As a young mathematician and astronomer, Thomas Harriot (c. 1560-1621), was hired by Sir Walter Ralegh, to train the captains of the ships ready to cross the Atlantic and claim some territory for England in the New World. Ralegh was a poet, politician, and frequenter of the court of Queen Elisabeth I. The faith of the two man was entangled since. A first expedition brought two native Americans back to England and Harriot learned their language and invented a phonetic alphabet to write it down. He even crossed the ocean himself to visit their home land during a second expedition. After his return, he wrote the only book published during his life: The Briefe and True Report of the New Found Land of Virginia (Virginia named after Elisabeth, the virgin queen). He continued working for Ralegh as a land surveyor. Later Harriot got employed by Henry Percy, 9th Earl of Northumberland. With observations and tedious computations he improved his skills as an astronomer, a mathematician, and a physicist.

Elisabeth, the short tempered virgin queen, depended on trusted advisors like Ralegh and Percy, but when Ralegh got married without her consent, she considered it treason. The period was turbulent with many political en religious tensions for example with the catholic Queen Mary of Scots, and hence also with France and Spain resulting in naval battles. Privateering was a lucrative pastime for the crew of the ships that were exploring the New World. Political compromises and treason, spying and conspiracies, were common games for Queen Elisabeth and her successor King James. Take on top of that the emergence of the scientific revolution of the 17th century, and the exploration of the North and South Americas, and Arianrhod has all the ingredients to write a thrilling and adventurous novel about it, and so he did. Only it is all based on true and well documented facts.

Arianrhod has found a good balance between explaining the mathematical and astronomical work of Harriot, and sketching what happened on a political and personal level of the main characters that he describes in the turmoil of events at the end of the 16th and the early 17th century. These main characters whose fortunes and misfortunes are told, are besides Harriot mainly Ralegh and to some extend also Percy but there are many others as well. Too many to keep track of if this were a fiction novel, but real life is not that simple. A name list in the appendix with one line description per name might have been welcome for a reader not so familiar with the period, its politics and its science.

It is characteristic of many biographers that they bring an idolatrous glorification of their subject. Somehow this struck me in this book too. It is clear that Arianrhod describes Harriot and Ralegh as the worthy heroes with almost sacred virtues. For example the attitude that Harriot and Ralegh have towards the native Americans, considering them as friends and treating them with respect, leaving their dignity is unusual for that time. The devotion of Ralegh for his queen, even when she locked him up in the Tower of London for many years (as she also did with Percy) is outspoken. His continued attempts to colonise parts of North and South America to flatter the Queen (which both turned out to be disastrous) and the noble way he behaved on the scaffold when he was beheaded under King James I are almost beyond human limits.

Harriot fell under the bad faith of his employers when they were accused of treason, and that shone on him and his work and ideas were scrutinized for possible atheistic elements. He was even imprisoned for a short while on the charge that he had cast an horoscope on King James during the Gunpowder Plot. However, he always tried to stay somewhat in the shadow, concentrating on his scientific work, and so he escaped most of the misfortunes that befell on his employers and could have been his faith too. This is one element of excitement, but the whole book is a thriller: will the pioneers survive crossing the ocean, will they survive in the midst of unknown tribes, will the prisoners of the Tower be executed, will the catholic Gunpowder Plot or the courtier's Main Plot against King James be a success, will the war at sea with Spain be won, will the money be raised for yet a new expedition,... all components that can bring some tension in an engaging story told with brio. That is why, besides Harriot, Ralegh, and Percy, many other (mostly political and scientific) characters are staged in this complicated interplay of intrigues. And Arianrhod is not the first to use these elements in a book. He suggests that Shakespeare has used some of the events described here as scenes in his plays.

When it comes to Harriot himself, these parts of the book are mainly about his scientific achievements. The reader is instructed about how Harriot explained the seamen what they should know to find the position of his ship, and how they could compute it in an efficient way. We learn about his study of the loxodromic curve and the equiangular spiral, how he unravelled the secret of the Mercator projection, how he measured the acceleration of free falling objects to study gravitation and how he computed the trajectory of a canon ball (that was before Newton formulated his laws of motion). Harriot studied the precession of the Earth and the Gregorian calendar, the refraction of light and gave an explanation for the rainbow. We read about his atomistic views, his exploration of probability theory, and of course his astronomical computations and his study of sunspots. He produced a map of the moon and he had some correspondence with Kepler. He was also one of the first to simplify algebra by introducing symbolic notation: he used letters for variables, he had a notation for exponents, a variant of our equal sign,... Arianrhod places all his discoveries in context, sometimes going back to Greek antiquity or by discussing contemporaries or scientists who came after Harriot who discovered the same things independently, and whose name became attached to these results.

It is a shame that Harriot did not publish more because that would certainly have given him a reputation comparable to Galileo, Kepler, and cartographers and mathematicians of his time. When at the age of sixty he seemed to be ready to start rounding up his work and publish it, he got health problems. It might have been a kind of cancer that started with his nose that finally killed him. It is not unlikely that it was caused by excessively smoking tobacco. Allegedly he, and his employer Ralegh, are responsible for introducing pipe smoking in England. He made his testament and asked some friend to order his notes and publish them posthumously. However not much came out of that. His notes got lost until they were rediscovered at the end of the 18th century, but again, it took a long time before it was recognized that Harriot had a lot of results that we now know by the name of other scientists, while Harriot had these already much earlier. Slowly Harriot's achievements were realized by historians analysing his notes that are now fully digitized and made available through the European Cultural Heritage Online.

To conclude: this is a marvelous book because of the engaging way it is told, very much unlike a dull biography with an enumeration of facts. Moreover it is also well documented by additional material to be found in the last 100 pages of the book. There you can find a number of graphic illustrations that are needed to understand some of the mathematics that are discussed. These are moved to the appendix probably to allow the reader to skip some of the mathematics if he or she is not interested. Many of these extra pages are filled with notes that explain some background or give the origin of a quote or a justification for a statement in the text. Of course the list of primary and secondary sources used are there too, and a well stuffed index of names and subjects. A warmly recommended read about England in the period of Shakespeare, shortly before Newton, with in the background a turbulent dance of politics, when war could still be avoided by marriage, but fighting over colonizing the Americas, and over religious controversies never ceased. On this canvas Arianrhod paints the bubbling emergence of the Scientific Revolution to which Harriot was a silent contributor.