Science as we know it today developed greatly during the Renaissance.
This began after the development of the printing press by Gutenberg and the free spread of ideas among the people.
People like Copernicus and Galileo were able to get their ideas published and made known to the world.
On the Ottoman side, people like Taqi ad-Din and Piri Reis made significant progress in astronomical physics and geography respectively. But, the observatory built by Taqi ad-Din was demolished within three years of being built. After these progresses in the sixteenth century, there were not many contributions towards science from the Ottoman empire.
However, on the European side, the Renaissance led to the Enlightenment.
Thanks to enlightened rulers like Frederick the Great of Prussia, an atmosphere of encouragement towards learning and the sciences came about. Note that the Enlightenment was composed of more social thinkers than natural or scientific thinkers.
Anyhow, all these progresses finally led to the industrial revolution and today’s modern world.