Freeman Dyson, writes in the introduction to Yuri Manin’s book, Mathematics as Metaphor.

Mathematics as Metaphor […] means that the deepest

concepts in mathematics are those which link one world of ideas with another. In the

seventeenth century, Descartes linked the disparate worlds of algebra and geometry

with his concept of coordinates, and Newton linked the worlds of geometry and

dynamics with his concept of ﬂuxions, nowadays called calculus. In the nineteenth

century, Boole linked the worlds of logic and algebra with his concept of symbolic

logic, and Riemann linked the worlds of geometry and analysis with his concept

of Riemann surfaces. Coordinates, ﬂuxions, symbolic logic and Riemann surfaces

are all metaphors, extending the meanings of words from familiar to unfamiliar

contexts. Manin sees the future of mathematics as an exploration of metaphors

that are already visible but not yet understood. The deepest such metaphor is the

similarity in structure of ideas between number theory and physics. In both ﬁelds

he sees tantalizing glimpses of parallel concepts, symmetries linking the continuous

with the discrete. He looks forward to a uniﬁcation which he calls the quantization

of mathematics.

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