Learning about the History of Mathematics

For many years, computing lessons in schools certainly in the UK where linked directly with the mathematics departments. Indeed I was among the first to experience a UK computer curriculum and this was pretty much dumped on our unsuspecting maths tutors who could barely turn on the console linked to our central mainframe. Obviously there’s a link between maths and computer programming, yet it’s certainly not the case that all mathematicians make good computer programmers.

Maths does form part of many higher education computer courses though, as a high level of numeracy is essential for any meaningful programming. Unfortunately often the history of mathematics is missed in computer linked maths curriculum presumably due to the time pressures. It’s an interesting subject though and one that there are quite a few decent TV shows and documentaries about if you look carefully – my favorite is called the History of Mathematics and was broadcast on the BBC last year. It’s not currently on the archive but is rebroadcast regularly, all you need ais a simple VPN to watch BBC TV abroad so it’s worth checking occasionally.

So what about the history of maths, how did it develop? Well here’s a very, brief introduction. Following on from when human communication develops, the next stage it is safe to assume is that human beings start counting. Even in primitive time, their fingers and thumbs supply nature’s abacus. The decimal system is definitely no accident. Ten has certainly been the basis of the majority of counting systems in history.

The moment any form of record is required, marks in a stick or a stone are the natural solution. In the earliest enduring signs of a counting system, numbers are developed with a repeated sign for each group of 10 followed by an additional repeated sign for 1. Math can not efficiently develop up until an effective numerical system is in place. This is a late arrival in the story of maths, necessitating both the concept of place value and the idea of zero.

As a result, the early past history of mathematics is that of geometry and algebra. At their elementary levels they both are simply mirror images of each other. A number revealed as two squared could additionally be described as the area of a square with 2 as the span of each side. Equally 2 cubed is the volume of a cube with 2 as the length of each dimension.

Babylon and Egypt: from 1750 BC

The very first enduring examples of geometrical and algebraic calculations derive from Babylon and Egypt in about 1750 BC

Of the 2 Babylon is far more advanced, with quite complex algebraic problems featuring on cuneiform tablets. A common Babylonian maths question will certainly be expressed in geometrical terms, however, the nature of its solution is ultimately algebraic (see a Babylonian maths question). Due to the fact that the numerical system is awkward, with a foundation of 60, computation depends predominately on tables (sums already worked out, with the solution given for future use), and numerous such tables endure on the tablets.

Egyptian mathematics is less sophisticated than that of Babylon; but an entire papyrus on the subject survives. Known as the Rhind papyrus, it was copied from earlier sources by the scribe Ahmes in about 1550 BC. It incorporates brainteasers such as problem 24: – What is the size of the heap if the heap and one seventh of the heap amount to 19?

The papyrus does suggest one essential element of algebra, in the usage of a basic algebraic symbol – in this case h or aha, indicating ‘quantity’ – for an unknown number.

Pythagoras: 6th century BC.

Early mathematics has actually reached the modern world mostly through the work of Greeks in the classical period, building on the Babylonian custom. A major figure among the very early Greek mathematicians is Pythagoras.

In around 529 BC Pythagoras relocates from Greece to a Greek colony at Crotona, in the heel of Italy. There he establishes a philosophical sect based on the view that numbers are the underlying and changeless truth of the universe. He and his supporters very soon make precisely the sort of breakthroughs to reinforce this numerical faith.

The Pythagoreans can show, for instance, that musical notes can vary in accordance with the length of a resonating string; whatever length of string a lute player starts with, if it is doubled the note consistently falls by precisely an octave (still the basis of the scale in music nowadays).

The followers of Pythagoras are also in a position to demonstrate that whatever the shape of a triangle, its three angles always add up to the sum total of two right angles (180 degrees).

The most well-known equation in classical mathematics is known still as the Pythagorean theorem: in any right-angle triangle the square of the longest side (the hypotenuse) is equal to the sum total of the squares of the two other sides. It is actually unlikely that the proof of this goes back to Pythagoras himself. But the theorem is typical of the accomplishments of Greek mathematicians, with their primary passion in geometry.


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