Few men in modern mathematics have had as great an impact as the Norwegian Niels Henrik Abel (1802 29), whose discoveries paved the way for several new branches of nineteenth-century mathematics. Tragically, Abel's short life was dominated by poverty and his scientific achievements were not fully recognised until after his death. This work, written by Carl Anton Bjerknes (1825 1903), was the first full biography of Abel. Originally published in 1880 and translated into French in 1885, it became a valuable resource for later Abel biographers and scholars of the history of mathematics. With...

The mathematician Charles Babbage (1791 1871) was one of the most original thinkers of the nineteenth century. In this influential 1830 publication, he criticises the continued failure of government to support science and scientists. In addition, he identifies the weaknesses of the then existing scientific societies, saving his most caustic remarks for the Royal Society. Asserting that the societies were operated largely by small groups of amateurs possessing only superficial interest and knowledge of science, Babbage explores the importance of the relationships between science, technology...

A Huguenot exile in England, the French mathematician Abraham de Moivre (1667 1754) formed friendships with such luminaries as Edmond Halley and Isaac Newton. Making his living from private tuition, he became a fellow of the Royal Society in 1697 and published papers on a range of topics. Probability theory had been pioneered by Pascal, Fermat and Huygens, with further development by the Bernoullis. Originally published in 1718, The Doctrine of Chances was the first English textbook on the new science and so influential that for a time the whole subject was known by the title of the work....

Great mathematicians write for the future and Georg Friedrich Bernhard Riemann (1826 66) was one of the greatest mathematicians of all time. Edited by Heinrich Martin Weber, with assistance from Richard Dedekind, this edition of his collected works in German first appeared in 1876. Riemann's interests ranged from pure mathematics to mathematical physics. He wrote a short paper on number theory which provided the key to the prime number theorem, and his zeta hypothesis has given mathematicians the most famous of today's unsolved problems. Moreover, his famous 1854 lecture 'On the hypotheses...

The Greek astronomer Aristarchus of Samos was active in the third century BCE, more than a thousand years before Copernicus presented his model of a heliocentric solar system. It was Aristarchus, however, who first suggested - in a work that is now lost - that the planets revolve around the sun. Edited by Sir Thomas Little Heath (1861 1940), this 1913 publication contains the ancient astronomer's only surviving treatise, which does not propound the heliocentric hypothesis. The Greek text is based principally on the tenth-century manuscript Vaticanus Graecus 204. Heath also provides a...

By the end of the eighteenth century, British mathematics had been stuck in a rut for a hundred years. Calculus was still taught in the style of Newton, with no recognition of the great advances made in continental Europe. The examination system at Cambridge even mandated the use of Newtonian notation. As discontented undergraduates, Charles Babbage (1791 1871) and John Herschel (1792 1871) formed the Analytical Society in 1811. The group, including William Whewell and George Peacock, sought to promote the new continental mathematics. Babbage's preface to the present work, first published in...

In 1844, the Prussian schoolmaster Hermann Grassmann (1809 77) published Die Lineale Ausdehnungslehre (also reissued in the Cambridge Library Collection). This revolutionary work anticipated the modern theory of vector spaces and exterior algebras. It was little understood at the time and the few sympathetic mathematicians, rather than trying harder to comprehend it, urged Grassmann to write an extended version of his theories. The present work is that version, first published in 1862. However, this also proved too far ahead of its time and Grassmann turned to historical linguistics, in which...

One of the great algebraists of the nineteenth century, Marie Ennemond Camille Jordan (1838 1922) became known for his work on matrices, Galois theory and group theory. However, his most profound effect on how we see mathematics came through his Cours d'analyse, which appeared in three editions. Reissued here is the first edition, which was published in three volumes between 1882 and 1887. While highly influential in its time, it now appears to us a transitional work between the partially rigorous 'epsilon delta' calculus of Cauchy and his successors, and the new 'real number' analysis of...

In his autobiography, Charles Darwin wrote of his time at Cambridge: 'I attempted mathematics but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.' First published in 1795 and reissued here in its 1815 sixth edition, The Elements of Algebra by James Wood (1760 1839) was...

From the end of antiquity to the middle of the nineteenth century it was generally believed that Aristotle had said all that there was to say concerning the rules of logic and inference. One of the ablest British mathematicians of his age, Augustus De Morgan (1806-71) played an important role in overturning that assumption with the publication of this book in 1847. He attempts to do several things with what we now see as varying degrees of success. The first is to treat logic as a branch of mathematics, more specifically as algebra. Here his contributions include his laws of complementation...