**MSRI Mathematical Circles Library**

Volume: 16;
2015;
158 pp;
Softcover

MSC: Primary 00;
Secondary 34; 68; 20; 11

**Print ISBN: 978-0-8218-9416-3
Product Code: MCL/16**

List Price: $29.00

Individual Price: $21.75

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#### Supplemental Materials

# Experimental Mathematics

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*V. I. Arnold*

Translated by Dmitry Fuchs and Mark Saul.

A co-publication of the AMS and the Mathematical Sciences Research Institute

One of the traditional ways mathematical ideas and even new areas of
mathematics are created is from experiments. One of the best-known
examples is that of the Fermat hypothesis, which was conjectured by Fermat
in his attempts to find integer solutions for the famous Fermat
equation. This hypothesis led to the creation of a whole field of
knowledge, but it was proved only after several hundred years.

This book, based on the author's lectures, presents several new
directions of mathematical research. All of these directions are based
on numerical experiments conducted by the author, which led to new
hypotheses that currently remain open, i.e., are neither proved nor
disproved. The hypotheses range from geometry and topology (statistics
of plane curves and smooth functions) to combinatorics (combinatorial
complexity and random permutations) to algebra and number theory
(continuous fractions and Galois groups). For each subject, the author
describes the problem and presents numerical results that led him to a
particular conjecture. In the majority of cases there is an indication
of how the readers can approach the formulated conjectures (at least
by conducting more numerical experiments).

Written in Arnold's unique style, the book is intended for a wide
range of mathematicians, from high school students interested in
exploring unusual areas of mathematics on their own, to college and
graduate students, to researchers interested in gaining a new,
somewhat nontraditional perspective on doing mathematics.

In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Undergraduate and graduate students and research mathematicians interested in mathematics.