People joke that Chennai has only two seasons --- hot and hotter. This is probably a bit unkind since it does rain in Chennai --- in two separate spells during the year. Chennai-ites will also rave about the setting-in of the afternoon sea breeze and the way it lightens up the evenings even on the hottest of days. That said, there are a variety of seasons in Chandigarh/Mohali that temperate climes like Chennai cannot begin to match. The torrid summer winds that come from over the desert, the wet monsoon, the hot and humid months that follow the monsoon, the onset of winter, the cold and foggy winter, the bluster and drizzle of late winter, the beautiful flowers of spring, the onset of warmth that precedes summer, the dry and dusty summer --- each season is distinct and is interesting in its own way.

Yet, we are not here to talk about the weather. There is a different kind of rotation of seasons that is peculiar to a teaching institute.

At a research institute, there are essentially only three seasons: the winter conference season, the summer workshop and summer school season and the rest of the year. In the latter, one day is more or less indistinguishable from another --- in fact, when I stayed on campus in TIFR, even the weekends were distinguished only by the fact that there was an occasional Images'' movie or anAMA'' concert.

On the other hand, here at IISER Mohali, we have the new kids on the block period in July-August, followed by the tension of the first mid-term examination, then the quieter time of consolidation between the two mid-semesters (also the time for a lot of extra-curricular activities), the 2nd mid-semester and holiday season, then the hectic time before the final examinations (for the students) and after the final examinations (for the faculty). The all too short winter break is followed by the start of the new term and another semester which follows a pattern similar (but not quite identical!) to the first. The end of the second semester is followed by the convocation ceremony and the start of the summer term. Some colleagues go for collaborations abroad while others stay on to toil along with summer and project students over the summer. Then comes admission season and the start of the new academic year.

In addition to the above, there is an overlay of the seasons that undergraduate students go through, as fresh first year-ites, confident second year-ites who then choose their major and go excitedly into their third year with the chosen major, then sit in small classes with big course numbers in their fourth year and strut about as research students in their final year.

Indeed, the seasons at IISER Mohali are worth enjoying and celebrating.

An important aspect of science is to look for patterns in the data and use that to grasp some simple underlying principles on the basis of which that data can be organised, studied, etc. Such a search for patterns is what mathematics (in its broadest form) is! Hence, it is no surprise that I would like to underline its importance.

Note that we are looking for simple principles. How does one understand simplicity? Is "simplicity" in the eye of the beholder? Indeed it often is! By the time we reach our teens we are looking at the world through thick layers of glasses of preconceived ideas --- some of them put there by our teachers --- and sometimes simplicity involves removing some of these filters/lenses.

The purpose of teaching is also simplification. Some may say that our purpose is to pass on the accumulated knowledge suitably distilled. However, "distillation" is insufficient to arrive at a learning time exponential lower than the time taken to collect the knowledge (note that what we teach in 12-15 years is based on 3000 years of data collection), unless this distillation involves simplification in a central way.

In other words, one of the functions of a teacher is to simplify what the teacher already knows --- and one measure of simplicity is that it should take the learner less time than it took the teacher to learn the same thing!

The bottom line for teaching-researchers is this: Do not tell your students that they need to spend years to learn something since it took you that long --- instead, do some research and try to simplify the material! [*]

The Hon'ble minister, who is himself an alumnus of an IIT, said nothing new (at least to IITans). In the proto-typical IIT pecking order, the top of the heap is the BTech students (themselves ordered by branch chosen), they are followed by 5-Year integrated students or 2-Year MTech students (depending on who you ask), then by the 2-Year MSc students and then the PhD students. The faculty occupies a variety of slots; mostly below the BTech "kings" with a few exceptional "fundoos".

There were a number of rejoinders to the Hon'ble Minister's remarks:

• "it may not be untrue, but it was unnecessary to say it" was what one IIT Director said.
• "compare the salaries and facilities at MIT/CalTech vs the salaries and facilities at IITs" said a blog post.
• "compare the competitive nature of student recruitment vs the way in which PhD students and faculty are recruited" said a newspaper article.

This post tries to take a different tack.

Have the IIT BTech alumnus made contributions to science and engineering research which justifies the enourmous expense of human resource (not to speak of financial and other resources) that they represent? To me it seems that the answer is "No!" (If IIT had delivered sufficiently many creative scientists and engineers, we could have seen the undoubted success of venture capitalists like Mr. Vinod Khosla, Fortune 500 company creators like Mr. Narayana Murthy and influential politicians like the Hon'ble Minister Mr. Jairam Ramesh himself as icing on the cake --- right now it just looks like sour cream!)

Why have the IITs failed to create a large number of creative engineering scientists?

The IITs represent the ambition of the middle-class in India to escape the mediocrity that they percieve around them. That is why parents are willing to invest so much time, money and mental energy on the task of getting their children admitted to these institutions. An IIT-JEE aspirant hopes to become part of an elite institute, an "island of excellence". However, the charm of the fancy labs and the professors with their strange accents quickly wears off. It then becomes the next aspiration to achieve "escape velocity" --- in our time this was through the landing of a "schol", while nowadays it is more often the plum MNC job.

However, this search is futile unless one discovers that mediocrity can only be erased by _creating_ excellence --- a much more difficult task than immersing oneself in it. The attitude with which most students enter coaching classes and then IIT negates the spirit of adventure and risk-taking that is critical to the creation of new ideas.

To escape mediocrity one must "boldly go where no one has gone before" or at least boldly go where the rest of your batch is scared to go! The few success stories of IIT alumni (to create new science and engineering ideas) come from people who did this.

So yes, Minister, the IIT students have sharper brains than most of their faculty. However, how many of these students realise their potential for creativity?

Mathematics is one of the oldest intellectual activities of mankind, so it is not surprising that the amount of mathematics that has already been done is enormous as compared with almost any other discipline. One consequence (that has not escaped notice!) is that people who prove theorems are often much older today than in earlier years.

Another important consequence is that for anyone active in mathematical research today, most mathematical learning has happened outside the classroom. Moreover, such non-classroom learning is far from linear. Monuments of mathematical beauty are built on wooden stilts; the latter are only turned into firm pillars when one finally writes down the fruits of one’s research.

The above paragraph is nothing new to working mathematicians, but each incoming generation must learn it anew. This is because courses and books in mathematics are often structured in a linear way. There are clearly defined prerequisites and everything new is either defined or proved in strict deductive order. This serves the important purpose that each fresh batch of students verifies the “grand edifice”. However, it also leaves many a student with the false impression that this is how mathematics is done. Even worse, it may leave the impression that classroom and textbook learning is what mathematics is about.

One should certainly strive to improve one’s classroom skills, to write more readable textbooks and to design better courses. However, one should never lose sight of the wide open spaces where many new mathematicial objects are built.

One of the ways people characterise science and technology is by saying that science is about prediction and technology is about design. This is not wrong but I feel that it misses something.

An astrologer too claims to predict the future and claims to tell you how to re-design your future. So the above explanation of science and technology could make it indistinguishable from magic!

One thing that does distinguish science is that the prediction and design is done by “calculation”; this is not restricted to mathematical calculation but includes recipes like “mix so much of this reagent with so much of that solvent”. In fact, the notion of calculation can be expanded to anything that I can teach someone else to do — even an “idiot” like a computer.

This leads us to the view that science is not only about making predictions and designing things but also about teaching others to do the same. At the very first level, this is done by providing “formulas” which other people can use to make predictions and design things.

However, this is not quite far enough, since it would still make the act of creating these formulas a magical thing! So we must take this a step further and be able to teach others how to create their own formulas. In other words, we want to provide formulas for creating new formulas.

It does look as if we could be in infinite regression here, for who will then create formulas to provide formulas for creating new formulas!

Luckily, the “monadic” thinking of Turing helps us here. He realised that “formulas for creating new formuals” are themselves just (slightly more complicated) formulas. Just as a gift-wrapped box containing a gift can be thought of as just a box containing a gift.