my efforts were to be directed at imparting these all-important problem-solving skills to my students. This is what all those coaching classes concentrate on too. While applying one's academic knowledge to solving real-life problems is not to be trivialized, the mere art of solving standard problems -- or "tricks" as you so aptly call it -- is all too often confused as an indicator of learning, for no better reason than that this measure can be quantified and standardized in a facile manner.

kapil said...

It is true that examinations reduce the importance of "concepts".
There appears to be no way to test concepts in a written examination
which cannot be defeated by coaching in "tricks". Examinations like
the JEE and the Tripos or even the Mathematics Olympiads or the Putnam
examination are certainly affected by this malaise.

A casual glance at the list of Putnam winners or Olympiad winners will
come up with a number of famous mathematicians as well as a number of
"Who _is_ that and what did he do later!?"

The great man (Alexander Grothendieck himself) said "There are no
tricks in mathematics".

However, I still agree somewhat with what Sukumar has written. Memory
and short-cuts (or tricks, if you must!) are quite important for
many a working scientist/engineer. So developing these skills is
almost on par with developing a conceptual understanding.

I would say that the main problem with examinations is that they
become the be-all-end-all goal of learning for many people. All these
"JEE-pass" students with finely honed problem solving skills never
learn the concepts that can be mixed in with these skills to do
creative/original work in science and engineering.

Neelima said...

`All these" JEE pass students `never learn'.......? A bit of a sweeping statement, don't you think?

Rahul Basu said...

I think there is nothing wrong with learning tricks -- we all use it in our research whenever possible to get to the answer faster. The problem comes when this becomes the be-all and end-all to the process.

However, hopefully students do learn something finally in their courses. After all, in my experience of a admittedly small sample of IIT B Tech students, they are way ahead of other students in their ability, intellectual nimbleness and most importantly, in being able to put in hours of slog work. I think the last is not be sneezed at and is 90% of the passport to success. (I feel it particularly today when a student came and showed me an indecipherable bug in his program and said he will be back in 2 weeks (!!!) with hopefully the bug removed.

gaddeswarup said...

There is a fascinating account of tripos in Old Cambridge Days by Leonard Roth

AmOK said...

Thanks for an interesting post, OLO. Indeed what is the correlation between EQ and IQ? The most influential are those who make others work for them. Those tricks keep changing but they are always there. How fast you learn new tricks is importat.

Rahul Basu said...

Gaddeswarup: Thanks very much -- indeed it's quite fascinating and that too from someone within the system. I also see now that Kanigel has 'borrowed' much of his description of Cambridge mathematics
at the turn of the century (including the 'Great Sulk') from this account.

gaddeswarup said...

I got the link from a comment in
which has more links.

Suresh said...

1. The problem is not the JEE per se but rather the lack of quality institutions. The quality once you get past the top few institutions is frightening. This is not just in engineering but in almost every subject.

2. You seem to forget that the JEE was started primarily because it was thought to be a better selection process than the alternative which was marks obtained in the school-leaving exam. Given the multiplicity of boards, not only is there an issue of comparison but the marks themselves seem to have drifted "upwards" over time. As a resident of Tamil Nadu, do tell me if they convey any useful information? When you have people obtaining 99% average?

3. The comparison of the Tripos (internal evaluation of students) and the JEE (admission of students to universities) is not, in my opinion, a valid one. In asking who are the world-class scientists produced by the JEE, you forget that success in the JEE only guarantees that you enter the IIT system. It doesn't say anything about what the student subsequently learns there. If you are going to compare like with like, compare the education system of the IITs with the Tripos system.

4. By the way, why just the JEE? Others (like AIIMS) also rely on the admission exam process. It tells us that the problem confronting the IITs confront others too.

5. As someone familiar with the American system and its reliance on the SAT (as one component of the admission process), you think there is no "coaching" for that?

6. The lack of quality institutions in our case is compounded by the reluctance to increase fees unlike American institutions. I suppose the argument is that using money as a "selection tool" favours the rich. But that is true for the most part even now. Note that money is being spent by students (or rather the parents): It's just that the coaching institutes at Kota and other places get that money. The upper class bias of the JEE is still very much there.

7. One thing that could be done is to use the JEE as one component of the admission process and use a broader range of criteria. This is similar to what is done in the USA. But that will make the admission process more resource-intensive. (More faculty time and so on.) I guess there are no easy answers to the problem that confronts us.

Just some thoughts.

kapil said...

@neelima: I agree that the statement was too sweeping --- especially considering where I come from!

Anant said...

Very strange that for a few days I did not peek into AIP and missed this post...well almost, because I have got to it albeit a little late. Not being smart enough to get RSS feeds and the like, there is a slight delay. While I have no doubt that there are lots of important fundas here, those of us who are attention-deficit disordered may have liked a quick summary. How about a condensed-AIP?

More seriously, as regards
The JEE is not a passport to greatness, not even as much as the admittedly flawed Tripos system... from your post, I believe that you are truly mistaken. You would be amazed how much these things matter in old-IIT boys (and few girls) networks.

Rahul Basu said...

Hmm! I wonder which old IIT boy is being referred to here....

vbalki said...

I have some comments on the JEE, the B. Tech. programme of the IITs, and so on, since I've spent a little bit of time as an interested ringside observer of these affairs. The matter actually deserves careful analysis, but I don't want to bore you (and your readership) with a lengthy account. Let me just say that, for a variety of reasons, the JEE is no longer what is was in the 1980s and 1990s (perhaps the "best" years of the JEE). At its best, it was a very good exam. It is not quite a farce as yet, but it'll get there.


melander58 said...

The eminent astrophysicist Arnab Rai Choudhuri refers to the Tripos/JEE brand of science as "schoolboy conception of science" in his essay: "Practising Western Science outside the West: Personal Observations on the Indian Scene" in Social Studies of Science, 15, 475 (1985). See JSTOR link:

Sourendu said...

Welcome back to the net. I seem to have missed seeing you glide back in to leave an interesting post.

The jee huzur is seen as a passport to increased earnings; therefore the visibility of the training industry around it. But any long running exam system generates an industry: it's not just the Tripos or the jee or the sat.

The training industry that has grown around school-leaving exams in India is something that all of us know about. Since this kills "understanding" just as efficiently as jee-training, and affects more students (by orders of magnitude) its effects are, in some sense, worse.

I found recently that even engineering students in Mumbai university go for coaching classes all through their coursework. This probably happens in other universities and for other courses as well.

Schools, colleges, and universities are regulated in various ways, and subject to quality checks of various kinds. However, this secondary industry is completely unregulated, and generates more revenue than the primary system.

Anant said...

There is a curious paradox in what Sourendu writes: if the regulated sector has quality checks, then it should be better than the unregulated one with no quality checks. So why do students still go for the latter? It must be a herd effect...the students must feel that they are missing something if they don't go to coaching classes (of a very dubious nature). Possible solution is to make the regulated sector so good with motivated teachers and good course material, books and the like so that there is no need to go to the unregulated one?