Dr. Venkata Balaji is one of the researches who visitied lately the Mathematics Faculty. His research is about Algebraic-Geometry cooperating with many lecturers who are specialists in this field like Prof Dr Styhler. He came to Göttingen at the end of August 2003 and hopes to finish his research during  one year.

1. A short biography.

 

 

I was born on the 6th of September, 1968, in Mannargudi, a small town in South India. I went to school initially at Bombay, a city in the North West of India, and later at New Delhi, the capital city of India. Finally I came to Madras, which has been my hometown for over 20 years now. I earned there my Bachelors', Masters', Master of Philosophy and Doctor of Philosophy titles in Mathematics. I was a visiting scientist at the Mathematics Department of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, for one and a half years. Thereafter I went back to India for a year and now I am in Göttingen.
 

2. What is your favorite color and what does it reflect in your personality?

 

 

I have, in fact, three favourite colours. One is green which reflects my feeling for the Earth as a Mother who should be respected and protected from pollution and destruction.
The second is bright blue which reflects the urge to maintain a high level of serenity in all circumstances.
The third is orange which reflects my faith that the Spirit of Nature, which for example is the source of Life, is also present in things which seem dead. For example, at the level of the atom there is the nucleus in which there are many interactions between protons and neutrons. But usually there are so many protons very close together, each having the same charge, so that one expects that the nucleus must come apart, but in some way there is a spirit that keeps them together.
 

3. You have been here since a month. What is your first impression about Göttingen?

 

 

In fact I have not traveled much around Göttingen but so far it seems to be a very nice place and a very suitable place for scientific work with a lot of natural greenery and serenity. I have heard that there are mountains, forests, and lakes in the city and its surroundings and I would like to visit them in the near future.


 

4. Why did you choose to make your research in Göttingen?

 

 

First of all as you know the Mathematics Department here has a great history and I am proud to conduct my research and study at the same institute where Gauss and Hilbert once worked.
Secondly, there are many good and eminent professors here in the faculty, for example Prof Dr Stuhler who works in Algebraic-Geometry. They are also specialists in their own fields and they are very friendly.
I was told that some well-known scientists will soon be visiting the department here and that adds as well to my attraction to work here.
 

5. What is the subject of your research?

 

 

It is called Algebraic-Geometry, and this is because it deals with studying algebraic equations involving polynomials (in some variables) and seeks to explain the geometric properties of the solutions to such equations. For example, consider the equation x²+y²=1 ---it defines geometrically a circle (or a cylinder if you are working in more than two dimensions) if you are working with the real numbers. But in addition if you are working with the same equation over the complex numbers, then Algebraic Geometry helps to explain the geometric properties of the `hypersurface', for example if it has curves lying on it or if it is flatter or more curved at a given point (which you can feel and see if you are working over the real numbers).
 

6. Briefly describe the most significant responsibility you have had in your career and what it taught you?

 

 

I have had  two responsibilities that have taught me significantly. I gave an intensive course at my institute in Chennai (Madras) between August and November 2002 on integration theory. I was given the independence to teach the way I wanted. I adopted a very axiomatic approach to the theory. I allowed the third year Bachelors' students, Masters' students and Ph.D. students to attend the course. I had thought that the Bachelors' students would not like it, and that though the Masters' students would like it mostly, only 50 percent of the Ph.D. students would have the interest in my approach to the subject. But at the end I found out that there were all types of reactions from students from all the three categories. So there were even some Bachelors' students who liked the course.  So the moral is: if you have any new approaches to teaching, you should not hesitate to try it on the students. In my situation for example, any Bachelors' student knows the notion of an integral in a geometric way but rarely does he or she know the axiomatic basis for a general theory. And I chose the axiomatic approach to teach the Bachelors' students so that they would learn it in a general framework which can be applied in many diverse situations in Mathematics. I was perhaps taking a small risk in teaching like this at the Bachelors' level, but at the end many Bachelors' level students liked the course.
The second responsibility from which I learnt something important is that of my tutoring a private student, whom I started teaching since the high school (the last two years of schooling). He was initially poor in his studies and had bad results in his exams. But I realized that he had the capacity and that something was wrong. I taught him through his high school and also later when he studied for a Bachelors' in Engineering---I taught subjects connected with Mathematics, Computer Data Structures, Algorithms, and Software. He improved very well and got very good results in the exams at high school and in the Bachelors. Thereafter, I wrote for him a recommendation letter, to help him continue his studies in the USA where he got a scholarship and is now going to complete a Masters in Computer Science. He told me recently that he wishes to do his Ph.D. in Bioinformatics and this news gave me much joy. So what all this taught me is that a teacher should not lose his faith in a student's inherent capacity but must always try to give him the chance to perform better. If  a student is not doing well in his exams, the teacher should not lose hope with the student but must try to bring out his hidden capacity. The marks usually may not reflect the real capacity of a student.


 

7. Tell me about a pressure situation you were in that would demonstrate your ability to work under pressure.

 

 

The year before last I had submitted a paper which had some theorems that I hadn't proved in the utmost generality. It unfortunately took around 8 months before the referee could read it, and he suggested to me that the paper would be excellent if I could prove those theorems in their utmost generality and include these as well. The problem was that I had only a little time to discover the proofs, because the referee and the editor wanted the final version ready in the short span of 3 months. Initially I thought that I may not be able to do it. But fortunately I could manage it.
When you are under pressure, it is very difficult to be creative. You can do, under pressure, some mundane or manual work faster though. For example if I have to put letters in their envelopes, and suppose that I could normally fill 100 envelopes per hour. Now suppose that I am forced to fill 120 envelopes in an hour. In this case it is O.K. and I can do with some additional effort. But in Mathematics (or any creative profession) it may not be easy to remain creative when you are under pressure. For example, your ideas may not work. Or you may have difficult computations to be done and then anything can happen.
 

8. How do you plan your work?

 

 

Some planning is always important for any kind of work. But one should not be too rigid in following schedules. For example in scientific research if one has several problems to solve---for each of which he or she normally devotes some time according to a pre-planned schedule---but suddenly gets an idea or inspiration relating to a particular problem, then he or she should concentrate on taking advantage of that and devote as much time as possible in order to get closer to the solution. In any creative work, much of the time spent in the later stages is most important. For example, suppose a painter is attempting to paint  the portrait of a beautiful girl. Suppose he does it in 1 hour, then it may be that although he would finish almost all of the painting in the first 45 minutes, it would be his finesse of the last 15 minutes which would bring out the beauty and breathe the life into that painting. So if he were to stop after 45 minutes then the painting, although complete, may not be alive or beautiful. So somehow time-management is important, you should not be restricted by cut-offs specified by schedules when you are doing something creative.
 

9. What are your three greatest strengths?

 

 

The first one is to learn from mistakes. But of course one always makes mistakes, so where is the problem? Usually, when you make a mistake and you realise that you could have avoided that mistake then this makes you feel very upset and could lead to depression. And to get caught in a fit of depression is what is wrong. Instead you should learn from the mistake---know how the wrong action came into play and try to avoid it the next time. People get discouraged very easily. But one has the power to change oneself and make oneself perfect and that power lies inside his spirit and that must be done.
The second strength is to develop the capacity to be able to help anyone without expecting anything in return. This is a very difficult virtue to have. I am not saying that I have this virtue but it has always been my urge to have it.
And the third strength and perhaps the greatest is the urge to be joyful and to see joy in everything within and around myself. To enjoy life is different from just having pleasure. Joy is something that does not die. Pleasure can end at any time and pain can take its place easily.


 

10. What are your long term career goals?

 

 

I would like to teach Mathematics in a way that would make people look at it as an interesting subject instead of a boring or mechanical one. Newer books should be written on Mathematics that convince people that Mathematics is an art and enable them to see the beauty in it. I want to be able to show this in my teaching. Usually if one wants to understand a theory, he or she finds a book related to it and starts reading it. There are then a number of chapters to be read, and pedagogically, the first few chapters are on the basics about the theory. So one has to wait till the end of the book or for many chapters to be read before one gets to the proof of a central theorem of the theory. This is what is usually done, and is a very boring way to learn. Books should be read upside down, theorems should be proved upside down! Don't worry if you didn't understand small details at the beginning and just proceed: then you get a feeling for how the elements of the theory fit in place; finally you get an overall picture of the technique of proof. Books should be written in an order which is reverse to the usual pedagogic one, but should finally lead to a solid understanding of all the fine points. People who read books and proofs upside down perhaps turn out to be the best researchers. This method of learning `upside down' is unfortunately sometimes not even touched upon, and books are usually pedagogic because the authors want to make sure that there are no mistakes in their theory.
I would also like to discover something new and exciting, say a principle in Mathematics that manifests in Nature or everyday life and is related to other subjects like Physics, Chemistry or Biology. This would instill our lot of Mathematicians with more morale and enthusiasm.
 

11. Do you have anything to add?

 

 

No thanks.

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