The simplicities of natural laws arise through the complexities of the languages we use for their expression.

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious.

The Unreasonable Effectiveness of Mathematics, *Communications in Pure and Applied Mathematics* **13** (1960)

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

The Unreasonable Effectiveness of Mathematics, *Communications in Pure and Applied Mathematics* **13** (1960)

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift, which we neither understand nor deserve.

The Unreasonable Effectiveness of Mathematics, *Communications in Pure and Applied Mathematics* **13** (1960)

JOC/EFR February 2006

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