Points in favour of open exam:
There is no fixed date or place for the exam. With many different Universities IITs and what-not we do lose students who are for one reason or another unable to come to a particular place on a particular day. From the time we started the open exam the number of candidates appearing for the test has increased dramatically.
The paper closely indicates the nature of problem-solving that is involved when getting a Ph.D. The problems consist of parts that can in principle be solved and put together the result is a reasonably interesting theorem. Problems of this nature cannot be put in a written exam due to time limitations. The paper does not demand a knowledge-base.
Many teachers (yes!) and students are encouraged to think about problems of the kind we are interested in. The questions asked contribute to the growth of mathematical culture in universities.
Since the interview is the basis of selection, the problem of "copying" is not serious. On the one hand if students discuss the questions with their teachers and other students it encourages them to engage in collaborative work---another aspect of research. It is expected (and checked at the time of interview) that they understand the solution they present in toto---another aspect of collaborative research.
(It is important that we decide in advance what score is adequate in order to alleviate the possibility the problem of missing an "honest" candidate from one who "merely copied". In other words we if we decide that a score of 40/100 is enough we should call all the students who have attained that score even if the number is 100 or more!)
Counterpoint in favour of open exam:
- In view of the above, the extra work involved in correction and the extra work involved in interviewing is not much. According to the last time when IMSc did the correction the extra faculty hours used in this work amounts to about 50-80 person hours per year. (HRI faculty appear to have a much larger figure).
Here are the points that I know in favour of the written exam:
A. The system is traditional. It is tried and tested and does the job. Students know what to expect.
B. The correction is much quicker. If one insists on "objective-type" tests it can be fully automated!
C. The test is better at screening poor candidates since the possibility of copying is reduced. For example in Computer Science at IMSc they do not correct the "non-objective-type" questions unless the student has scored a certain minimum on the "objective-type".
The additional counterpoints in favour of the written exam:
D. Even granting all the benefits of the open exam, the increase in applications has not led to an increase in actual JRF's selected.
E. The job of taking mathematics to the universities should be pursued through some other channels.