Academics like few things more than to complain about the state of their profession. A recurrent gripe is that their fields have descended into hyper-specialisation, with an overload of knowledge – books, articles and now various forms of digital material – leading to the death of the great generalists of yesteryear, who were able to leap bravely between fields and even departments. In my own field, history, the complaint was recently synthesised by two high-profile historians in a provocative book, The History Manifesto, the title of which was deliberately chosen to mimic Marx and Engels’s call to arms. The book, heavily promoted on social media, was full of seemingly authoritative graphs demonstrating how historians had become overspecialised pedants, the periods they studied growing ever shorter since the 1970s.

Unfortunately, other historians soon revealed that the authors of The History Manifesto had misinterpreted their own data: the periods studied had in fact grown longer. What was interesting was what the episode revealed about the self-identity of the profession. In the words of Ian Tyrrell, who has offered examples of historians lamenting specialisation from the 1890s to the 1990s, ‘So common have criticisms of overspecialization been that their continuing appearance registers a failure of … historians to examine the history of historical practice.’

With that lament in mind, it is most welcome to find a great historian, Peter Burke, tackling the history of the intellectual persona who refuses to be stymied by disciplinary boundaries: the ‘polymath’. Burke has compiled a list of five hundred individuals. Pleasantly, it has an even wider chronological range than (in the words of the subtitle) ‘Leonardo to Sontag’, beginning with Filippo Brunelleschi and ending with the American evolutionary biologist Stephen J Gould and the Bulgarian literary critic and essayist Tzvetan Todorov (here misnamed ‘Tristan’). In between we have a mesmerising array of philosophers, scientists, anthropologists, economists, artists, engineers, physicians, lawyers and men and women of letters from across Europe and the Americas.

Given this range, it would be impossible not to find something interesting in this book. Particularly welcome is Burke’s coverage of figures from Spain and Latin America, such as the remarkable 17th-century Mexican nun Juana Inés de la Cruz, and the 18th-century Jesuit palaeographist Lorenzo Hervás y Panduro. But with range comes an inevitable lack of depth. Burke’s approach is typically to assign one paragraph to each of his putative polymaths, consisting of a pithy biography, a list of their interests and a remark to the effect that their learning went beyond their primary interests. So we read, for instance, of Philip Melanchthon: ‘now remembered as a theologian, Luther’s right-hand man in Wittenberg, studied or taught not only rhetoric and Greek but also mathematics, astronomy, astrology, anatomy and botany’. The result is that the book has a somewhat encyclopedic quality, with many of the descriptions being summaries of other summaries, in the case of scientists usually from the Dictionary of Scientific Biography. There are also errors, even with respect to the early modern period in which Burke specialises. The great 16th-century Spanish biblical scholar Benito Arias Montano was not a member of the Family of Love sect; the Huguenot encyclopedist Pierre Bayle did not leave his academic post in 1684 but almost a decade later – nor did he ‘give it up’, but was rather forced out of it for political reasons.

The book is at its best when Burke steps away from individuals and considers the structural complexities in the history of disciplinarity, especially in the 19th and early 20th centuries. A particularly astute observation is that ‘paradoxically … the foundation of new disciplines in an age of specialization offered a new role for polymaths, at least in the short term, since a new discipline is necessarily taught in the first generation by professors who have been trained in something else’. In turn, ‘the second generation is trained in the new discipline and so reinforces specialization’. Computer science offers a good example of this phenomenon, though even here all the foundational figures – Norbert Wiener, John von Neumann, Alan Turing and Claude Shannon – were united by mathematical training and expertise.

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Burke’s story is ultimately one of decline, from the ‘monsters of erudition’ of the 17th century to the present era of specialisation. Early modernists may feel that he is slightly cheating in his description of their period by setting up as separate disciplines subjects that were always studied together. For example, optics, astronomy and geometry were all part of ‘mathematics’, and it was effectively impossible to specialise in only one of them; in these terms, anyone who practised the subject was a polymath. This being admitted, some figures omitted here seem more worthy of inclusion than others who do appear: for example, the Flemish Simon Stevin made seminal contributions to pure and applied mathematics, as well as engineering, music theory and bookkeeping, while also practising chemistry, among many other disciplines.

In general, I feel that Burke sometimes sets the qualifying bar too low. Many of his premodern figures were encyclopedists or talented vulgarisateurs, but it is not clear that they made the ‘original contributions to several (if not “many”) disciplines’ that is Burke’s principal criterion for admission. Take, for example, the aforementioned Bayle. To be sure, his vast biographical Dictionnaire Historique et Critique (1697) was widely read. But it is certainly not the case that he was ‘well informed about recent developments in what we call the natural sciences’ – his correspondence reveals him to have been a mathematical incompetent, even by the standards of the time, to whom Huygens had to explain the most basic ideas.

As for the later period, many of Burke’s polymaths are from the humanities and ranged widely in their roles as ‘critics’, ‘cultural commentators’ or ‘public intellectuals’. Does this really qualify them for the title of polymath? It is one of the realities of Western history that someone who has done well in a humanistic field, has a vague talent for prose and, more often than not, is from a privileged background and has the right connections is frequently invited to offer their opinions on subjects in which they have no discernible expertise. To pick an easy target from those mentioned by Burke, there can be no doubt that Noam Chomsky is a seminal linguist, but it is not clear that without his prior reputation his writings on politics would be taken very seriously (this point applies across the political spectrum).

Indeed, it might even be claimed that the mythology of the polymathic public intellectual is inherently elitist: why should the political opinions of a philosopher, historian or novelist receive more attention than those of a nurse or teacher? Indeed, perhaps there are good reasons why they should not. Burke addresses briefly the accusations of superficiality, dilettantism and even charlatanism that have been levelled at polymaths throughout history. I would have liked to hear more about this. Burke does not mention that one of the most recent figures on his list, Gilles Deleuze, was exposed as having misused mathematical concepts as part of a process of mystification and deliberate obscurantism (every student should read Alan Sokal and Jean Bricmont’s debunking of his work, Intellectual Impostures). Perhaps the real modern polymaths are the hidden ones who do not themselves grab the limelight but have the expertise to bring together different fields of knowledge: librarians, teachers, editors of literary journals…

The sobering reality is that making true contributions to knowledge is incredibly difficult. It usually comes precisely from the pathological pedantry and the obsessive search for minuscule clues that subject-hopping intellectuals often disdain. Burke’s explanation for what he takes to be the growth of specialisation is that it is a regrettable necessity in the face of information overload: it ‘may be regarded’, he writes, ‘as a kind of defence mechanism, a dyke against the deluge of information’. Accordingly, he finishes with a quotation from Leibniz about the need for ‘universal men … who can connect all things’, particularly in our ‘age of hyper-specialization’. But perhaps the very example of Leibniz reveals that there is a more positive case to be made for specialisation. When Isaac Newton announced his theory of universal gravitation, Leibniz dismissed it as not being science (or ‘natural philosophy’) at all: Newton had supplied a mathematical description but had not offered a full causal explanation at the metaphysical level. Leibniz himself spent many fruitless years trying to come up with a metaphysics of inertia as part of his aim to ‘connect all things’. In the meantime, Newton’s theory of universal gravitation led to yet more spectacular discoveries, without the unifying secrets for which Leibniz so strived ever being revealed (three hundred years on, we are yet to discover a graviton).

Newton was no narrow-minded advocate of rigid disciplinarity. But what he and his successors recognised was the extraordinary emancipatory power of confining the mind to a limited set of questions. The search for connections and grand meta-philosophies often has a totalitarian dimension; much of modern European intellectual history is the story of its emancipation from such philosophising. It is no coincidence that the campaign for interdisciplinarity has been vocally taken up by some ultra-reactionary Catholics, who claim that Thomism, with its synthesis of philosophy and theology, is the only intellectual system ever to have offered a truly interdisciplinary approach to knowledge.

This lesson applies also to the modern humanities. In the name of interdisciplinarity, many fields – especially in the USA but increasingly in the UK too – are now in thrall to a grand theory derived in part from the writings of another of Burke’s polymaths, Michel Foucault (although Burke himself certainly is not). According to this theory, knowledge is just another form of power and the history of knowledge is reducible to the history of power relations. Whatever one thinks of Foucault, there can be little question that the influence of a simplified version of this totalising idea has been disastrous, leading to a stymying of curiosity and the emergence of a rigid intellectual dogmatism. It is only the specialists, driven by their pedantic curiosity, who stand in the way of its suffocating tentacles.