It is often asked, answered and debated why Alfred Nobel didn't include Mathematics as one of the subjects along with Physics, Chemistry and Physiology or Medicine when he first instituted the first five Nobel Prizes; Literature and Peace being the other two.
There are multiple explanations for the exclusion of Mathematics. Some say Mathematics was not considered as a fundamental science which could directly human well being. Some say that there were plans of a prize being instituted by the King of Norway and Sweden, who himself was also a mathematician, for excellence in Mathematics. While some other points out to personal angle wherein it is said that the woman he proposed to rejected his proposal in favor of a Swedish mathematician of the period, Gösta Mittag-Leffler, and hence he despised of mathematicians and mathematics.
There are many prestigious awards instituted in Mathematics. of which two come very close the stature and prestige of Nobel prize. Those are Abel Prize and Fields Medal. Most of the surveys conclude these two being the top awards in Mathematics and both of them are alternately referred as the equivalent of 'Nobel in Mathematics'.
The Abel Prize is awarded by the King of Norway every year and is directly modeled on the Nobel Prize. It is named after Norwegian mathematician Niels Henrik Abel and was first awarded in 2003. However this award was originally proposed to be instituted by the King of Sweden and Norway around the same time as the Nobel Prizes by the Swede Alfred Nobel but the dissolution of the union between Norway and Sweden hampered the plan.
The Fields Medal is awarded by the Internationals Mathematical Union to mathematicians under 40 years of age. This award was first awarded in 1936 and since 1950 is given away every 4 years.
Most of us can easily reckon the name of Nobel Laureates who are either Indians or have an Indian origin. And we are also to an extent aware of the ground breaking work they would have done which helped them gain the ultimate recognition. However very few of us actually know the same about Abel Prize or Fields Medal. Abel Prize and Fields Medal has so far being won by 3 geniuses who trace their roots to India; one of them won the Abel Prize while the rest two won the Fields Medal.
In this first post we will take a look at the works of Dr. Varadhan, the only person of Indian origin to have won the Abel Prize.
S.R. Srinivasa Varadhan an Indian American mathematician won the Abel Prize in 2007. He was awarded the Abel Prize “for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations.”
Dr. Varadhan was born in Chennai and completed his undergraduate studies at Presidency College, Chennai and completed his masters from the University of Madras. He completed his PhD from ISI, Kolkata where C.R. Rao was his doctoral advisor. At ISI he was one of the 'famous four' students of C.R. Rao along with Ranga Rao, Parthsarathy and Varadarajan.
It is widely known that noted Russian mathematician Andrey Kolmogorov was the foreign examiner for Varadhan's PhD thesis and recommended that the thesis deserved a 'second degree in Russia'; first degree in Russia corresponds to PhD elsewhere and second degree could be taken as almost equivalent to DSc.
Varadhan was awarded the Abel for his work on probability theory which were published in the 1966 paper "Asymptotic Probabilities and Differential Equations".
In probability limit laws govern the results when the same experiment is repeated a large number of times. One of the limit laws is the Law of Large Numbers (LLN) which states that the results approach the expected value when the same experiment is repeated a large number of times. Thus the probability of getting heads in a coin tossing experiment approaches 0.5 when the experiment is repeated a large number of times.
The other is Central Limit Theorem (CLT) which states that the distribution of a statistical property which is dependent on a large independent, random variables follows a bell shaped curve i.e. a normal distribution. For example if we plot a large number insurance claims associated with vehicle accidents then they are mostly expected to follow a bell shaped pattern.
However the scenarios which are not covered by the CLT and LLN are 'large deviations'. This is specially of interest in insurance mathematics where the insurance companies have to keep the premiums at a level which can cover an unprecedented bad year in which an exorbitantly large number of insurance claim hits them.
An interesting case in view is the case of Poe Financial Group which was one of the largest insurance providers in Florida and mostly had customers based out of Florida. 2004-05 was one of the most devastating Hurricane seasons to hit Florida. These two seasons cleared off the entire profit earned by the company since 1993 and the company went insolvent.
The CLT and LLN were shown to fail in such scenarios of large deviations by Harald Cramer, a distinguished insurance mathematician, while investigation insurance 'ruin theory'.
In his path breaking 1966 paper Varadhan revealed the Law of Large Deviations which stated the underlying governing principles for large deviation scenarios. His general principle answered questions associated with behavior of a random system which otherwise couldn't be answered by LLN or CLT. The proposed theories of Varadhan found a wide array of applications in fields of quantum physics, statistical physics, econometrics, finance, population dynamics etc. One of it's application is explaining the behavior of 'Weiner Sausage' which in turn was used to explain the results of a Bose-Einstein Condensate.
Another work of Dr. Varadhan which find metion in the citation of Abel Prize is related to his work on the application of martingale problem for diffusion processes which ultimately led to book 'Multidimensional Diffusion Processes' in the year 1979, co-authored with D.W. Stroock.
In probability a martingale is a random process in which the probability of the next state in equivalent to that of current state and has no relation to the earlier states. A diffusion process on the other hand is a Markov process with continuous sample paths. A Markov process is characterized by the property that the expectation of the next state in the process is independent of current state and all previous states. Vardhan's theory answered such Markov or diffusion processes in terms of martingales. This has again found wide spread application in the field of population genetics and hydrodynamics.
The Abel citation states: 'Varadhan’s work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time.'
Dr. Varadhan is associated with the Courant Institute of Mathematical Sciences, New York.
In a subsequent post I will discuss on the works of the other two prodigies who won the Fields Medal.
References:
There are multiple explanations for the exclusion of Mathematics. Some say Mathematics was not considered as a fundamental science which could directly human well being. Some say that there were plans of a prize being instituted by the King of Norway and Sweden, who himself was also a mathematician, for excellence in Mathematics. While some other points out to personal angle wherein it is said that the woman he proposed to rejected his proposal in favor of a Swedish mathematician of the period, Gösta Mittag-Leffler, and hence he despised of mathematicians and mathematics.
There are many prestigious awards instituted in Mathematics. of which two come very close the stature and prestige of Nobel prize. Those are Abel Prize and Fields Medal. Most of the surveys conclude these two being the top awards in Mathematics and both of them are alternately referred as the equivalent of 'Nobel in Mathematics'.
Most of us can easily reckon the name of Nobel Laureates who are either Indians or have an Indian origin. And we are also to an extent aware of the ground breaking work they would have done which helped them gain the ultimate recognition. However very few of us actually know the same about Abel Prize or Fields Medal. Abel Prize and Fields Medal has so far being won by 3 geniuses who trace their roots to India; one of them won the Abel Prize while the rest two won the Fields Medal.
In this first post we will take a look at the works of Dr. Varadhan, the only person of Indian origin to have won the Abel Prize.
Dr. Varadhan was born in Chennai and completed his undergraduate studies at Presidency College, Chennai and completed his masters from the University of Madras. He completed his PhD from ISI, Kolkata where C.R. Rao was his doctoral advisor. At ISI he was one of the 'famous four' students of C.R. Rao along with Ranga Rao, Parthsarathy and Varadarajan.
It is widely known that noted Russian mathematician Andrey Kolmogorov was the foreign examiner for Varadhan's PhD thesis and recommended that the thesis deserved a 'second degree in Russia'; first degree in Russia corresponds to PhD elsewhere and second degree could be taken as almost equivalent to DSc.
Varadhan was awarded the Abel for his work on probability theory which were published in the 1966 paper "Asymptotic Probabilities and Differential Equations".
In probability limit laws govern the results when the same experiment is repeated a large number of times. One of the limit laws is the Law of Large Numbers (LLN) which states that the results approach the expected value when the same experiment is repeated a large number of times. Thus the probability of getting heads in a coin tossing experiment approaches 0.5 when the experiment is repeated a large number of times.
The other is Central Limit Theorem (CLT) which states that the distribution of a statistical property which is dependent on a large independent, random variables follows a bell shaped curve i.e. a normal distribution. For example if we plot a large number insurance claims associated with vehicle accidents then they are mostly expected to follow a bell shaped pattern.
However the scenarios which are not covered by the CLT and LLN are 'large deviations'. This is specially of interest in insurance mathematics where the insurance companies have to keep the premiums at a level which can cover an unprecedented bad year in which an exorbitantly large number of insurance claim hits them.
An interesting case in view is the case of Poe Financial Group which was one of the largest insurance providers in Florida and mostly had customers based out of Florida. 2004-05 was one of the most devastating Hurricane seasons to hit Florida. These two seasons cleared off the entire profit earned by the company since 1993 and the company went insolvent.
The CLT and LLN were shown to fail in such scenarios of large deviations by Harald Cramer, a distinguished insurance mathematician, while investigation insurance 'ruin theory'.
In his path breaking 1966 paper Varadhan revealed the Law of Large Deviations which stated the underlying governing principles for large deviation scenarios. His general principle answered questions associated with behavior of a random system which otherwise couldn't be answered by LLN or CLT. The proposed theories of Varadhan found a wide array of applications in fields of quantum physics, statistical physics, econometrics, finance, population dynamics etc. One of it's application is explaining the behavior of 'Weiner Sausage' which in turn was used to explain the results of a Bose-Einstein Condensate.
Another work of Dr. Varadhan which find metion in the citation of Abel Prize is related to his work on the application of martingale problem for diffusion processes which ultimately led to book 'Multidimensional Diffusion Processes' in the year 1979, co-authored with D.W. Stroock.
In probability a martingale is a random process in which the probability of the next state in equivalent to that of current state and has no relation to the earlier states. A diffusion process on the other hand is a Markov process with continuous sample paths. A Markov process is characterized by the property that the expectation of the next state in the process is independent of current state and all previous states. Vardhan's theory answered such Markov or diffusion processes in terms of martingales. This has again found wide spread application in the field of population genetics and hydrodynamics.
The Abel citation states: 'Varadhan’s work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time.'
Dr. Varadhan is associated with the Courant Institute of Mathematical Sciences, New York.
In a subsequent post I will discuss on the works of the other two prodigies who won the Fields Medal.
References:
- Abel Prize citations
- Wikipedia
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