Many of the most important scientific theories that exist today were made possible by glass. Modern medicine owes its existence largely to the invention of the microscope. Telescopes played a crucial role in the development of astronomy, and it is hard to see how modern chemistry could have evolved without the ability to study chemical reactions in a glass vessel. Observing a chemical reaction from above a pot of boiling liquid isn't a good idea. You need to be able to observe chemical reactions without breathing in poisonous fumes or getting steam in your face.
Astronomy as a science is essential for several reasons. It played a crucial role in the development of nautical sciences, such as how to navigate by the moon, sun, planets, and sun (celestial navigation). Perhaps an even more important reason is that it allowed the development of the theory of gravity by Sir Isaac Newton. The theory of gravity brought forth a revolutionary new idea: Local events on our planet, such as an apple falling to the ground, happens for the same reason that planets and moons move in orbits. Newton was able to connect phenomena that look very different and happen at very different scale. Nobody had done that kind of connection before. That is the essence of science. Scientific theories have a way of connecting numerous phenomena which look entirely unrelated to the untrained eye and unify them into a single theory. Scottish physicist James Clerk Maxwell for instance connected electricity, magnetism, and light into one theory.
Let us not get carried away about scientific theories. The point is that a single innovation can have a long series of knock-on effects. Let us start at the beginning.
Glassmakers in Venice and Florence began grinding and polishing glass to make lenses for spectacles in the mid 13th century. They could not have imagined that their trade would spread to the Netherlands through trade networks. There, somebody would get the idea in 1595 to put two spectacle lenses after each other and create the first compound optical microscope. Decades later, in the 1670s, Antonie van Leeuwenhoek would see microorganism, bacteria, red blood cells and muscle fibers through a microscope he made with strong lenses. His discovery opens the door for modern medical science. Until he made his discovery, microorganisms were unknown. Ironically, he wasn't even a scientist. He was a businessman who wanted to quality check the fibers of the textiles he sold.
Another discovery was made within the Dutch spectacle-making centers in 1608: The refracting telescope. Only a year later in 1609 famous Italian scientist Galileo Galilei constructed a telescope with 8-9 times magnification which allowed him to study craters and mountain ranges on the moon. He was even able to discover the four largest moons of Jupiter.
A microscope is made by combining two convex lenses, while a telescope is obtained by combining a concave and a convex lens. Telescopes allowed the construction of a variety of instruments:
Sextant – Evolved from the octant. Used to measure the angle between the horizon and a celestial object (moon, sun, star, or planet). Initially used to help ships navigate, but later adopted for use in airships, airplanes, and even early astronauts in outer-space.
Theodolite – Used in land surveying. Coordinates of different features in the landscape can be determined by measuring the horizontal and vertical angle to that point.
Nautical telescope – For use in navigation at sea.
Astronomer's telescope – Looking at stars and planets.
Glass in general has had many important applications in Science. Newton used a glass prism to discover that white light is composed of many colors. Glass allowed construction of vacuum chambers which helped in the development of pneumatics, understanding gasses and thermodynamics which laid the foundation for steam engines. Glass made it possible to construct thermometers and barometers.
Magnifying glasses have been used in a variety of industries for quality control: Inspecting quality of fibers, metal work, map making and printing.
Cameras and their forerunner the Camera obscura were made possible with glass lenses. An obscura is like a camera without a photosensitive film. Instead, the camera image is projected onto a canvas and a painter has to manually trace the image seen and apply paint.
It is not accident that the period where the spectacle industry established itself in the Netherlands, they also became famous for their painters such as Vermeer is believed to have used a Camera obscura to create realistic paintings. In fact, art historians remark that there is a noticeable and dramatic increase in the realism of paintings around the time lenses become prevalent in Europe. In Asia, where there was very limited usage of lenses there was no such transition to realistic art.
One might ask what relevance does science have to art? In the early modern period, art and science were very much interwoven. The study of light and optics was of interest to artists seeking to make realistic paintings. It is no coincidence that Leonardo da Vinci was both a painter, scientist, and engineer.
Perhaps the most overlooked significance to science was the spectacles. Before spectacles, learned men and women would have to give up their pursuit of knowledge as their deteriorating eyesight would prevent them from reading books and studying things in detail. Without glasses, scientists, engineers, and artists became handicapped when their knowledge and skill was often at its peak. Spectacles added another 10-15 productive years to the intellectual life of learned men and women.
Long before lend grinding was mastered in the 8th century, sandglasses were in use in Europe, possibly as early as Ancient Greece and Rome. For centuries, sandglasses offered the only moderately accurate way of measuring time at sea. Sandglasses are considerably more accurate than water clocks, which work poorly at sea. With a sandglass, navigators could measure the speed of the ship and thus estimate their position. To better understand how this estimation was done, read about dead reckoning.
In short, our modern world owes a lot to this simple substance made from melted quartz sand.