Understanding what is going on in most of Greek science is well within the competence of any intelligent person, as it was in antiquity. Take heart! If you read an ancient scientific text and feel, not that you are out of your depth scientifically, but more or less bewildered by the contents, then you are probably reading it through modern spectacles, so to speak. Assume always that the ancient author makes sense: what he wrote was considered sensible by enough people over enough centuries – more than a thousand years in some cases – for that text to have been repeatedly copied and thus survive for us to read now. The task then is to discover in what sense he makes sense. As Klein put it with respect to mathematics, ‘our task consists precisely in bringing the content of Greek mathematics to light not by externally transposing it into another mode of presentation but rather by comprehending it in the one way which seemed comprehensible to the Greeks’. This search for sense can apply to the structure of a work as well as its contents: our task in that case is to recognize the principle of organization at work in what otherwise appears to be a set of more or less disorganized notes, as for example in the cases of Aristotle’s History of Animals, Theophrastos’ History of Plants, or Dioskorides’ Herbal.

The essential difference between science and related forms of intellectual activity is very difficult to define exactly. A dictionary definition of science is an accurate reflection of what some people understand by the term ‘science’, and then only in the period and place in which the dictionary was written. Most people live their lives and use their language without reference to a dictionary. Even sticking to the dictionary definition, what the word ‘science’ has meant to different people has varied over time and cultures, and its meaning continues to change. As such, the term itself can be a source of anachronism in the study of science in ancient times. For we naturally tend to find in ancient authors just those sorts of things which we recognize as science in our own times, and to ignore those things which are incomprehensible or just plain wrong – to our way of thinking. And we naturally tend to organize what we find into categories which reflect our way of dividing up the world into subjects and disciplines. Thus things that the ancients linked together, we tear apart and treat separately. In particular, some we include in the category of science, others we exclude.

Physical theories underlie all other theories in Greek science, for physics concerned the nature of stuff. If offered answers to the question ‘what is it made of?’, where the ‘it’ could be anything and everything. Consequently, all other subjects looked to one or another theory in physics for understanding of the nature of the stuff of their study, be it heaven, earth, soul, or whatever. Consider two examples.

Mathematics probably ranks as the Greeks’ greatest achievement, in the eyes of many modern scientists. And amongst the general public it is fair to say that some Greek mathematicians are better known than any other figures from antiquity, with the possible exception of Alexander the Great. For example, Pythagoras, Euclid, and Archimedes are household names two thousand years after they lived and wrote their mathematics. The Greek alphabet, or some of it anyway, is widely known today because modern mathematics uses it by preference for symbols. For example, α, β, and θ for angles, the amazing π, Σ as the summation sign, and the χ-square test. The Greeks gave us ‘square’ and ‘cube’ numbers, e.g. 22 and 33. ‘Squaring the circle’ is modern English idiom for an impossible task – the original task, set by the Greeks, being the mathematical problem of constructing a square with the same area as a given circle. Aristophanes mentions this problem. Famously, Plato forbade the geometrically-challenged to enter his Academy. He also found mathematically interesting numbers for his ideal Republic. Greek mathematical texts are rich in mathematical concepts, methods, and results. Like Greek plays, they contain timeless insights and truths. Also like literary works they require analysis and interpretation.

Astronomy is often considered the zenith of ‘the exact sciences’ in antiquity. Highly mathematical, it is quite distinct from cosmology, and was more concerned with modelling celestial phenomena than with speculation about why the heavens appeared as they did. In modelling the heavens astronomers sought to ‘save the phenomena’, that is, to ‘explain’ observations by means of a mathematical construction which located certain celestial bodies at certain places and certain times. Each construction aimed to be systematic – even axiomatic in the Euclidean style – and leave as few as possible ‘anomalies’, i.e., unexplained phenomena. After centuries of effort by mathematicians and astronomers, Claudius Ptolemy synthesized and developed their achievements to produce the Almagest. This is the Arabic name by which his Mathematical Syntax, the rules of the motion of the heavens, is better known. It became the bible of astronomy in the West and the Islamic world for the next 1500 years, until displaced in the Copernican Revolution.

Geography is a broad and diverse area of study, a large tree with many branches. The different branches are so different that they tended even in antiquity – with less subject specialization and more polymaths – to be pursued by different people. The main types are (i) human geography, focusing on the landscape of human life, (ii) physical geography, focusing on the land, sea, and sky, and (iii) mathematical geography, focusing on mathematical modelling of aspects of physical and human geography. Where geography and biology meet, we now have ecology and environmental science. This tends in ancient authors to be dealt with under biology and agriculture. The more sophisticated works, such as Theophrastos’ works on botany, consider the effect of geology, soils and microclimates on plant physiology and growth.

Ptolemy practised mathematical geography, and his reconstructed maps often feature as frontispieces in modern books on the history of geography. He scorns human geography of the type written by his predecessor Strabo, much as Thoukudides scorns his predecessor Herodotos’ type of history. We won’t push the analogy while noting that Ptolemy’s Geography is about as much fun to read as a telephone book, which it resembles, strongly. Strabo, for his part, complained that his predecessor Poseidonios’ On the Ocean has too much mathematics and astronomy in it for geographers like himself (so too for would-be writers of geography like Cicero).

Biology and medicine form a huge area. I am treating them together because there is a very close link between all the life sciences in the ancient sources. The Greeks were never in any doubt that humans are a type of animal, and not some special separate kingdom of life on earth. Aristotle’s famous dictum ‘man is an animal meant to live in a polis’, Arion’s dolphin, Herodotos’ werewolves (4.105), people turned by gods into animals and plants, Aesop’s fables, Medusa, the centaur, minotaur, siren, and other half-human and half-animal creatures, all reveal the depth of the perceived affinity between humans and other species of life on earth. In the field of medicine, ideas about human anatomy were based to a significant extent on animal anatomy. People and animals could be observed to suffer from the same epidemic disease, and the same cure for X could be offered as treatment for people or animals. [Aristotle] Physiognomics is a politically very incorrect comparison of physical features of people with those of different animals, and likens such appearances to corresponding personal characteristics.

In 1864 the biologist George Lewes wrote (p. viii) ‘Numerous and exhaustive as are the works devoted to Aristotle’s moral and metaphysical writings, there is not one which attempts to display, with any fullness, his scientific researches . . . Although Aristotle mainly represents the science of twenty centuries, his scientific writings are almost unknown in England. Casual citations, mostly at second hand, and vague eulogies, often betraying great misconception, are abundant; but rare indeed is the indication of any accurate appreciation extending beyond two works, the De Anima, and the History of Animals. The absence of translations is at once a cause and a sign of this neglect.’

Things have improved, a bit, in the intervening 135 years. Cohen and Drabkin brought together a large and diverse selection of English translations of ancient scientific works in 1948. Every year for the last 25 years, on average, there has been a new edition or notification of the discovery of a new scientific text. Galen has been the focus of a recent scholarly project whose proportions reflect his corpus. Nevertheless, despite the 9,000 printed pages of that vast corpus already published, there are still unedited and untranslated treatises surviving in full in Arabic, and two-thirds of the corpus still awaits an English translation. The state of editions and translations of ancient scientific works as a whole remains scandalous by comparison with the torrent of modern works on anything unscientific – about 100 papers per year on Homer, for example. And an embarrassingly large number of classicists are as (if not more) ignorant of Greek scientific works as their predecessors were in 1864.