Distinguished mathematician who won the Fields medal for his contribution to number theory

In 1966 the start of a new era in number theory was marked by Alan Baker, who has died aged 78, joining the department of pure mathematics at Cambridge University. With a cascade of papers, he had published solutions to a series of problems from a line of inquiry that went back to the third-century mathematician Diophantus of Alexandria. On the basis of this exceptional work, in 1970 Alan was awarded the Fields medal, one of the discipline’s highest distinctions.

The interest of Diophantus’s approach to equations lies in whether they can be solved in ways that produce only whole numbers, or integers. From school, we know Pythagoras’s theorem for right-angled triangles: if the sides are 3, 4 and 5 units long, then 32 + 42 = 52, (9 + 16 = 25), and there are other whole-number solutions, or Pythagorean triples, that can be found with squared numbers (5,12,13; 7, 24, 25; and infinitely many more). But can the equivalent be done with cubed numbers, or numbers at higher powers?

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