This is the story of American mathematics during the past century. It contains articles and excerpts from a century of the American Mathematical Monthly, giving the reader an opportunity to skim all one hundred volumes of this popular mathematics magazine without actually opening them. It samples mathematics year by year and decade by decade. The reader can glimpse the mathematical community at the turn of the century, the controversy about Einstein and relativity, the debates about formalism in logic, the immigration of mathematicians from Europe, and the frantic effort to organize as the war began. More recent articles deal with the advent of computers and the changes they brought, and with some of the triumphs of modern research.

Includes section "Recent publications."

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics. Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.

Founded in 1894, The American Mathematical Monthly is one of the world's premier journals of mathematics. With articles covering a wide range of topics in pure and applied math, the Monthly is an indispensable resource for mathematicians at all levels. This authoritative publication is a must-read for anyone interested in the latest developments in mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...W. GREENWOOD. B. A. (Oxon). Professor of Mathematics and Astronomy in McKendree College, Lebanon, 111., and W. W. LANDIS, Dickinson College. Carlisle, Pa. AB cuts any one of the sides of the triangle produced, say PQ, in X. Determine the point harmonically separated from X by P and Q and call this point r. The line joining R and Y cuts AB in the required point G. For the sheaf CX, CP, CY, GR being harmonic it is cut by any line parallel to CXin four harmonic points one of which is at infinity, therefore the remaining three points intercept equal segments. Also solved by F. D. Posey, San Mateo, Cal.; R. A. Wells, Hellenic. Neb.; and G. B. M. Zerr, Parsons, W. Va. CALCULUS. 176. Proposed by B. F. FINKEL. A. M.. M. Sc, 204 St. Marks Square. Philadelphia. Pa. Show by any method, Riemann's excepted, that / 6 e-Icos 2ffr=41 (-)e-'2cos&/2. Bemark by S. A. C0BE7, Hiteman. Iowa. Solved by Dr. G. B. M. Zerr in his paper entitled On the Evaluation of Certain Definite Integrals in the Monthly of March, 1904, page 57, 2. 177. Proposed by 0. W. ANTHONY Heao of Mathematical Department, DeWitt Clinton High School, New York City. Find the volume of the minimum cone which can be circumscribed about a hemisphere. Solution by A. H. HOLMES. Brunswick, Maine, and S. A. COBEY, Hiteman, Iowa. Let sr=altitude of cone, r=radius of sphere, J =radius of base of cone, 0=angle between x and the line joining vertex and circumference of base of cone. Then, from similar triangles, sr=r/sin0, R=r/m&0. Volume V of cone is, V=i: Rix/S=-r/3eoH10sm0. MECHANICS. 167. Proposed by EDWIN S. CRAWLEY. Ph.D., Professor ol Mathematics in the University oi Pennsylvania. An anchor ring or torus is produced by the revolution of a circle of radius r, ...

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