Alexander Grothendieck, who has died aged 86, was the leading figure in reshaping the contours of mathematics in the second half of the 20th century. Born in Germany but brought up in France, he established his international reputation with a paper published in Japan in the Tohoku Mathematical Journal (1957). It came to be known just as the Tohoku paper, and put forward a radically new application of algebraic techniques to the investigation of the broadest categories of mathematical structure.
The core of his work concerned the connection between space and structure, and he set himself enormous research programmes intended to reveal the underlying connections between whole areas of mathematics. His ambition was to unite algebra and geometry, arithmetic and topology in the most general terms, and in so doing to bring together concepts of symmetry and geometry.
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