An Early History of Recursive Functions and Computability traces the development of recursive functions from their origins in the late nineteenth century, when recursion was first used as a method of defining simple arithmetic functions, up to the mid-1930's, when the class of general recursive functions was introduced by Godel, formalized by Kleene and used by Church in his thesis. The book explains how the proposal given in Church's 1936 paper, now known as Church's thesis, first arose and concludes with the consideration of another class of functions, the Turing computable functions, that were specially created to be equivalent to the class of effectively calculable functions. The book includes previously unpublished letters between the author and many of the key historical figures.

An Early History of Recursive Functions and Computability from Godel to Turing

Science & Math

Adams, Rod

Mathematics

Docent Press

Mina Spiegel Rees (1902-1997) was an American mathematician who had a significant impact on mathematical research and eduction in the United States. She received a PhD in mathematics at the University of Chicago, writing under the direction of L.E. Dickson. She was the head of the Mathematical Sciences Division of the Office of Naval Research during World War II and was the Dean of Graduate Studies at CUNY after the war. This book covers in depth Rees' many contributions to the US mathematical scene.

In Service to Mathematics: The Life and Work of Mina Rees

Biographies & Memoirs

Shell-Gellasch, Amy

Community & Culture

<p>This bibliography of Raymond Clare Archibald (7 October 1875-26 July 1955) has been compiled from 1) the Publications list in the Raymond Clare Archibald fonds at Mount Allison University, 2) the curriculum vitae of R. C. Archibald in the George Sarton Archives at Harvard University, 3) the bibliography in Sarton's obituary in Osiris 4) on-line resources and 5) the author's own complete holding of the two journals to which R. C. Archibald made significant contributions, Mathematical Tables and Other Aids to Computation and Scripta Mathematica.</p>

Bibliography of Raymond Clare Archibald

Reference

Guthery, Scott B.

Catalogs & Directories

Calculating Curves is a book about a beautiful but forgotten paper of Thomas Hakon Gronwall. Gronwall was a Swedish mathematician and an American immigrant who published over 80 papers in pure and applied mathematics.  He was a practicing civil engineer in Europe and the United States as well as a professor at Princeton University. The paper considered in  the book was the first work to produce a necessary and sufficient condition for the representability problem of a graphical problem-solving construct called an alignment nomogram.  The book includes a biography of Gronwall, a translation of the paper with an extensive commentary and a complete bibliography of Gronwall's work.

Calculating Curves: The Mathematics, History, and Aesthetic Appeal of T. H. Gronwall's Nomographic Work

Gronwall, Thomas Hakon

Doerfler, Ron

Gluchoff, Alan

Hamburg, Paul

Guthery,Scott

Research

From the 1890s to the 1920s American mathematical research grew substantially in quantity and quality. However, few mathematicians were able to pursue research exclusively; most mathematicians, whether active researchers or not, were employed as teachers by colleges and universities. Their degree of interest in the teaching role varied greatly: while some shunned instructional issues, a few mathematicians became deeply involved not only in teaching undergraduates but in attempting to influence mathematics education in the secondary and even the elementary schools. This book seeks to understand these divisions among the mathematicians regarding pedagogy, to explore alliances and conflicts between mathematicians and other educators, and to explain the resulting effects on educational institutions and on the mathematicians themselves.

American Mathematicians as Educators, 1893--1923: Historical Roots of the "Math Wars"

Roberts, David Lindsay

The book begins with a discussion of Benjamin Peirce’s linear associative algebra and then considers this and other early influences on the logic of is son, C. S. Peirce. A discussion of the early algebraic logicians such as Boole, Jevons and De Morgan follows, culminating in a detailed analysis of C. S. Peirce’s seminal paper “Description of a Notation for the Logic of Relatives.” His further developments of the 1880s, including quantificational logic are also traced. At the end of his life, Peirce looked to his graphical logic system - the existential graphs - to provide the logic of the future.

Relations between Logic and Mathematics in the Work of Benjamin and Charles S. Peirce

Walsh, Alison

In 1881 the American philosopher Charles S. Peirce published a remarkable paper in The American Journal of Mathematics called “On the Logic of Number.” Peirce’s paper marked a watershed in nineteenth century mathematics, providing the first successful axiom system for the natural numbers. Awareness that Peirce’s axiom system exists has been gradually increasing but the conventional wisdom among mathematicians is still that the first satisfactory axiom systems were those of Dedekind and Peano. The book analyzes Peirce's paper in depth, placing it in the context of contemporary work, and provides a proof of the equivalence of the Peirce and Dedekind axioms for the natural numbers.

Charles S. Peirce on the Logic of Number

Shields, Paul

The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number? What, in particular, is a real number? What is the true nature of continuity itself? Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities? Is the concept of an infinitesimally small quantity even logically coherent? What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line? The main question to be addressed, of course, is whether mathematical continuity exists at all.

The Continuity Debate: Dedekind, Cantor, du Bois-Reymond, and Peirce on Continuity and Infinitesimals

Buckley, Benjamin Lee

<p>Peirce’s logic of continuity is explored from a double perspective: (i) Peirce’s original understanding of the continuum, alternative to Cantor’s analytical Real line, (ii) Peirce’s original construction of a topological logic –- the existential graphs -– alternative to the algebraic presentation of propositional and first-order calculi. Peirce’s general architectonics, oriented to back-and-forth hierarchical crossings between the global and the local, is reflected with great care both in the continuum and the existential graphs.</p>

Peirce's Logic of Continuity: A Conceptual and Mathematical Approach

Zalamea, Fernando

Perfect Mechanics captures the excitement of Georgian "big science" and the starring roles played by London instrument makers in the scientific expeditions to measure the shape of the earth, to find and map unknown lands in the Pacific, and to explore the heavens. Yet these indispensible practitioners of "mixed mathematics," recognized and honored by the Royal Society through fellowship and the awarding of the Copley Medal, became increasingly marginalized by the gentlemanly FRS after 1800 and the essential tensions between commerce and science, mechanical and craft production, and social classes brought an abrupt halt to this dynamic and inventive period.

Perfect Mechanics: Instrument Makers at the Royal Society of London in the Eighteenth Century

Sorrenson, Richard

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