Research

The Creative Spark

The moment a theorem is proved after fine-tuning the various arguments, studying all the cases where it is applicable, and finally polishing it for publication; that moment when no one in the world knows about it except the person who has proved it — that moment becomes an exhilarating moment for the prover.

It does not matter how deep the theorem is; it may be path-breaking, or it may also be a simple, previously unobserved result, that moment of completion is like a light-bulb moment for the creator, sparked by the magic of creativity.

The theorem or its ramifications will only be known tomorrow, or possibly even after a month, but the creator has already had the privilege of knowing them in the present. Not only one’s result, but even that of a colleague who may have shared their work with you or maybe you are the referee of the result, both instances give one the same feeling as if embracing all of its infinite possibilities.

There are several interesting anecdotes about such moments. Once, a scientist walked away from his workspace and sheltered under the vast expanse of the peaceful skies with his lover. This romantic setting prompted her to point at the distant stars and remark— see how beautiful those stars are. He promptly responded— at this moment, the only person in the world who knows why stars shine is the person on whose shoulders you are resting and admiring them. He had just made this discovery moments ago in his workspace, which even then was a well-guarded secret for the rest of the world.

Translated from Assamese by Manjil P. Saikia

● Introduction to Elliptic Curves and Modular Forms – Neal Koblitz

● Rational Points on Elliptic Curves – Joseph H. Silverman, and John T. Tate

● Web of Modularity : Arithmetic of the Coefficients of Modular Forms and q-series – Ken Ono

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● An Introduction to q-analysis – Warren P. Johnson

● An Invitation to the Rogers-Ramanujan Identities – Andrew V. Sills

● Number Theory in the Spirit of Ramanujan – Bruce C. Berndt

● Ramanujan’s Lost Notebook (Part I, Part II, Part III, Part IV, Part V) – George E. Andrews, and Bruce C. Berndt

● Ramanujan’s Notebooks (Part I, Part II, Part III, Part IV, Part V) – Bruce C. Berndt

● The Theory of Partitions – George E. Andrews

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● Abstract Algebra – David E. Dummit, and Richard M. Foote

● Algebraic Graph Theory – Chris Godsil, and Gordon Royle

● Number Fields – Daniel A. Marcus

● Concrete Mathematics : A Foundation for Computer Science – Ronald L. Graham, Donald E. Knuth, and Oren Patashnik

● Enumerative Combinatorics (Volume 1, Volume 2) – Richard P. Stanley

● Proofs and Confirmations : The Story of the Alternating Sign Matrix Conjecture – David M. Bressoud

● Proofs That Really Count : The Art of Combinatorial Proof – Arthur T. Benjamin, and Jennifer J. Quinn

● The Art of Computer Programming (Volume 1, Volume 2, Volume 3, Volume 4A) – Donald J. Knuth

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● An Introduction to Sieve Methods and Their Applications – Alina Carmen Cojocaru, and M. Ram Murty

● Multiplicative Number Theory – Harold Davenport

● Opera De Cribro – John Friedlander, and Henryk Iwaniec

● Prime Numbers : A Computational Perspective – Richard Crandall, and Carl Pomerance

● The Distribution of Prime Numbers – Dimitris Koukoulopoulos

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● Number Theory in the Spirit of Liouville – Kenneth S. Williams

● An Exploration of Combinatorial Interpretations for Fibonomial Coefficients – Richard Shapley (Bachelor of Science Thesis)

● Primes with a missing digit: distribution in arithmetic progressions and sieve-theoretic applications – Kunjakanan Nath

● Topics on Alternating Sign Matrices and Aztec Rectangles – Manjil P. Saikia

● Prof. Nayandeep Deka Baruah [wiki] (Additive number theory)

● Prof. Rupam Barman (Algebraic number theory)

● Prof. Anupam Saikia [wiki] (Algebraic number theory)

● Dr. Manjil P. Saikia [wiki] (Combinatorics)

● Dr. Kunjakanan Nath (Analytic number theory)

● Ayan Nath (Algebra, Analytic number theory)

● More »