Millenium Problems - Gonit Sora

Gonit Sora

Millenium Problems

A collection of 8 posts

Fermat's Last Theorem and a Failure of Unique Factorization

Fermat's Last Theorem and a Failure of Unique Factorization

A webinar on number theory was held on 12 July 2020 by Gonit Sora in association with Lumding College. The webinar was delivered by Dr. Debopam Chakraborty. The slides of the talk can be downloaded here. The full video of the talk is available in our YouTube channel as well

The Congruent Number Problem and Elliptic Curves

The Congruent Number Problem and Elliptic Curves

A webinar on number theory was held on 10 July 2020 by Gonit Sora in association with IQAC, Lakhimpur Girls’ College. The webinar was delivered by Prof. Anupam Saikia. The slides of the talk can be downloaded here. The full video of the talk is available in our YouTube channel

Anti-Dühring: 1+2+3+4+…

Anti-Dühring: 1+2+3+4+…

Anti-Dühring is a book by Friedrich Engels published in 1878. It is a defense of Marxism from Eugen Dühring’s vision of socialism. It contains interesting scientific references as well, which is the reason I am putting a spotlight on it. First of all, it would be polite to explain:

Birch Swinnerton-Dyer conjecture

Birch and Swinnerton Dyer Conjecture

Birch Swinnerton-Dyer conjecture

This is a conjecture regarding the number of rational points in elliptic curves i.e. curves in two-dimensional plane with the equation y2 = x3 + a x + b for some whole numbers a,b. In the early 1960’s, the British mathematicians Brian Birch and Peter Swinnerton-Dyer started to use computers

Quantum Yang-Mills Theory

Millenium Problems

Quantum Yang-Mills Theory

[Editor: This is next part in our series of articles on the Millennium Problems.] In classical physics, there were two kinds of entities, material particles governed by Newtonian mechanics and fields governed by appropriate field equations eg Maxwell’s equations for electromagnetic field. However just before and after the beginning

Hodge Conjecture

Hodge Conjecture

Hodge Conjecture

[Editor: This is the next part in our series on the Millennium Problems. William Vallance Douglas Hodge FRS (17 June 1903 – 7 July 1975) was a Scottish mathematician, specifically a geometer. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and

Poincare Conjecture

Gregory Perelman

Poincare Conjecture

[Editor’s Note: Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed

Riemann’s Hypothesis

Bernhard Riemann

Riemann’s Hypothesis

[Editor: This is the second post in a series about the Millenium Problems. This post is about the Riemann Hypothesis, probably the single most fascinating unsolved problem in all of mathematics. This hypothesis was first proposed by the mathematician Bernhard Riemann. Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20,