A liberal education is important to be an informed citizen. However, I think it is always important to keep ones options open whether you know, as you graduate from high school, exactly what you want to do with your life or not. In the US and some countries it is possible, but im many it is not.

Let me give you two examples. A classmate of mine was a physics major as an undergraduate, but some how wanted to be a historian. He tried desperately to register for a PhD in History at the University of Calcutta (he had a masters in management from a prestigious school). The university flatly denied to accept him merely because his bachelors was from the faculty of science, not arts.

The poor chap had to go to Canberra, Australia to get his doctorate in history. He worked as a Professor at ANU, and a few years ago was invited by the University of Chicago (http://en.wikipedia.org/wiki/Dipesh_Chakrabarty)  to hold an endowed chair in history (he is a labour historian).

The second example refers to a colleague and a friend of my father, T.A. Davis (who was my loco parentis in Calcutta), whose only qualification was a bachelors in Chemistry. He was vegetating at a research Institute (there was nothing non-chemical he could do in India those days, and that is true even today). Fortunately for him one of the greatest biologists of the 20th century, JBS Haldane, while visiting, took a liking for him and took him to the Statistical Institute in Calcutta. He completed his doctorate (the last student of the famed C.R. Rao) in statistics shortly before he retired, but made fundamental contributions to folial symmetry (which follows Fibonacci numbers), and even became one of the senior officers of the Fibonacci Society (also a visiting professors at Michigan, Berkeley, Chicago,...) (see http://www.genetics.org/content/185/1/5.full.pdf).

It is important that one have a choice either way. If you know precisely what you want to do, you should be able to do it, but if you realise you made a mistake you should be able to correct it. That is not possible in many countries even today.

The most important thing in education is to keep an open mind, and for the educational system to ensure that there are no obstructions to keeping an open mind. I'll close with the commencement address by the great mathematician Paul Erdos at the Indian Statistical Institute in 1984:

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Child Prodigies

Paul Erdos

Professor, Mathematical Institute, Hungarian Academy of Sciences

… let me illustrate this idea of having your mind open with a story. It seems to be a true story, though I have not examined the original documents. There were two men, one whose mind was open and another whose mind was not open. Now there was Rontgen – the German physicist who discovered X-ray in the U.S., they are known as Rontgen rays. Rontgen in 1891 noticed by accident that if you leave a photographic plate near a Crook's tube then the

photographic plate gets darkened. Now from this Rontgen somehow noticed that this must be an important phenomenon and for a few weeks he did not do anything else but work on this subject and these few weeks of course changed the world. After he finished work on X-rays, Rontgen rays were discovered for which a few years later he received the first Nobel Prize in physics. These rays have immediate applications in medicine. Rontgen noticed very soon that

one would take pictures of the internal organs an enormously important application. Very soon their curative effects for cancer were discovered, its dangers were realized very soon and that one must be very careful in working with these rays. Also next year radio-activity was discovered by Bequerel and then the Curies came along, and a few years later the atom bomb was discovered and now we are not yet sure that you will survive this discovery.

Anyway the world was never the same after Rontgen discovered X-ray.

Now let me tell the story of a man whose mind was not open. Crook – who

incidentally was a great physicist himself discovered the cathode rays and the Crook's tube – also noticed that the photographic plate gets darkened if you leave it near a Crook's tube, but he only deduced that you should not leave a photographic plate near a Crook's tube. He put up a warning in his laboratory for colleagues not to do so. As a joke, I sometimes call it the biggest mistake in the history of science. I could tell from my own career of some instances when my mind was not open; for example, Hajnal and I missed the discovery of the fact that the inaccessible cardinals are not measurable. There are a few other examples. I missed the discovery of the extremal theory of graphs which I should have done two years before Turan did so. Every mathematician will find cases where he really should have made the discovery and he did not make it. This is true of course for every subject in the world.

Source: http://www.isical.ac.in/~isiaa/ISIAA_Bouquet-of-Remembrances.pdf 

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