Almagest

This article draws on the debates over evolution in the United States to explore efforts to define and defend the boundaries of science. When the first organized opposition to evolution appeared in the early 1920s, antievolutionists insisted that evolution should not be taught because its speculative nature placed it outside the boundaries of science. By the last quarter of the century, however, they had largely abandoned that position in favor of arguing that creationism and intelligent design should themselves be regarded as science. This dramatic shift reflected a major reinterpretation of the U.S. Constitution, especially the First Amendment, which states, "Congress shall make no law respecting an establishment of religion". Until after World War II the U.S. Supreme Court limited the application of this provision to the federal government. That practice began to change in the late 1940s, when the Court began applying First Amendment restrictions against the establishment of religion to the individual states and public school districts by way of the 14th Amendment; by the early 1960s it was asserting a goal of "neutrality" with regard to religion in public education. Because teaching "bad science" does not violate the Constitution, opponents of creationism have embraced the tactic of demonstrating that creation-science and Intelligent Design are essentially religious doctrines - and thus that teaching them in public schools is unconstitutional.

Euler’s Vollständige Anleitung zur Algebra (1770) is the prototype of a successful textbook on elementary algebra. The selection of problems by Euler displays a great familiarity with the typical recreational and practical problems of Renaissance and 16th-century algebra books. A detailed study into the sources of Euler revealed that he copied most of his problems from Christoff Rudolff’s Coss, which was first published in 1525 and reissued in 1553 by Michael Stifel. Why would Euler found his popular textbook on algebra on a book published 250 years earlier? Part of the motivation could be sentimental. Euler was taught mathematics by his father using Stifel’s edition of the Coss, and the young Euler spent several years studying the problems from the book. However, we propose an explanation based on the evolving rhetorical function of problems in algebra textbooks since the first printed book on algebra by Pacioli (1494). We discern six stages in the evolution from abbacus problem solving to algebraic theory. The first theory emerged through the extraction of general principles from the practice of problem solving. The algebra textbooks of the 18th century close a circle of continuous rhetorical development by using problems for practicing general principles and applying the algebraic language. Euler’s Algebra is a prime example of the new rhetoric of problems still prominent in today’s textbooks.

In the light of recent works on the use of the history of mathematics in education, this article offers an analysis of the theoretical issues that arise in such studies. After the presentation of some intrinsic difficulties of a good definition of the different fields involved (a discipline, its didactic and its history), some new elements for a didactical analysis (double field hypothesis, double field paradox and its handling) are proposed. Applied on a few examples, these concepts are aimed at being part of a new framework for empirical studies on the use of history of mathematics in education.

In this paper, we follow the surprising trajectory of Kiril Popoff (1880-1966), a Bulgarian astronomer and mathematician who specialized in ballistics during the Great War and he was invited in the 1920s to teach a course on the subject at Paris University. To complete the picture, we also present the social and political context of Bulgaria at the beginning of 20th century.

This paper focuses on a specific textbook, published in 1943, that was written by a Brazilian mining engineer educated in France - Alberto Betim Paes Leme, aiming to investigate its intellectual roots, structure and purposes. To discuss these issues I shall make use of some aspects of the theoretical framework put forward by Ludwik Fleck (1896-1961), especially the Denkstil (thought-style) and Denkkollektiv (collective of thought). The textbook under scrutiny here was a substantial general manual of geology, with extensive information about Brazil, and a representative bibliographical review, which comprised both national and international texts. Through the textbook, the author intended to address a wide educated public (Fleck’s exoteric circle), but also people illiterate in geosciences.