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  •  Panini (1+ / 0-)
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    Panini and modern linguistics:

    ...the influence of Pāṇini on the founding father of American structuralism, Leonard Bloomfield, is very clear, see e.g. his 1927 paper "On some rules of Pāṇini".[11]

    Noam Chomsky has always acknowledged his debt to Pāṇini for his modern notion of an explicit generative grammar.[12] In Optimality Theory, the hypothesis about the relation between specific and general constraints is known as "Panini's Theorem on Constraint Ranking". Pāṇinian grammars have also been devised for non-Sanskrit languages. His work was the forerunner to modern formal language theory (mathematical linguistics) and formal grammar, and a precursor to computing.[13]

    The Backus-Naur form (Panini-Backus form) or BNF grammars used to describe modern programming languages have significant similarities to Pāṇini grammar rules. Pāṇini's grammar can be considered to be the world's first formal system, well before the 19th century innovations of Gottlob Frege and the subsequent development of mathematical logic. To design his grammar, Pāṇini used the method of "auxiliary symbols," in which new affixes are designated to mark syntactic categories and the control of grammatical derivations. This technique was rediscovered by the logician Emil Post and is now a standard method in the design of computer programming languages.

    "Most significant contributions by Indian mathematicians in the post-WW2 period seem to have come in theoretical computer science (which can be considered to be a branch of mathematics) and related areas. "

    I doubt if there are any significant contribution of Indians based in India in the fields of math or computation/computer science. as can be seen from the Nobel prizes of 4 Indians post Independence, (in physics, biology, economy and teh latest in chemistry) who were based in the US or UK.

    •  AKS primality testing. (0+ / 0-)
      "I doubt if there are any significant contribution of Indians based in India in the fields of math or computation/computer science."

      AKS primality testing work was done entirely in India:

      AKS primality test

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      The AKS primality test (also known as Agrawal-Kayal-Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by three Indian Institute of Technology Kanpur computer scientists, Manindra Agrawal, Neeraj Kayal, and Nitin Saxena on August 6, 2002 in a paper titled PRIMES is in P.[1] The authors received many accolades, including the 2006 Gödel Prize and the 2006 Fulkerson Prize for this work.
      The key significance of AKS is that it was the first published primality-proving algorithm to be simultaneously general, polynomial, deterministic, and unconditional. Previous algorithms have achieved any three of these properties, but not all four.

      Thanks for the extra info on Panini's work. I'll check his theorem out shortly :)


      Most (but not all) of the top Indian scholastic talent gets induced into the IITs, which are engineering schools. Although some 5 year science/math MS degrees were offered, they never caught on. Personally, I wanted to pick a 5 yr MS math program when I was choosing my area at IIT, but my father didn't allow me to take that route (because job placement for math/science degree holders was poor in India, unless you end up going all the way to do a good phd, and end up becoming a prof at a top school like the IITs), and so I ended up doing an engineering degree for my Bachelors (against my will, if you will :)).

      Typically the top IIT/JEE rankers choose computer science as their major (since the late 70s when the CS programs came to exist; before that, the subject was covered in electrical/electronics engineering streams), implying that some of the best Indian brains have IIT computer science (and related) degrees, and some 90-95% of the IIT CS grads come over to the US for their graduate studies. So, it follows that, more or less, the best scientific work from Indians over the last 30 years would be in computer science, and done in the US for the most part since many of them also stayed back after their phds in the US academia. Since there is no Nobel prize in either CS or math, obviously one can't expect many Indian Nobel prize winners from this generation of Indian minds, unless they changed directions and went into Physics or Economics later on (Biology and Chemistry are sort of out of the way for a typical engineer.)

      Drs. Chandrasekhar and Khorana did their college work before the IITs came to exist, and when Dr. Sen went to college, the IITs were just getting started. So only Dr. Ramakrishnan, among the post-colonial Indian Nobel Laureates (non-peace), chose a science stream even though IITs were the leading institutions in India by his time. I think, in order to produce world-class talent (and thus research) in the basic sciences (which I kinda feel the very best of Indian minds are better suited for, over technological fields), India should create a handful of IIScs, and popularize the science degrees offered (at the undergrad level) in the IITs, draw some top science talent from around the world to work in all of these programs, create an infrastructure with attractive pay scales for people to stay back for phds and subsequent academic work, with incentives for publications in the top international journals. A ton of investment, but I think it will pay off in the longer run for India as well as the world of science.

      Did you know that Indians invented the # 0 and the decimal/binary systems: a primer on Indian mathematics.

      by iceweasel on Sun Oct 11, 2009 at 01:23:20 PM PDT

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