Bold experiments and unique innovations in the field of mathematics were carried out by Muslim mathematicians who developed this science to an exceptionally high degree. Their contributions stretched from the end of the eighth(8th) century to about the middle of the fifteenth(15th) century. Al-Kharizmi was the inventor of Al-gebra (Algebra)
The regions from which the “Muslim mathematicians” came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain(Andulusia), and to the east as far as the borders of China.
Algebra may be said to have been invented by the Greeks, but according to Oelsner, “it was confined to furnishing amusement for the plays of the goblet”. Muslims developed it and applied it to higher purposes. Thus, the first great Muslim mathematician, the Muslim Al-Khawarizmi, invented the subject of algebra (al-Jabr), which gave mathematics a whole new dimension and development path so much broader in concept than before.
Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.
Al-Khawarizmi also introduced a method similar to long division to extract the square root (jithr) of a number. He was the first to introduce the concept of mal (power) for the squared unknown variable. He perfected and developed the geometric representations of quadratic equations having two variables, e.g the circle, ellipse, parabola and hyperbola (conic sections) etc. Al-Khawarizmi’s work, in Latin translation, brought the Arabic numerals along with the mathematics to Europe, through Spain (Andulusia) The word “algorithm” is derived from his name.
The Muslims invented the symbol for zero (The word “cipher” comes from Arabic sifr), and they organized the numbers into the decimal system – base 10. They invented spherical trigonometry, discovered the tangent and were first, “to introduce the sine of arc in Trigonometrical Calculations” Zero is an invaluable addition made to mathematical science by the Muslims.
They have also shown remarkable progress in mathematical geography.