Find out the facts of algebra history and where it really came from.
The earliest we know where algebra came from was egypt, about 5000 years old. It dates from around when the pyramids were built.
The ancient egyptians used words 'aha', meaning 'heap', to mean an unknown number. In the same way, we might use the letter x today.
Problems have even been discovered which were clearly set as exercises for young mathematicians.
One of these was a problem about houses, cats, mice and grain and was a very early version of the rhyme I learnt as a kid:
As I was going to St Ives,
I met a man with seven wives,
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kits,
Kits, cats, sacks, wives,
How many were going to St Ives?
(Answer as usual, is at the bottom)
825 - Muhammed ibn Musa Al-Khwarizmi
Algebra played a huge role in the work of Islamic scholars in the ninth century. Al-Khwarizmi was a well known mathematician and astronomer who lived in baghdad during this time.
He wrote a book called kitab al-jabr wa al-nuqabalah, which was about solving equations and practical problems in terms of linear and quadratic equations.
The word algebra comes from the word al-jabr
1070 - Omar Khayyam
Later still, Omar Khayyam is famed for writing the Rubaiyat, and the immortal lines (in translation)
A Jug of Wine, a Loaf of Bread - and Thou
Beside me singing in the Wilderness
At the young age of 22 (when most of us are just getting to grips of it) , he wrote a book in which he investigated the solution of cubic equations.
1545 - Girolamo Cardano
His great work on mathematics was published in 1545. It was a turning point in the theory of equations, in-particular it contained a wealth of results for cubic and quartic equations (cubic is x3, and quartic involves x4).
His flurry of research showed that the quadratic, cubic and quartic equations could all be solved by formulae involving only the operations +, -, ×, ÷, √ (the last one means the square root).
The formulae for solving cubics and quartics are long and tedious, but they certainly exist.
What has puzzled mathematicians is that they could not produce a formula for a quintic equation, (quintic involves x to the power of 5, x5).
What is so special about x to the power of 5?
1828 - Niels Abel
In 1826, Abel came up with an answer to the quintic equation conundrum. He proved a negative concept, which in my opinion is probably more difficult than proving something can be done.
He proved that there could not be a solution to solving all quintic equations and tried to convince top mathematicians.
This news took a long time to filter through to the mathematical world.
Even though some mathematicians refused to accept his result, people were still publishing his work well until the 19th century which claims to have found this non-existent formula.
The modern world
For 500 years algebra meant 'the theory of equations', but things started to develop in the 19th century. People realized that symbols in algebra could represent more than just numbers - they could represent 'prepositions' and so algebra could be related to the study of logic.
They could even represent higher-dimensional objects such as those found in matrix algebra. And, as you and many non-mathematicians have suspected, they can represent nothing at all and just be letters and symbols moved about according to certain formal rules.
1843 - William Rowan Hamilton
Hamilton, an Irishman discovered the quaternions in 1843. This was a significant event for modern algebra. He was trying to find a system of symbols that would extend two-dimensional complex numbers to higher dimensions. For many years he did try three-dimensional symbols, but with no satisfactory result.
When he used to come down for breakfast each morning, his sons would ask him, 'Well, Papa, can you multiply triplets?' and he would always answer that he could only add and subtract them.
Success came unexpectedly. He had an inspiration when he was walking along the Royal Canal to Dublin.
The three-dimensional hunt was a dead end and he should have gone for four-dimensional symbols. The 38 year old, Astronomer Royal of Ireland apparently carved the relations into the stone on Brougham Bridge. There is a plaque in his acknowledgment.
He lectured on it for years and published two books on his what he called, 'westward floating, mystic dream of four'.
1844 - Hermann Grassmann
In 1844, Hermann Grassman a German liguist and mathematician published another algebraic system. But with rather less drama than Hamilton.
His work was ignored and looked over but it turns out to be far reaching. Today both quaternions and Grassmanss's algebra have applications in geometry, physics and computer graphics.
In the 20th century the dominant example of algebra was the axiomatic method.
Euclid used this as a basis for geometry, but it wans't applied to algebra until comparatively recently.
1908 - Emmy Noether
Noether was the champion of abstract algebra. In particular the study of chain conditions on ideals of rings. The main idea is the study of structure where individual examples are secondary to the general abstract notion.
She was described by Hilbert and Einstein and others as the most important woman in the history of mathematics.
On this great note about Noether, we will end this subject, the history of algebra.
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Answer to: how many were going to St Ives? 1 of course
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