Babylonian mathematics

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# Conclusion

In conclusion, what is Babylonian mathematics about? Although it is not easy to answer this question precisely, because of the difficulties of interpretation such as you saw with Plimpton 322, the overwhelming impression is of the study and use of numbers, and various techniques for solving problems involving numbers. Where the numbers arise from—whether land measurement, economic questions, idealised geometrical objects (cubes, triangles and so on), or just fairly abstractly—seems a relatively secondary matter. As Otto Neugebauer has put it:

The central problem in the early development of mathematics lies in the numerical determination of the solution which satisfies certain conditions. At this level there is no essential difference between the division of a sum of money according to certain rules and the division of a field of given size into, say, parts of equal area.

O. Neugebauer, The Exact Sciences in Antiquity pp. 44–5.

The Babylonian problem-solving skills, as we infer them from the problem texts, were remarkable. The Babylonian scribe, for example, received a training in these matters far in advance of anyone in medieval Christian Europe 3000 years later. The Old Babylonian knowledge was preserved somehow through all the alarums and excursions of subsequent Mesopotamian history, and filtered through in some measure to the later Alexandrian Greeks. Just what knowledge, however, and when, is not precisely known at present.

Babylonian techniques are sometimes described as algebraic, although other historians would reject the applicability of the term. You can begin to see that the style of mathematics used in some culture or period can be a better way of trying to understand and empathise with past mathematical activity than is the desire to fit topics of concern into pre-ordained slots. For, as we have already seen, the ostensible subject matter, the language used, and the techniques applied do not always fit together in past cultures in the way they do in ours. It is some combination of all these things that is characterised by the word style.

MA290_2

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