We all have something of Al-Marrakushi in us
A 13th century mathematician, Ibn al-Banna’ al-Marrkushi is part of a long lineage that began with Al Khawarizmi. He stood out more for his conceptual approach than for his erudition.
More than 50 treatises are attributed to him, including a “book of the foundations and preliminaries of the art of algebra”, a course dictated to his students under the title of a “brief exposition of the operations of calculation”, as well as a commentary and demonstration of his previous work entitled “lifting the veil on the different calculation processes”.
Prolix author of difficult access, due to the absence of any symbolism in the use of mathematics of the time, (the resolution of an equation in the form being identical to a literary text), Ibn al-Banna’ al-Marrakushi made algebra an art of truth on a theoretical level and a science of truth on a practical level.
By an approach more inclusive than exploratory, Ibn al-Banna’ al-Marrakushi brought together, on the one hand, the thought of Plato who sees in mathematics the underlying of all sciences, and Aristotle who compartmentalizes the sciences among themselves. , seeing in geometry and arithmetic only a view of the mind.
We owe him, among other things, a holistic description of numbers in place of a definition, a detachment from geometric representations in the algebraic demonstration, the extension of its operations to zero, as well as the non-utilitarian use of mathematics outside usual fields of application (sharing of inheritance, measurement of land, level of an irrigation canal, etc.).
He was also the first to establish the principle of the fraction as the ratio between two numbers, and above all an algorithm for extracting square roots with congruence criteria to determine those relating to a whole number or perfect squares.
Ibn al-Banna’ al-Marrakushi also maintained a metaphysical relationship with number, considering that it is a primary element linked to our human consciousness. Unity would be the source, then becoming a principle which would have no prerequisites.
The parallel between the number and the fitra of the Muslim on the one hand, and between the numerical unit and the tawhid on the other hand, seems to appear implicitly. Ibn al-Banna’ al-Marrakushi is therefore deeply imbued with his cultural environment, seeking to find a logical foundation there, including in decimal numbering. Ibn al-Banna’ al-Marrakushi thus attempted to build concordance in all things, without concordism, between his convictions and mathematics.
Passed to posterity in complete discretion, Ibn al-Banna’ al-Marrakushi, whose name was attributed by the International Astronomical Union to a lunar crater in 1976, is in the image of his “Talkhis Amal Al Hissab”, introduced in 1865 by A. Marre, with what could have been an epitaph: “contrary to what is seen every day in the world, but in accordance with what is sometimes found in Arabic manuscripts preserved in our libraries, the label announces less than reality and the precious volume gives more than it promises“.