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.

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’.

The one person who comes closest to the legacy of Hermann Weyl was Freeman Dyson, who contributed enormously to both Physics and Mathematics. His books and talks are testaments to his prolificity in writing widely on the world at large and on science and mathematics in particular. To name a few of his books, he has (talked and) written on ‘Bombs and Poetry’, ‘Imagined Worlds’, ‘Origins of Life’ and ‘Birds and Frogs’. Remarkably, Dyson contributed handsomely to what is termed ‘pure mathematics’. One would expect a physicist-mathematician to interest himself mainly in problems of an ‘applied’ nature. Here, we take a necessarily brief peek into some of his ‘purely mathematical’ work. The suggested read-ing at the end can be referred to for more details.