The Mathematics of the Ancient Romans. Part I

By on 07/09/2017

A new contribution from the Italian journal XlaTangente. Initially thought as the Italian edition of the French magazine “Tangente. L’aventure mathématique“, in the last few years the paper edition evolved in a website,, whose goal is to continue to offer “chewable mathematics”, thanks to the contributions of young mathematicians, increasingly aware of the need to maintain a dialogue with society. The website is addressed specifically to students of secondary schools and their teachers.
This contribution was first published in XlaTangente no. 38, April 2013. 

The ancient Romans: a pragmatic lineage of bellicose peasants? Is there a truth beyond this stereotype? In this article and in the next ones, you may discover some aspects of ancient Roman civilization that you would have never expected!


One of the most widely read books on the history of mathematics is Morris Kline’s Mathematical Thought From Ancient to Modern Times (1972), a rather detailed study that devotes the first two hundred pages to mathematics in the ancient world. Kline writes: “The Romans were practical people and they boasted of their practicality. They undertook and completed vast engineering projects […] but refused to consider any ideas beyond the particular concrete applications they were making at the moment. ” This is a rather extreme judgment for a detailed work such as that of Kline, which continues to say that their inability [of the Romans] to make progress in mathematics strikes because they ruled a worldwide empire. But this observation is not developed and drowns in the sea of contumelies that the American mathematician writes about Rome.

As an example of the brutality of the Romans, Kline cites the destruction of the Alexandria Library by Caesar’s troops (“Two and a half centuries of book-collecting and half a million manuscripts, which represented the flower of ancient culture, were wiped out.”), which actually did not take place until the end of the third century AD and definitively in the 7th century AD, and recalls their expansionist policy in these terms, worthy of a nineteenth subsidiary: “The subjugated areas became colonies, from which a great wealth was extracted by expropriation and taxation. Since most of the Roman emperors were self-seekers, they ruined every country they controlled. When uprisings occurred, as they did, for example, in Alexandria, the Romans did not hesitate to starve and, when finally victorious, to kill off thousands of inhabitants. “

It is a surprise that a historian would consider these crimes as hateful only referring to a single people, when these were common practices in antiquity. For example, in 335 BC Alexander the Great rushed to the ground Thebes exterminating the population and deporting the survivors, and it is difficult to find ancient peoples and nations, starting with the Greeks, who did not use these methods to expand their territorial and commercial horizons (and if you think about it, they were used until very recent times). Kline’s essay is written with scrupulousness, unlike the fascinating but imaginative E.T. Bell’s book, Men of Mathematics (1937), still on the ridge of the wave, in which the author gives ample venture to his poetic itching, plowing in the alley of many commonplaces. Here is an example: “In the death of Archimedes we shall see the first impact of a crassly practical civilization upon the greater thing which it destroyed – Rome having half demolished Carthage, swollen with victory and imperially purple with valour, falling upon Greece to shatter its fine fragility.”!

One can ask where this unanimous chorus of cutting remarks against the “brutal” Romans destroying the “sophisticated” Greeks comes from (although in fact, all these authors are talking about Grecism meaning Hellenism). The sources are the great treatises of nineteenth-century scholars, infatuated with Hellenistic thought, who saw in other ancient civilizations – especially in the Romans and the Parthians, who had the “wrong” to conquer and annex the Hellenistic realms – all the evil that they avoided to attribute to the Hellenistic world. In fact, besides the Romans – the bellicose peasants – we find the Persians, considered slave, theocratic and corrupt people, according to a stereotype also in popular culture, as shown by the picturesque description Frank Miller provides in the comics 300.

Indeed, if the eighteenth century was the century of the admirers of Latin culture (just think of the consideration shown by  Illuminists for Cicero and Seneca), the nineteenth century was that of Romanticism, which regarded ancient Greece as the golden age of Art and Thought. Great philologists studied, translated and edited critical editions of Hellenistic and Greek mathematics, for example, we owe to the Danish scholar Johan Ludvig Heiberg the monumental editions of Euclid and Ptolemy, and the discovery of Archimedes’ famous Palimpsests in 1906, which deserves a story by itself. The quote that follows, perhaps the remote mother of the precedents, is excerpted from Mathematics and physical science in classical antiquity (1922, original edition 1920)[ii]: “The Romans, with their narrow and rustic perspective, their practical sobriety and short-sightedness, had always, in the depths of their hearts, a mixture of suspicion and contempt for pure science that is still the sign of the semi-educated, which sometimes boast about it. ” The source is a Cicero motto that we will reveal in due course.

But the long wave of this disdainful deception to an entire people lasts until today: a remarkable example is the famous and well-known book by Lucio Russo, The Forgotten Revolution (original edition 1997), which contains a lot of first-hand detailed information on Hellenistic mathematics (which makes it a unique and irreplaceable work), collected however to serve the hypothesis that science, as it is conceived today, is a Hellenistic invention and not a seventeenth-century invention. In the glorification of the Hellenistic culture and science, there is no shortage of criticism of the Roman conquerors, with the same arguments that we find in earlier authors, and a few more, economically based.

[ To be continued…]

[i] A colourful vernacular expression that could be translated with “Oh gosh, the Romans are coming!”

[ii] We propose here a translation from the Italian edition by Guido Castelnuovo (1927) as we were not able to consult an English edition.


Paolo Caressa,
translated by Daniela Della Volpe

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