Mathematics and slavery

Question

I think that ancient Greek mathematics is a miracle. Think about Euclid. Developing mathematical arguments from a small set of axioms is incredibly modern. And their influence on modern mathematics is huge. So one naturally wonder why they came up with so great mathematical ideas. I think one of the main reasons is slavery. You need much free time to do mathematics. Was there anybody who expressed a similar idea as mine? Please don't misunderstand me. I'm not advocating slavery.

Answer 1

I'll provide two excerpts from A Concise History of Mathematics by Dirk Jan Struik. Both of them are from the part of the book dealing with ancient Greece. The second quote suggests that slavery was not in all circumstances helpful for the development of science.

Page 44:

Typical of this new period in Greek history was the increasing wealth of certain sections of the ruling classes combined with equally increased misery and insecurity of the poor. The ruling classes based their material existence more and more upon slavery, which allowed them leisure to cultivate arts and sciences, but made them also more and more averse to all manual work.

Page 56:

The spread of a slave economy in such a society was fatal to all original scientific work. Slave owners as a class are never interested in technical discoveries, partly because slaves can do all the work cheaply, and partly because they fear to give any tool into the hands of slaves which may sharpen their intelligence. Many members of the ruling class dabbled in the arts and sciences, but this very dabbling promoted mediocrity rather than productive thinking.

Answer 2

The answer yes, such ideas have been mentioned before; so yours is not a new thought. However, this is an idea that can too easily be exaggerated.

To some extent, the role of leisure in culture, and in mathematics in particular, is well-acknowledged. It even goes all the way back to Aristotle, who himself was wealthy and had the leisure to study. The book "A History of Greek Mathematics" (1921) by T. L. Heath has this to say:

Dealing, at the beginning of the Metaphysics, with the evolution of science, Aristotle observes that science was preceded by the arts. [... T]hose arts naturally came first which are directed to supplying the necessities of life, and next came those which look to its amenities. It was only when all such arts had been established that the sciences, which do not aim at supplying the necessities or amenities of life, were in turn discovered, and this happened first in the places where men began to have leisure. This is why the mathematical arts were founded in Egypt; for there the priestly caste was allowed to be at leisure. Aristotle does not here mention Babylon; but, such as it was, Babylonian science also was the monopoly of the priesthood.

It is in fact true, as Gomperz says, that the first steps on the road of scientific inquiry were, so far as we know from history, never accomplished except where the existence of an organized caste of priests and scholars secured the necessary industry, with the equally indispensable continuity of tradition.

Although Heath (and of course Aristotle) doesn’t say this, these remarks also seem to apply (as far as my personal knowledge from reading goes) to the Indian tradition of mathematics. Much of Indian mathematics was done by Jain monks and Brahmins, in both cases communities of people for whom doing mathematics was an acceptable occupation. Note that neither of them was wealthy or owned slaves.

On top of this, mentions of slavery specifically in Greek mathematics can also be found in various books:

• Dirk Jan Struik, true to his Marxist principles, says in an article Some Sociological Problems in the History of Mathematics (p. 379) that

“At this point slavery may have played a role [..] by freeing an elite from hard labor and enabling it to discussing politics [..] including art and mathematics [..]. Thus the existence of slavery inside the setting of the polis may help to understand how Greek mathematics was founded”.

• He says the same thing in A Concise History of Mathematics, pages 44 and 56, which Martin Sleziak in his answer has quoted.

• Other authors too: Tracey Elizabeth Rihll, in "Introduction: Greek Science in Context"

It could be argued that the most important institution supporting ancient science was slavery. Greeks and Romans had time for many things because they did not work hard by modern standards and because they had slaves. Slavery was the institution which underwrote science in ancient Greece, in contrast to the redistributive economies of Babylon and Egypt, which enabled kings to employ e.g. astronomer-priests as full-time practitioners of their art. Let us be clear here. I am not suggesting that slavery was a sufficient condition for the emergence and practice of science in antiquity. [...] What I am suggesting is that widespread slavery provided such leisure for many people; that it facilitated widespread participation in activities such as science as well as in politics.

• Also: some words here, here, the hypothetical conversation here, and so on.

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I am however sceptical of drawing a correlation between slavery specifically and mathematics specifically. Slavery can buy you some physical comfort and save you from some chores; yet the urge to do mathematics is a function of one’s inner urges and one’s position in society (i.e. having a slave does not automatically give you leisure). Indeed, even rather poor people in Greece or Rome often had slaves. And even with leisure, the fraction of society that is drawn to mathematics (rather than business or politics or hundreds of other things) isn't significant or affected by slavery.

Consider how, in the modern world, no one would credit their mathematical achievement to their owning a washing machine or car. Even though not owning these might indeed take a lot of time away, it is a fact that most people who own these implements accomplish nothing mathematical, and in fact don’t even have copious free time.

See for example this page, In Search of Excellence: Historical Roots of Greek Culture by Alexander Makedon which points out in response to the slavery idea that:

“almost all the non-Greek peoples that ancient Greeks came in contact with also maintained slaves, sometimes to a much greater extent than they, and yet not all of them reached the same heights of educational achievement. Even among the Greeks, there is hardly anyone who reached artistic, scientific, or intellectual excellence who is also known to have been either very wealthy, or to have maintained slaves. Instead [...] most of them were either absolutely devoted to their craft (as was Thales of Miletus [..who..] was poor until his historic prediction of the sun's eclipse); or constantly tried to hone their skills [...]. We may surmise, then, that having slaves, as did the ancient Greeks, is not a sufficient precondition for greatness, just as wealth alone is not, although it can "buy" both labor and leisure.”

What really seems to help, in the ancient (and even to some extent in the modern) world, is that doing mathematics be seen as a viable occupation: either because you have royal or institutional patronage, or you have some alternative source of income, or you belong to a community where this sort of thing is common (and at least your social status is assured, although not necessarily your financial). Owning slaves is neither necessary nor sufficient for this, and in fact I would say there is no correlation.