Here is how Al-Khwarizmi (the father of Algebra) solves the equation x² + 10 x = 39 he writes (in the 800's):

... a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5 leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square.

The geometric proof by completing the square follows. Al-Khwarizmi starts with a square of side x, which therefore represents x² (Figure 1). To the square we must add 10x and this is done by adding four rectangles each of breadth 10/4 and length x to the square (Figure 2). Figure 2 has area x² + 10 x which is equal to 39. We now complete the square by adding the four little squares each of area ⁵/₂ ⁵/₂ = ²⁵/₄. Hence the outside square in Fig 3 has area 4 ²⁵/₄ + 39 = 25 + 39 = 64. The side of the square is therefore 8. But the side is of length

⁵/₂ + x + ⁵/₂ so x + 5 = 8, giving x = 3.

From: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Al-Khwarizmi.html

Other mathematicians born in Iran:

Al-Sijzi Wafa ; Al-Farisi ; Al-Kashi ; Al-Khazin  ; Nasir al-Tusi ;Sharaf al-Tusi; Khayyam; Al-Mahani; Al-Nasawi; Al-Nayrizi; Al-Quhi ; Ulugh Beg

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Non-European  scientists and scholars have contributed immensely to human knowledge especially in the period between 8th and 14th century CE. However, their contributions have been largely ignored, forgotten or have gone un-acknowledged. Below are some examples:

 Middle Eastern scientists and scholars

Yaqub Ibn Ishaq al-Kindi 800 Jabir Ibn Haiyan died 803 Mohammad Bin Musa al-Khawarizmi died 840 Thabit Ibn Qurra 836 Ali Ibn Rabban al-Tabari 838 Abu Abdullah al-Battani 858 Al-Farghani 860 Mohammad Ibn Zakariya al-Razi 864 Abu al-Nasr al-Farabi 870 Abul Hasan Ali al-Masu'di died 957 Abu al-Qasim al-Zahrawi (father of surgery)936 Abul Wafa Muhammad al-Buzjani 940 Abu Ali Hasan Ibn al-Haitham 965    Abu al-Hasan al-Mawardi 972 Abu Raihan al-Biruni 973

Abu Marwan Ibn Zuhr 1091 Al-Idrisi 1099    Ibn Rushd 1128       Abu Hamid al-Ghazali 1058   Jalal al-Din Rumi 1207    Ibn Sina (doctor of doctors) 980 Omar al-Khayyam 1044   Ibn al-Nafis 1213 Ibn Khaldun 1332 Ibn Battuta - the great traveller Al-Jazari   Ibn al-Baitar died 1248 Nasir al-Din al-Tusi 1201

About Eurocentric History of Mathematics

"The term Greek, when applied to times before Alexander  (356-323 BC), refers to a number of independent  City-states, often at war with one another but exhibiting close ethnic or cultural affinities and, above all , sharing a common language. The conquests of Alexander changed the situation dramatically, for at his death his empire was divided among his generals, who established separate dynasties, the two notable dynasties from the point of view of mathematics were the Ptolemaic dynasty of Egypt, and the Seleucid dynasty which ruled over territories that included the earlier sites of the Mesopotamian civilization. The most famous center of learning and trade became Alexandria in Egypt, established in 332 BC and named after the conqueror. From its foundation, one of its most striking features was its cosmopolitanisms part Egyptian and part Greek, with liberal sprinkling of Jews, Persians, Phoenicians and Babylonians, and even attracting scholars and traders from as faraway as India. A lively contact was maintained with the Seleucid dynasty. Alexandria thus became the meeting-place for ideas and different traditions. The character of Greek mathematics changed as a Jesuit of cross-fertilization between different mathematical traditions, notably the algebraic and empirical basis of Babylonian and Egyptian mathematics interacting with the geometric and anti-empirical traditions of Greek mathematics. And from this mixture came some of the greatest mathematicians of Antiquity, notably Archimedes and Diophantus."

From: The crest of the peacock  Non-European Roots of mathematics (George Cheverghese Joseph) 

From: The crest of the peacock  Non-European Roots of mathematics (George Cheverghese Joseph) 

Indian scientists and scholars

Aryabhata (476–550 CE)	Bhaskara I  (600 – 680 CE)  Bhāskara II (1114–1185)
Brahmagupta (598–668 CE)	Aryabhatiya (a Sanskrit astronomical treatise)
Halayudha (10th century)	The Bakhshali Manuscript
Mādhava(1350 –1425)	Karanapaddhati (an astronomical treatise)
Parameshvara	Yuktibhasa(the first textbook of calculus!)

Movies to watch about Iranians:

No one knows about Persian cats

The Circle

Crimson Gold

Offside

Ten

Persepolis

The keeper