The Beginnings and Evolution of Algebra

The elements of algebra were known to the ancient Mesopotamians at least 4000 years ago. Today algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? How did its constituent ideas and concepts arise, and how have they changed over the years? These are the questions that the authors address in this work. The authors challenge the existing view that the development of algebra was driven by the investigation of determinate equations and in particular their solution by radicals. In short they claim that the study of indeterminate equations was no less important. Historians of mathematics, as well as working algebraists who want to look into the history of their subject, will find this an illuminating read.

Isabella Bashmakova, renowned authority on Diophantine analysis, obtained her training in mathematics at Moscow State University and has spent here professional career teaching there in the Faculty of Mechanics and Mathematics. She obtained both her PhD in Physics and Mathematics and the Degree of Doctor of Science from Moscow State University. She has written many books in the Russian, including "History of Diophantine Analysis from Diophantus to Fermat" (in collaboration with E.I. Slavutin) and "Lectures on the History of Mathematics in Ancient Greece". An English translation of her book "Diophantus and Diophantine Equations" was published by the Mathematical Association of America in 1997. Professor Bashmakova has been the recipient of numerous honorary degrees from the USSR Academy of Sciences and the Ministry of Higher Education..

Galina Smirnova was born in Russia, and studied at Moscow State University where she received her PhD in mathematics under the supervision of Isabella Bashmakova. She has taught at Moscow State University since 1987. Her research includes the history of algebra, number theory, and differential geometry. She has made significant contributions to the study of the history of algebra in Western Europe in the 16th century.