Surreal Numbers

D.E. Knuth

Addison-Wesley 1974
A book review by Danny Yee © 2022
A lightly dramatised introduction to surreal numbers, Surreal Numbers involves characters Alice and Bill on an idealised desert island, where they uncover a stone tablet with an inscription that begins "In the beginning, everything was void, and J.H.W.H. Conway began to create numbers..." and gives the basic rules for Conway numbers. Prompted by this, they progressively construct a theory of surreal numbers. This involves extending ideas and replacing or abandoning them, getting stuck, flashes of inspiration, backtracking and rethinking, and so forth.

This could be used as an introduction to surreal numbers, but though complete enough it is not at all systematic. It is, rather, an attempt to give a feel for how mathematical work is actually done. Knuth writes "my primary aim is not really to teach Conway's theory, it is to teach how one might go about developing such a theory". (Though few mathematicians manage quite as much sand and sex in their collaborations.)

August 2022

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%T Surreal Numbers
%A Knuth, D.E.
%I Addison-Wesley
%D 1974
%O paperback
%G ISBN-13 9780201038125
%P 119pp