All of the scientists that you have mentioned belonged to Bihar, Rajhastan, Karnataka and Bengal etc. And the ‘brutal’ islamic invasions invasions of Ghaznavi and Ghauri were limited to Western part of India. I dont think the two were interested in ruling the areas they invaded.
Anyways, as far as moghuls are concerned.
The Mughal legacy | DAWN.COM
Leitner’s report of 1882 confirms the educational status of just the Punjab as having 330,000 pupils learning “all the sciences in Arabic and Sanskrit schools and colleges, as well as Oriental literature, Oriental law, Logic, Philosophy and Medicine were taught to the highest standard”. After 1857, when the British system of education took hold the number of pupils taking this form of education diminished to 190,000. Nevertheless, Leitner’s analysis of the indigenous system of education proved that it was far superior to that set by the British in 1835 with Macaulay’s Minute on Education for the Indian colony.
How then was education delivered in Mughal times? Firstly, schooling of Mughal princes was taken very seriously. Great importance was given to an all round education of the princes with the study of logic, philosophy, mathematics, astronomy, law and medicine. Particular emphasis was put on female education by Mughal emperors and most princesses were highly educated, too. Secondly, almost all Mughal emperors encouraged education by setting up schools and seminaries with generous grants to scholars, writers, poets and teachers to keep up the high standard of education.
Although Akbar was unlettered, he gave much thought to education, syllabi and their content, and the teaching methodology for his subjects. Ain-i-Akbari records that there were 52 universities in and around Thatta in Sind during Jehangir’s time. Poets and historians have left outstanding literary works in prose, poetry, history and religious study. Mughal emperors Babar and Jehangir wrote their own biographies — Tuzk-i-Barbari and Tuzk-i-Jehangiri. Under Aurangzeb, the Fatwa-i-Alamgiri was compiled which added to the literature on Muslim law. Most books were transcribed by hand, yet a personal library was essential for a Mughal scholar as well as a Mughal nobleman. In 1641, the library at Agra contained 24,000 volumes and was valued at six and a half million rupees. When the Imperial Library at Delhi was torched by the British in 1803, the vast accumulated knowledge of the Mughal Empire was lost forever.
Literacy in Mughal times is gauged by a reading public among whom the most commonly read books were Gulistan, Bostan, Akhlaq-i-Nasiri and Anwaar-i-Suhaili. Education is also visible in the conduct of governance and administration. Ministers were well read and the empire functioned effectively with separate departments dealing with Agriculture, Trade, Justice, Education, Military and the running of the royal households. Law and order was maintained throughout the empire with justice accorded by Qazis and Muftis, a system later emulated by the British.
education : The Mughal period – Britannica Online Encyclopedia
THE MUGHAL PERIOD
The credit for organizing education on a systematic basis goes to Akbar (1542–1605), a contemporary of Queen Elizabeth I of England and undoubtedly the greatest of Mughal emperors. He treated all his subjects alike and opened a large number of schools and colleges for Muslims as well as for Hindus throughout his empire. He also introduced a few curricular changes, based on students’ individual needs and the practical necessities of life. The scope of the curriculum was so widened as to enable every student to receive education according to his religion and views of life. (100 of 123,990 words)