Adrian Rice

Mathematics unbound : the evolution of an international mathematical research community, 1800-1945

The evolution of an international mathematical research community, 1800-1945: An overview and an agenda by K. H. Parshall and A. C. Rice The end of dominance: The diffusion of French mathematics elsewhere, 1820-1870 by I. Grattan-Guinness Spanish initiatives to bring mathematics in Spain into the international mainstream by E. Ausejo and M. Hormigon International mathematical contributions to British scientific journals, 1800-1900 by S. E. Despeaux International participation in Liouvilles \textit{Journal de mathematiques pures et appliquees} by J. Lutzen The effects of war on Frances international role in mathematics, 1870-1914 by H. Gispert Charles Hermite and German mathematics in France by T. Archibald Gosta Mittag-Leffler and the foundation and administration of \textit{Acta Mathematica} by J. E. Barrow-Green An episode in the evolution of a mathematical community: The case of Cesare Arzela at Bologna by L. Martini The first international mathematical community: The \textit{Circolo matematico di Palermo} by A. Brigaglia Languages for mathematics and the language of mathematics in a world of nations by J. J. Gray The emergence of the Japanese mathematical community in the modern western style, 1855-1945 by C. Sasaki Internationalizing mathematics east and west: Individuals and institutions in the emergence of a modern mathematical community in China by J. W. Dauben Chinese-U. S. mathematical relations, 1859-1949 by Y. Xu American initiatives toward internationalization: The case of Leonard Dickson by D. D. Fenster The effects of Nazi rule on the international participation of German mathematicians: An overview and two case studies by R. Siegmund-Schultze War, refugees, and the creation of an international mathematical community by S. L. Segal The formation of the international mathematical union by O. Lehto Index.

“Shutting up like a telescope”: Lewis Carroll's “Curious” Condensation Method for Evaluating Determinants

Adrian Rice (arice4@rmc.edu) received a B.Sc. in mathematics from University College London in 1992 and a Ph.D. in the history of mathematics from Middlesex University in 1997 for a dissertation on Augustus De Morgan. He is currently an associate professor of mathematics at Randolph-Macon College in Ashland, Virginia, where his research focuses on 19thand early 20th-century British mathematics. His recent publications include Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945, edited with Karen Hunger Parshall, and The London Mathematical Society Book of Presidents, 1865–1965, written with Susan Oakes and Alan Pears.

Why Ellipses Are Not Elliptic Curves

Summary Elliptic curves are a fascinating area of algebraic geometry with important connections to number theory, topology, and complex analysis. As their current ubiquity in mathematics suggests, elliptic curves have a long and fascinating history stretching back many centuries. This paper presents a survey of key points in their development, via elliptic integrals and functions, closing with an explanation of why no elliptically-shaped planar curved line may ever be called an elliptic curve.

The rise of British analysis in the early 20th century: the role of G.H. Hardy and the London Mathematical Society

It has often been observed that the early years of the 20th century witnessed a significant and noticeable rise in both the quantity and quality of British analysis. Invariably in these accounts, the name of G.H. Hardy (1877–1947) features most prominently as the driving force behind this development. But how accurate is this interpretation? This paper attempts to reevaluate Hardys influence on the British mathematical research community and its analysis during the early 20th century, with particular reference to his relationship with the London Mathematical Society.

In Search of the “Birthday” of Elliptic Functions

ConclusionIs it possible to answer the questionWhat is the “birthday” of elliptic functions? Yes, but far from uniquely. But does the overabundance of possible answers occasioned by the inherent näivety of the question mean that such lines of inquiry are pointless for the historian? Can questions regarding the temporal origins of mathematical areas and the research to which they lead ever be useful or instructive?

The early mathematical education of Ada Lovelace

Ada, Countess of Lovelace, is remembered for a paper published in 1843, which translated and considerably extended an article about the unbuilt Analytical Engine, a general-purpose computer designed by the mathematician and inventor Charles Babbage. Her substantial appendices, nearly twice the length of the original work, contain an account of the principles of the machine, along with a table often described as ‘the first computer program’. In this paper we look at Lovelaces education before 1840, which encompassed older traditions of practical geometry; newer textbooks influenced by continental approaches; wide reading; and a fascination with machinery. We also challenge judgements by Dorothy Stein and by Doron Swade of Lovelaces mathematical knowledge and skills before 1840, which have impacted later scholarly and popular discourse.

Partnership, Partition, and Proof: The Path to the Hardy–Ramanujan Partition Formula

Abstract The year 2018 marks 100 years since the publication of one of the most startling results in the history of mathematics: Hardy and Ramanujan’s asymptotic formula for the partition function. To celebrate the centenary, this paper looks at the creation of their remarkable theorem: where it came from, how it was proved, and how the assistance of a third contributor helped to influence its ultimate form.

Commutativity and collinearity: a historical case study of the interconnection of mathematical ideas. Part I

This two-part paper investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated mathematical work of two late third-century mathematicians, a link that went unnoticed for well over 1500 years. In this, the first installment of the paper, we examine the initial chain of mathematical events that would ultimately lead to the discovery of this remarkable link between two seemingly distinct areas of mathematics, encompassing contributions by a variety of mathematicians, from the most distinguished to the relatively unknown.

James Clerk Maxwell. Perspectives on his life and work, by Raymond Flood, Mark McCartney and Andrew Whitaker (eds)

Although the name of Maxwell is as inextricably linked with the history of science as those of Newton and Einstein, to the general public his name evokes less immediate recognition than his equally illustrious peers. Even among most practicing physicists, the sole reason for their familiarity with his name is usually the four ‘Maxwell’s equations’ of electromagnetism. This is of course no mean claim to fame. Indeed, in the words of Richard Feynman:

Trigonometry without Triangles

S uppose you know everything there is to know about calculus: You understand the Fundamental Theorem of Calculus, the Chain Rule, the Mean Value Theorem, implicit differentiation, the whole lot. But mysteriously, every trace of trigonometry has been erased from your memory. You’re in luck though, because it is a little-known fact that with the clever use of calculus you can re-create the whole subject of trigonometry from the formula for the arc length of a circle, without the use of any triangles whatsoever—particularly ironic, considering that the word “trigonometry” literally means “triangle measuring”! Another fact that deserves to be better known is that all trigonometric functions are ultimately based on the sine function: