Who first made calculating numbers a discipline and called it mathematics? Matilda Day, aged 10, Dordogne, France
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Here’s looking at Euclid. Lots of people contributed to the early development of mathematics and he was perhaps the first to organise axiomatic systems and proofs – the modern logical basis for mathematics – in his 13 books on geometry. He also reminds us that mathematics is about far more than numbers and calculation. angusprune
A sadist, obviously. Leonie Hertig
The Pythagoreans, about 2,600 years ago in Greece, are recognised as turning their structured studies into what they called mathema. It’s possible that prehistoric findings of carved bone in Africa contain markings that might be tallies, or even show a primitive understanding of number systems, dating back around tens of thousands of years. Dorkalicious
Other civilisations were doing formal reasoning using mathematical concepts long before the Pythagoreans, but they weren’t calling it mathematics, simply because that’s a Greek word, not a Chinese or Urdu or Assyrian or Mayan word.
In many cultures, some of the earliest developments of “mathematics” (as opposed to mere arithmetic) are associated with astronomy, which was essential to agriculture, as it permitted the development of regular calendars that dictated planting cycles. I believe the Egyptians had the beginnings of what eventually came to be called algebra (we get that word from the title of a book written in the early 800s by the Persian polymath al-Khwarizmi, the name of which evolved into the modern word “algorithm”). If I recall correctly, they used it for such things as calculating the area of a field, the volume of a storage bin and so on. This was useful for, among other things, levying taxes.
One curious point of “argument” among the anthropological community – mere hypothesising, really – is which came first: ordinal numbers (first, second, third) or cardinal numbers (one, two, three). Of course, we will never know. LouisRiel
Much the same can be said for the Sumerians, who probably started earlier than the Egyptians. We know more about them than the Egyptians, though, because of the cuneiform writing system, which is the oldest one known (and, as the Sumerians wrote on clay tablets, has proved to be very durable). We know that they did algebra “rhetorically”, like the Egyptians, and they solved some surprisingly complicated problems. They could solve linear equations and quadratics, by a procedure that amounts to completing the square, and they could sum arithmetic and geometric progressions. It is also clear that they knew the Pythagorean theorem. They had tables of squares and square roots and cubes and cube roots. Presumably, these were useful for geometric and building problems.
They certainly had a better number system than the Egyptians (or the later Greeks and Romans, for that matter), which was founded on bases 12 and 60; this makes the “difficult” operation of division easier. We still count time and measure angles that way, 5,000 years later. We don’t know why they divided circles into 360 equal parts, although we can speculate that it is the nearest multiple of 12 and 60 to the number of days in the year. FinrodFelagund
The BBC’s recent documentary on the latest Stonehenge research demonstrated the geometrical constructions used to lay out the stones. They had a pretty impressive understanding of geometry about 4,500 years ago in the Neolithic. Of course, we have not the foggiest idea of what they called it, but does that really matter? Forlornehope
The oldest writing systems in the world represent 6 as 5+1, showing an ability to add up. So, as mathematics is older than writing, we will never know. Wikipedia reckons that counting beyond the number of fingers and toes goes back 40,000 years. Socialismnow
A readable book on the subject is Alex’s Adventures in Numberland by Alex Bellos, puzzler of this parish. He’s a mathematician and a philosopher who tells tales very well. He deals with the range of maths, which is far from being a single subject, and each chapter is free-standing. Plus, you don’t have to do the hard sums; they’re in the back of the book. Fallowfield
