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Ottoman science developed further owing to the personal interest of Mehmed II and the educational institutions which he established after the conquest of Istanbul. Consequently, some brilliant scholars emerged in the sixteenth century and made original contributions to science in this most vivid period of Ottoman history of science. Mehmed the Conqueror patronized the Islamic scholars and at the same time he ordered the Greek scholar from Trabzon Georgios Amirutzes and his son to translate the Geography book of Ptolemy into Arabic and to draw a world map. Mehmed II's interest in European culture had started while he was the own prince settled in the Manisa Palace. In 1445, Italian humanist Ciriaco d'Ancona and other Italians who were in the Palace taught him Roman and European history. While Patriarch Gennadious prepared his work on the Christian belief İ'tikad nâme (The Book on Belief) for the sultan, Francesco Berlinghieri and Roberto Valtorio wished to present their works Geographia and De re Militari. On the other hand, Mehmed II encouraged the scholars of his time to produce works in their special fields; e.g. for the comparison of al-Ghazzali's criticisms of peripatetic philosophers regarding metaphysical matters, expressed in his work titled Tahafut al-Falasifa (The Incoherence of the Philosophers), and Ibn Rushd's answers to these criticisms in his work Tahafut al-Tahafut (The Incoherence of Incoherence), he ordered two scholars of his time, Hocazade and 'Ala al-Din al-Tusi, each to write a work on this subject (Adıvar, 1983; İhsanoğlu, 1992/1). No doubt the most notable scientist of the Conqueror's period is Ali Kuşçu, a representative of the Samarkand tradition. The total number of his works on mathematics and astronomy is twelve. One of them is his commentary on the Zij-i Uluğ Bey in Persian. His two works in persian, namely, Risala fi'l-Hay'a (Treatise on Astronomy) and Risala Fi'l-Hisab (Treatise on Arithmetic) were taught in the Ottoman medreses. He rewrote these two works in Arabic with some additions under new titles, al-Fathiyya (Commemoration of Conquest) and al-Muhammadiyya (The Book dedicated to Sultan Muhammed), respectively. Another noteworthy scholar of the Bayezid II period (1481-1512) was Molla Lûtfi. He wrote a treatise about the classification of sciences titled Mawdu'at-Ulum (Subjects of the Sciences) in Arabic and compiled a book on geometry titled Tad'if al-Madhbah (Duplication of Cube) which was partly translated from Greek. Mîrîm Çelebi (d. 1525) who was a well known astronomer and mathematician of this period and the grandson of Ali Kuşçu and Kadızâde-i Rûmî, contributed to the establishment of the scientific traditions of mathematics and astronomy and was renowned for the commentary he wrote on the Zij of Uluğ Bey.

Scientific literature developed considerably in the period of Sultan Süleymân the Magnificent. We find two major mathematical books in Turkish entitled Jamal al-Kuttab wa Kamal al-Hussah (Beauty of Scribes and Perfection of Accountants) and 'Umdat al-Hisah (Treatise on arithmetic) by Nasuh al-Silahi al-Matraki (d. 971/1564). His book in Turkish entitled Beyân-ı Menâzil-i Sefer-i Irakeyn (Description of the Stopping Places of the Campaign to the Two Iraqs), related to geography, should also be mentioned. Musa b. Hamun (d. 1554), one of the famous Jewish physicians from Andalusian descent, was appointed as Sultan Süleymân's physician and wrote the first Turkish and one of the earliest independent works on dentistry which is based on Greek, Islamic, and Uighur Turkish medical sources and in particular Sabuncuoğlu Ceerefeddin's works (Terzioğlu, 1977). In the sixteenth century, important works on astronomy were written by the representatives of the Egypt-Damascus tradition of astronomy-mathematics. The greatest astronomer of this period was Taki al-Din al-Rasid (d. 1585) who combined the Egyptian-Damascus and Samarkand traditions of astronomy and mathematics in his studies. He wrote more than thirty books in Arabic on the subjects of mathematics, astronomy, mechanics, and medicine.

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