Archive for the ‘Problem Section’ category
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 of the twentieth century, experimental [...]
A geeky party trick
You are at a friend’s place having good time together, watching TV, maybe playing classic video games, or whatever you are in mood for. Soon it all gets pretty boring. You are in mood for some fun and you want to have a bet with your friend over a game. Imagine a 2-player [...]
Ramanujan Magic Square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2. The term "magic square" [...]
Hilbert's Axioms of Geometry
David Hilbert was a German mathematician who is known for his problem set that he proposed in one of the first ICMs, that have kept mathematicians busy for the last century. Hilbert is also known for his axiomatisation of the Euclidean geometry with his set of 20 axioms. These axioms try to do away [...]
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 pertaining more generally to [...]
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 during his lifetime. This is the second problem discussed under the Millennium Problem series.] Since the days [...]
Number magic
Recently I found all the 22 existing ways to put 0 to 9 in the equation of a product such that each number occurs exactly once. And here they are: 5694×3=17082 6819×3=20457 6918×3=20754 8169×3=24507 9168×3=27504 3907×4=15628 7039×4=28156 9127×4=36508 5817×6=34902 3094×7=21658 4093×7=28651 9304×7=65128 9403×7=65821 594×27=16038 495×36=17820 402×39=15678 396×45=17820 715×46=32890 367×52=19084 297×54=16038 927×63=58401 345×78=26910 Also, [...]
A closer look into a well-known quotient ring
The ring is quite a well- known ring in Algebra. Further, being a principal ideal domain, every ideal of is generated by a single element say and so can be taken in the form We now consider the quotient ring and try to look for a precise way of representing the [...]
The Millennium Problems
Recently Prof. Malay Dutta (Department of Computer Science and Engineering, Tezpur University) gave a talk on the Millennium Problems in mathematics. We present to you a series of 8 articles written by Prof. Dutta where he speaks about the problems in detail. This is the introductory post and will be followed very soon by [...]
Indian National Mathematical Olympiad 2012
The Indian National Mathematical Olympiad 2012 was held on 5th February, 2012 at various centres all over the country. The North East had three centres at Guwahati, Shillong and Agartala. The questions are given below: 1. Let be a quadrilateral inscribed in a circle. Suppose and subtends degrees at center of circle . Find [...]
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