Contrary to what we believed until today, ‘algebra’ is not an arabic innovation. A new study proves that, much earlier, the ancient Greeks have invented ‘algebric’ ways to solve practical problems.
If you want to have success while searching old manuscripts, it would be good to obtain some of the qualifications that old knitters had! An eye trained to details, observingness, concentration, discipline, patience, good knowledge of every stitch and every little mark you may meet, it is worthy to give importance even to the margins, to have a sense of the complete work, additionally some experience, maybe some luck, and definetly infinite time!
Fortunately, there are still people interested to pass not only days or weeks, but even years doing this, even without reward; and university Professors, too, who besides providing guidance, can evaluate a possible find.
“I found something which I think you will find interesting. In Theon’s commentary, in book 13 of ‘Syntaxis’, in many points there is the quote ζήτει το εξής εν τοις σχολίοις’…”.
This is how an email from the (then) candidate Dr. Ioanna Skoura to her Professor, Jean Christianidis (deputy Professor in History of Mathematics in the special section of Theory of Science), started. The Professor from his side, being himself one of the most devoted scholars of Diophantus, realized from the beginning that this ‘something’ would interest many more people than the few specialized sholars of Ptolemy, Diophantus, Theon’s commentary and of the later Greek antiquity. He realized that it would give a new dimension to the opinion related to the ability of usage, by the Greek mathematicians, of ‘algebric’ problem-solving methods. Centuries before the Arabs present their own, undoubtedly useful, systematization of ‘algebric’ methods, after the 9th century AD.
The leap to equations
As mr. Christianidis explains, there is a general tug-of-war in universal level related to the contribution of Arabs towards what we call ‘algebra’. The quotation marks are put so that it is stressed that we are not talking about the complete shape of the edifice we know today, as a separate branch of Mathematics, with positive and negative numbers, with variables and parameters, with theorems about groups, rings and bodies. What took the name ‘algebra’ was in its nucleus an expression with equations, of a general way to solve problems. In a few words, Greek mathematicians had found, already from Diophantus’ era (and we cannot estimate how much earlier), the way to solve practical problems by ‘translating’ the practical problem to an equation, something proportional to our modern ‘unknown X’. The importance of the discovery by Christianidis and Skoura lays on the fact that it was found and proved that Theon used the ‘algebric’ methods of Diophantus in other fields, too. Most likely, it was in common use for the people of the time for the solving of practical arithmetic problems. What he did was that he proceeded to the solution of a purely geometrical metering problem, from Astronomy, related to the trajectory of planet Mars, converting it to an equation. It is the first time something like this is confirmed, with the help of the manuscript and the comments engraved on it. As an important consequence, we must look somewhere else for the roots of this pre-modern ‘algebra’, rather than the ones believed until today.
One school of sholars still insists that all has begun by the Arabs and that before them there was nothing relative to the mathematical thinking in ‘algebric’ terms. Against this view stood another absolute school, claiming that the Arabs did nothing more than translating and preserving texts and they didn’t add a single line to the body of already known mathematical theories. Now, after the find of the two Greek mathematicians was published in one of the strictest Journals, in the Japanese SCIAMVS (14, 2013 41-57), we can so-forth claim that the basic roots of ‘algebra’ must be traced in a different direction. Diophantus and Theon show this direction.
(NovoScriptorium: Please find and read the actual paper here http://www.academia.edu/11436349/Solving_problems_by_algebra_in_late_antiquity_New_evidence_from_an_unpublished_fragment_of_Theons_commentary_on_the_Almagest)