Thomas Harriot remains an enigma. A man of extraordinary talent and achievement, certainly comparable to that of his great contemporaries Galileo and Kepler, he remains comparatively little known, largely because most of his work went unpublished. For this, he was upbraided during his lifetime. Several of the authors of the chapters in this book quote the famous letter of his friend Sir William Lower telling Harriot that he is losing credit for his work as others are publishing ahead of him. Only a pamphlet on his explorations in North America and a posthumous work on algebra saw printed form close to his lifetime. The reasons have never been fully established. It may be that it was because his patrons, Sir Walter Ralegh and the Earl of Northumberland, were dangerous people to be associated with, often accused of heretical and radical ideas, and spending much of their lives in prison. It may also be that secrecy was necessary when so much of the work was connected with navigation and so commercially sensitive.

In addition to avoiding print, Harriot also often avoided committing his thoughts to manuscript. There are pages of calculation without explanation. While enough of Harriot's work was published in the posthumous Artis analyticae praxis to have some effect on the historical development of algebra, the true extent of his mastery has only been evident recently with Jacqueline Stedall's restoration of his ‘Treatise on equations’, which is discussed in the third chapter. Jon Pepper also writes on Harriot's mathematics, stressing his work on equations, interpolation, binary numbers, exponentials, the rectification of curves, conformality, the equiangular spiral and the area of a spherical triangle, and his application of his mathematical discoveries to physical problems such as the rainbow and the theory of impact. There is no doubt that Harriot here is in his element. It is impossible to deny greatness to anyone who could produce so many outstanding results in so many different areas decades before they were achieved by other mathematicians.

In relation to physics or natural philosophy, Matthias Schemmel and John Henry take opposite viewpoints about whether or not Harriot was an ‘English Galileo’. Schemmel highlights the parallels in that both men discovered a version of the law of free fall and worked out the kinematics of projectile motion, though using different pathways. The interesting question here is whether we can describe such completely independent development as an example of ‘convergent evolution’. Would the same physics have resulted if these individuals had never existed? Contrary to Schemmel, Henry sees Harriot as a dedicated mathematician rather than a natural philosopher. Harriot certainly had ideas on atoms, which are not based totally on mathematics, and was in some sense an alchemist, but there is less evidence for qualitative physical thinking in other areas. However, absence of evidence is not necessarily evidence of absence. Atomism was certainly a dangerous doctrine in Harriot's time because it was liable to lead to accusations of atheism. Harriot faced such accusations in his lifetime and could conceivably have avoided committing ‘philosophical’ ideas to paper when their meaning could be relatively easily misunderstood. This is a debate that is unlikely to be resolved without further evidence, even if we accept the idea that mathematics and natural philosophy can be treated as separate disciplines.

Some idea of Harriot as a natural philosopher is given in Ian Maclean's discussion of his work on ‘Combinations’, which cuts across three areas – language, natural philosophy and mathematics – and in Robert Goulding's account of his ideas on refraction in connection with his theory of the structure of matter, which touches on ‘alchemy’. Interestingly, and characteristically, Harriot here initiated a correspondence with Kepler which concealed more than it revealed. Some idea of one of the reasons for Harriot's reticence is revealed in Stephen Pumfrey's discussion of Harriot's lost Arcticon, his unpublished work on navigation. Pumfrey believes that Ralegh and Northumberland ‘were too politically compromised to advance their client properly’ (p. 141), but he also evidences the difficulties that Edward Wright experienced over his published Certaine errors in navigation, due to the intense rivalry with cartographers and other prospective authors of navigational works. Harriot, of course, knew about sea voyaging from his own experience on the expedition of 1585 to North America, and Pascal Briost gives us a detailed analysis of the technical knowledge that he acquired, and his own original solutions to the problems that arose.

Several other major issues are discussed in the course of the book. Robert Fox's Introduction provides an overall view of Harriot's life and achievements in the context of his time. In the final chapter, Mark Nicholls proposes that Ralegh's legend arose mainly from the remarkable way in which he faced his death. Larry E. Tise gives us a cautionary tale about how the ‘first edition’ of a book may not be all that it seems in respect of examining many copies of the De Bry edition of Harriot's A briefe and true report. Charles Fantazzi emphasizes the high quality of Harriot's Latin in the captions he added to this work. Finally, the artist Diccon Swan describes his experiences in painting a copy of the disputed portrait of Harriot in Oriel College, Oxford, which he thinks may well be the work of an amateur and also a self-portrait. Overall, this volume should be seen as part of an ongoing project to which we can expect many further contributions. We cannot expect a work of this kind to give a unified picture of Harriot, but we should value it for its numerous individual insights.