**History of Mathematics**

Volume: 35;
2009;
195 pp;
Hardcover

MSC: Primary 60;
Secondary 01

**Print ISBN: 978-0-8218-4899-9
Product Code: HMATH/35**

List Price: $56.00

Individual Member Price: $44.80

#### Supplemental Materials

# The Life and Times of the Central Limit Theorem: Second Edition

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*William J. Adams*

A co-publication of the AMS and the London Mathematical Society

*The study of any topic becomes more meaningful
if one also studies the historical development that resulted in the
final theorem. …This is an excellent book on mathematics in the
making.*

—Philip Peak,

*I find the book very interesting. It contains
valuable information and useful references. It can be recommended not
only to historians of science and mathematics but also to students of
probability and statistics.*

—Wei-Ching Chang,

*In the months since I wrote…I have read it
from cover to cover at least once and perused it here and there a
number of times. I still find it a very interesting and worthwhile
contribution to the history of probability and statistics.*

—Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975

The name *Central Limit Theorem* covers a wide variety of results
involving the determination of necessary and sufficient conditions under
which sums of independent random variables, suitably standardized, have
cumulative distribution functions close to the Gaussian distribution. As
the name Central Limit Theorem suggests, it is a centerpiece of
probability theory which also carries over to statistics.

Part One of *The Life and Times of the Central Limit Theorem,
Second Edition* traces its fascinating history from seeds sown by Jacob
Bernoulli to use of integrals of \(\exp (x^2)\) as an approximation
tool, the development of the theory of errors of observation, problems in
mathematical astronomy, the emergence of the hypothesis of elementary
errors, the fundamental work of Laplace, and the emergence of an abstract
Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov.
This closes the classical period of the life of the Central Limit Theorem,
1713–1901.

The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920–1937), in particular through contributions of Lindeberg, Cramér, Lévy, and Feller.

The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.

#### Table of Contents

# Table of Contents

## The Life and Times of the Central Limit Theorem: Second Edition

#### Readership

Undergraduate students, graduate students and research mathematicians interested in the history of mathematics, especially of probability theory.

#### Reviews

[The second edition] is a refinement of its first edition...interesting to read.

-- Fuchang Gao, Mathematical Reviews