Fun facts, the patron of Almagest Abassid Caliph Al-Ma'mun was also the founder of Baitul Hikmah in Baghdad that was aggressively translating important foreign manuscripts due to weight gold equivalence for Greek/Indian/etc manucsripts translation compensation [1],[2].
According to history, the Caliph once back off his plan of conquering Constantinople (that were later achieved by Ottoman Caliph Fatih) due the Roman (Byzantine) offered him an offer he cannot refused, the original copy of Ptolemy Almagest as important part of the truce arrangements. He certainly capable of overcoming and conquering the Constatinople since during his time, Afghanistan was conquered under Islamic rule for hundred of years that modern Russia and USA cannot achieved. The fact that his mother Marajil, was a princess originally from Afghanistan. This is where the popular saying that asserted only Afghanistan people can conquer Afghanistan. Point in case, the most recent Afghanistan conqurer was Mughal Empire, who was originated from Indian sub-continent Afghanistan. During his time, Al-Khwarizmi published his infamous Algebra book namely Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah (The Concise Book of Calculation by Restoration and Balancing), where we got the word algebra, and from his name Al-Khwarizmi now we have the word "algorithm" [2].
In addition to having translation Baitul Hikmah in Baghdad, Iraq and in other Islamic knowledge center in Toledo Spain (before fall to Spanish Christian and started the European Renaissance), the Islamic civilization also engaged in contributing to science, math, astronomy, etc. Al-Haitham (Alhazen), the founder of optics, and he's also the founder of modern scientific methodology [3].
Having said that, there several Islamic astronomers (Arab/Persian/etc) already proposing against the geocentric idea that most probably that was inspired Galileo. I think he most probably did not come with the original idea of heliocentric model and the Islamic astromoners mosy probably have proposed it before Galileo, but he failed to credit them properly as normally practiced by European scientists at the time.
[1] al-Ma'mun:
https://en.wikipedia.org/wiki/Al-Ma%27mun
[2] Graeco-Arabic translation movement:
https://en.wikipedia.org/wiki/Graeco-Arabic_translation_move...
[3] Ibn al-Haytham:
Beyond the facts corrected by other user, graemep, the translator school was in fact established after the christian kingdom of Castile conquer the city of Toledo, and the king Alfonso X [1], actually is what is studied as main promoter of it. [1] https://en.wikipedia.org/wiki/Toledo_School_of_Translator
Then, first heliocentrism with some approximations of size and distance, as far as I know was Aristarchus of Samos, but there is not much that we know about it. [2] https://en.wikipedia.org/wiki/Aristarchus_of_Samos
> Al-Khwarizmi published his infamous algebra book
Math can be hard, but calling that book "infamous" is a bit too much... /s
There are a number of factual mistakes, misleading/unclear statements and speculation in your "fun facts".
Al-Ma'mun failed to conquer Byzantium and died while preparing his next attempt to do so: https://en.wikipedia.org/wiki/Al-Ma'mun
He cannot possibly have been the patron of the Almagest as Ptolemy lived centuries before he did. Maybe you mean of a translation.
Everyone knows Galileo did not originate a heliocentric model, because he was promoting the Copernican model.
Heliocentric models had been proposed by ancient Greeks, but the Copernican model was a huge advance. There is big difference between just speculating that the sun was the centre of the the universe and an actual mathematical mode.
There is a lot more to the scientific method than al-Haytham's minor contribution: https://en.wikipedia.org/wiki/Scientific_method