Stephen Wolfram was a child prodigy, receiving his PhD in particle physics at the age of 20. His subsequent achievements include significant work on cellular automata, the creation of the computer-algebra system “Mathematica” and the computational knowledge system “Wolfram Alpha”. He also wrote a large and controversial book, *A New Kind of Science* (2002), which argues that computation is key to understanding our universe. But you don’t need to know about his achievements to read Wolfram’s latest book,* Idea Makers: Personal Perspectives on the Lives and Ideas of Some Notable People*, not least because they are rather frequently mentioned in the text.

*Idea Makers* is exactly what the subtitle suggests: it presents a very personal view of a number of people who have interested Wolfram, who is himself a significant scientific thinker. Some are major past figures from the history of science, such as Gottfried Wilhelm Leibniz, Ada Lovelace and Alan Turing. Others the author himself knew and worked with, including the likes of Richard Feynman – one of Wolfram’s PhD examiners, whom he later came to know well – Steve Jobs and Solomon Golomb. I knew of Golomb as the inventor of “pentominoes” (a generalization of dominoes, which involves joining five equal squares edge-to-edge) but his work, I found out from the book, is of fundamental importance in electronic engineering. Most of the people featured in the book only appear briefly, as their entries are written to mark an anniversary, an event or a death. Many of the entries do focus on Wolfram’s personal connections with his subjects, but this is understandable given the premise of the book.

While most of the subjects are well known, the name of Russell Towle was new to me. Towle, a US mathematician who died in a road accident in 2008, used Mathematica to explore zonohedra, a special kind of polyhedra, and corresponded with Wolfram about his work. The chapter on Towle includes some of his fascinating images, and I am delighted to have learned about Towle and his work.

Wolfram does not attempt to provide a complete portrait of his subjects: instead, he is interested in particular aspects of their work (naturally, those which relate to his own ideas), and there is a diversity of approach. The very interesting chapter on Feynman is largely personal reminiscence, while the section on Kurt Gödel (written on the centenary of his birth) argues that Gödel’s “abstruse theorem of mathematics” has set the agenda for 21st-century science.

Wolfram’s first-hand research into archival material, coupled with his enthusiasm for investigating the past, comes to light in the three more comprehensive chapters, on Lovelace, Leibniz and Srinivasa Ramanujan. The extended essays were, for me, particularly intriguing. Wolfram quotes extensively from original documents in arguing for Lovelace’s importance. When I first heard of Lovelace, there was a view that, while she undoubtedly played an important role in helping Charles Babbage develop his calculating engines, there were doubts as to the extent of her personal technical contribution. Wolfram, along with other recent researchers, convincingly dispels any such doubts. Happily, following last year’s bicentenary of her birth, Lovelace’s reputation has never been higher, and Wolfram puts forth even more convincing evidence of her abilities.

The chapter on Ramanujan delves into his unique way of doing mathematics, as well as his extraordinary insights into mathematical patterns. Wolfram goes as far as recommending the reader adopt a similarly adventurous and experimental attitude in mathematics. Personally, I’m enough of a traditional “pure” mathematician to want proof to go along with experimentation, and in some ways, I found this the least convincing section of the book.

In writing about Leibniz, Wolfram analyses Leibniz’s thinking about computation. He concludes that Leibniz didn’t take discrete systems seriously enough to anticipate modern ideas of universal computation; but he is interested in Leibniz’s use of binary and in his calculating machine. Although Wolfram’s approach is not entirely that of a historian – he is comfortable drawing conclusions from the perspective of our present-day thinking – the chapter is nevertheless illuminating and thought-provoking.

Wolfram writes very well: he is always entertaining and his ideas are interesting. While it is somewhat natural that he relates his subject’s ideas to his own, reading the frequent speculations about how these great thinkers might have appreciated Wolfram’s work became slightly overwhelming for me. There are sections with headings such as “What if Ramanujan had Mathematica?”, many comments along the lines of “I’m sure he [John von Neumann] would have been a big Mathematica user today”, and “perhaps long ago he [Turing] would have campaigned for the creation of something like Wolfram|Alpha”. The book discusses why John von Neumann did not anticipate Wolfram’s insight that cellular automata with simple rules can generate very complex behaviour. Despite this, I don’t think Wolfram intends to be self-congratulatory. To his credit, in the chapter on Benoit Mandelbrot, he quotes the fractalist’s highly unfavourable opinion of A New Kind of Science. Reading this book, one wonders whether his description of Mandelbrot as “constantly seeking validation and constantly fighting to get his due”, might also apply to himself.

Because of the personal nature of the book, Wolfram provides a very partial view of his subjects, in more than one sense of the adjective. The reader will meet some fascinating characters who deserve to be better known, and will gain insights into some of the major figures in the history of science and technology, both recent and from the more distant past. They will also learn a lot about the author and his own thoughts – more explicitly than most scientific biographers would allow themselves. Whatever you think of Wolfram’s big ideas, his thoughts and perspectives are illuminating and are worth careful consideration.

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