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Volume 21 Issue 4 April 2016 pp 353-368 General Article
Counting, Recounting and Matching
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Volume 22 Issue 1 January 2017 pp 89-90 Think It Over
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Volume 22 Issue 5 May 2017 pp 441-454 General Article
Igor Rostislavovich Shafarevich: Ш
(may we say "shah"?) of Number Theory A magician from Moscow did stitcha maze of Galois groups and abelian varieties whichled math to progress by leaps and bounds,scale new heights and break new grounds.It behoves us to thank Igor Shafarevich!
Shafarevich was an algebraist and geometer of the highest orderwho pioneered several topics in both. The fundamental resultshe proved, as well as the conjectures he made, were beacons formathematical progress and universal landmarks. The first part Ш(pronounced “Sha”) of his surname was borrowed to denote an intriguing,elusive object called the ‘Tate–Shafarevich group’. Shafarevichheld strong views on the philosophy of mathematics andwrote at length on it. Here, we pick out some of the mathematicalgems resulting from Shafarevich-craft, so to say. In particular,we discuss his theorems and conjectures on Galois groups over Qand the role of his conjecture on curves and abelian varieties inthe proof of Mordell’s conjecture.
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Volume 22 Issue 10 October 2017 pp 943-953 General Article
Unearthing the Banach–Tarski Paradox
Greeks used the method of cutting a geometric region intopieces and recombining them cleverly to obtain areas of figureslike parallelograms. In such problems, the boundaryis ignored. However, in our discussion, we will take everypoint of space into consideration. The human endeavour tocompute lengths, areas, and volumes of irregular complicatedshapes and solids created the subject of ‘measure theory’.The paradox of the title can be informally described as follows.Consider the earth including the inside stuff. It is possibleto decompose this solid sphere into finitely many piecesand apply three-dimensional rotations to these pieces suchthat the transformed pieces can be put together to form twosolid earths! The whole magic lies in the word ‘pieces’. Thepieces turn out to be so strange that they cannot be ‘measured’.
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Volume 23 Issue 5 May 2018 pp 613-617 Research News
Robert Langlands Wins the 2018 Abel Prize
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Volume 24 Issue 9 September 2019 pp 931-932 Editorial
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Volume 25 Issue 2 February 2020 pp 163-168 Article-in-a-Box
On Tate and His Mathematics – A Glossary
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Resonance – Journal of Science Education
Current Issue
Volume 25 | Issue 5
May 2020
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Resonance – Journal of Science Education | News