For the record the word Algebra comes from the title of a book wriiten somewhere between 750 and 850 AD by an arab scholar in the Dar al-Hikma in Baghdad.

The book was entitled

al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala

(A handbook of calculation by completion and reduction)

In it he restudies an equation first studied by Diophantus (the Greek) some 600 years earlier.

The author, al-Khwarizimi was responsible for another book introducing the indian decimal number system and its place settings to the middle east and was much copied at this time in europe by medieval scholars as the 'new arithmetic'

These european scholars called themselves 'algorismists'.

Which word was later to become our present day usage algorithm.

3 minutes ago, studiot said:

Which word was later to become our present day usage algorithm.

Indeed, and quite possibly similarly misunderstood...

On 8/10/2025 at 6:37 AM, Sensei said:

That would be difficult, because Algegra is an Islamic word..

Tr

On 8/10/2025 at 6:37 AM, Sensei said:

That would be difficult, because Algegra is an Islamic word..

The thread is intended to be provocative and inspire discussion of the infinite possibilities. It helps to understand our past and consider the future.

47 minutes ago, Eric Smith said:

The thread is intended to be provocative and inspire discussion of the infinite possibilities. It helps to understand our past and consider the future.

On 8/2/2025 at 8:26 PM, Eric Smith said:

Consider the following.

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks. How would that knowledge hurt their development of geometry and how would it have helped further the advancement of algebra.

How would our world be different today?

The point is that neither the Greeks nor the Arabs had a suitable system to take advantage of algebra as we know it.

Both were missing something to complete the picture.

It is quite natural for Geometry to come first as we can draw representations and take measurements.

But to perform calculations you need two more things.

You need a suitable system of symbols

And of course you need a suitable system of numbers.

The Greeks had a suitable of symbols, but did not have a suitable system of numbers.

The Arabs on the other hand had no system of symbols, all their problems were written in words.

But they had borowed a suitable system of numbers from further East in India.

These were combined by European scholars between the 13th and 15 centuries AD.

Here is a simple quadratic equation as we would write it any time after about 1500 AD, followed by its form in Greek as solved by Diophantus (about 230 AD) and as it appears in Al-Khwarizmi's book about 830 AD (English translation of the words).

Having a unified system for exchanging information between different scientists from different countries obviously speeds up the development process. But first, you need to have this exchange of information between people from different countries. In ancient times, only rulers and perhaps merchants exchanged messages. Most people could not read or write.

On 8/15/2025 at 2:08 AM, studiot said:

The point is that neither the Greeks nor the Arabs had a suitable system to take advantage of algebra as we know it.

Both were missing something to complete the picture.

It is quite natural for Geometry to come first as we can draw representations and take measurements.

But to perform calculations you need two more things.

You need a suitable system of symbols

And of course you need a suitable system of numbers.

The Greeks had a suitable of symbols, but did not have a suitable system of numbers.

The Arabs on the other hand had no system of symbols, all their problems were written in words.

But they had borowed a suitable system of numbers from further East in India.

These were combined by European scholars between the 13th and 15 centuries AD.

Here is a simple quadratic equation as we would write it any time after about 1500 AD, followed by its form in Greek as solved by Diophantus (about 230 AD) and as it appears in Al-Khwarizmi's book about 830 AD (English translation of the words).

I love the story of these silent revolutions.

Wasn't the last step due to François Viète in the 16^th century?

1 hour ago, Sensei said:

Having a unified system for exchanging information between different scientists from different countries obviously speeds up the development process. But first, you need to have this exchange of information between people from different countries. In ancient times, only rulers and perhaps merchants exchanged messages. Most people could not read or write.

yes I agree +1.

Interestingly 21 century anthropological research suggests that the very significant chnage from 'picture writing' - one symbol per word, all different ie many many symbols - to an 'alphabet' to use over and over again to make up words occurrred during the time of the construction of the Great Pyramids 0f Egypt, about 3000 BC.
The interesting thing is that it was not an invention of the scribes of the day but an invention of slaves or near slaves who worked the turqoise and copper mines of Egypt.
They scratched copied the magnificent carved 'glyphs' of the rulers but could only scratch crude abbreviations into the rocks of the mineworkings and caves they lived in.

The last programme of the BBC series I linked to and some members turned their noses up at showed how these scratches became letters and morphed into alpha beta etc over time.

1 hour ago, joigus said:

I love the story of these silent revolutions.

Wasn't the last step due to François Viète in the 16^th century?

Well really it was an ongoing accelerating process from Fibonacci (Leonardo of Pisa ) on.
Several other italian algebraicists - and one frenchman who introduced superscript or index notation - worked on it and published books etc before Viete and Descartes.

That acceleration has continued to this day.

I'm sure you would enjoy both these algebra study books.