Mathematics
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History of mathematics
Mathematics originally developed from a need to measure and count. Early advances were made in Mesopotamia, ancient Egypt, ancient Greece and the Islamic world. Trading, observation of the stars and planets , and the desire to understand nature all helped to drive the study of mathematics over the years. The first counting was done with notches on bones or wood, with just one symbol. The earliest calculating device was the abacus, a counting frame along which beads are moved to make calculations. It dates from 2700–2300 BC in Sumeria, present-day Iraq.
Babylonian maths
The first advances in mathematics were made by the people of Mesopotamia from about 2700 BC to the fall of Babylon in 539 BC. The Babylonian number system was based on the number 60. This is why we have 60 seconds in a minute and 360 degrees in a circle. No one is sure why they used this number, other than the fact it very usefully can be divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. One idea is that they counted to 12 on one hand by pointing the thumb to each of the three bones on the four fingers in turn, allowing them to count in groups of twelve. Each group was counted on the thumb and four fingers of the other hand, and 12 x 5 is 60.
The Babylonians used their new number system for trade, for writing complicated tables on to clay tablets to make calculations easier, and for using fractions.
We know a lot about Babylonian maths from the discovery of around 400 clay tablets made in the 1850s. They are written in an early script called cuneiform. They show the Babylonians had an understanding of multiplication and division, fractions, square roots, algebra, the Pythagoras Theorem (centuries before it was explained by Pythagoras), geometry—they knew how to measure areas and volumes, and had calculated an approximate value of pi (π)—and other branches of mathematics.
Ancient Egypt
The Egyptians used a number system based on 10, probably because we have ten fingers and so are familiar with counting to that number. This number system is called base ten or decimal, and is widely used today. Their ability to count accurately, combined with an understanding of shapes (geometry) was vital in the design and building of pyramids.
Ancient Greece
The Greeks were the first people to study mathematics for its own sake, exploring its ideas and showing how to use the rules and logic of mathematics to explain the world and the Universe. Many of their advances were to do with numbers and shapes. For example, Pythagoras showed that in a right-angled triangle, the length of the longest side (hypotenuse) multiplied by itself (squared) is equal to the squared measures of the other two sides.
Euclid
Euclid published a series of books called Elements in which he explored what numbers are and proved various rules of shapes and angles (geometry). Many of these are still used today, such as the rule that all right angles are equal and that we can draw a straight line between any two points. Euclid is known as the Father of Geometry, and the set of rules explaining lines, points, shapes and solids is known as Euclidean geometry.
Archimedes
Among many inventions and mathematical advances, Archimedes calculated an accurate estimate of π (pi), the ratio between a circle's diameter and its circumference (edge). He showed that it is between 223/71 and 22/7, which in decimal figures is about 3.14. Pi is used today in many areas of mathematics, science and engineering to measure the lengths of arcs and curves, the areas of curved surfaces and the volumes of many solids.
Archimedes also developed a way of carrying out calculations with huge numbers, partly to investigate how many grains of sand would fit into the Universe. He suggested that a "myriad" (Greek for infinity) could stand for 10,000, and then proposed a number system using a myriad myriads, or 100 million. This work suggested for the first time the enormous scale of our Universe.
Eratosthenes
Eratosthenes of Cyrene (276 BC–195 BC) was a Greek scholar: a mathematician, geographer, poet and astronomer. He is best known for being the first person to calculate the circumference of the Earth, which he did using geometry: comparing angles of the midday sun at two places, Alexandria and Syene in Egypt, which were a known distance apart on a direct north-south line. His calculation, 44,100 kilometres (27,400 miles), was remarkably accurate (it is 40,075 kilometres or 24,901 miles around the Equator). Eratosthenes created one of the first maps of the world, incorporating lines of latitude and longitude based on the available geographical knowledge of his time. He also introduced what became known as the Sieve of Eratosthenes, a method of identifying prime numbers.
Hindu and
Islamic maths
Although ancient Egyptian and Greek scholars made some use of zero, it was Hindu mathematicians in India who in about 500 AD started to use a circle to show zero. This is because it allowed them to show numbers in an easier form, using what is called positional notation. The system was invented by the Babylonians, although they did not have a zero symbol.
In our modern decimal (base ten) system, digits are written in a row from left to right, each place having a different value. So, with the number 245 for example, the 2 represents—or has a place value of—200, the 4 represents 40, and the 5 represents five units. The Babylonian and Hindu idea of positional notation and the way the Hindus wrote numerals was taken up by Islamic scholars and has survived to this day. This is why we call our written numbers Arabic numerals. Islamic scholars also built on Greek mathematics and developed a new branch called algebra, which helps to solve problems.
Fibonacci
Arabic numerals reached Europe during the Middle Ages thanks to an Italian mathematician called Leonardo Fibonacci (c.1170–c.1250). He developed an idea that still fascinates mathematicians today: the Fibonacci Sequence. Each number in the sequence is made by adding up the two before it. So it begins 0, 1, 1, 2, 3, 5, 8, 13 and continues into infinity.
Intriguingly, the Fibonacci Sequence describes the pattern of leaves on a plant, the segments in a pineapple or a pine cone or the spiral of a sea shell, showing how mathematics links with nature. It also used an important mathematical idea: infinity—something without an end. The ancient Greeks were the first to explore the idea of infinity.
Maths for science
In the 17th century, much of the mathematical development grew from an eagerness by scientists to understand the stars and the planets. For example, Johannes Kepler used algebra to show that the planet Mars had an elliptical (oval-shaped), rather than a circular orbit, round the Sun. There was also much interest in studying probability to examine the mathematics behind games of chance.
The development of another branch of mathematics, calculus, by Isaac Newton and, at the same time, Gottfried Leibniz, allowed Newton to develop his theories of gravitation and motion, which he published in 1687.
The 18th century saw the introduction of many modern mathematical terms and notation, led by Swiss mathematician Leonhard Euler (1707–83). This included the use of the Greek letter π to represent pi.
Consultant: Mike Goldsmith