why is it that we can burn diamond in liquid oxygen and not glass?

Diamonds have a reputation for being invincible and their very stiff sp3 hybrid bonds dense fd3m crystal structure lets them deserve some of that, but in the end you are correct and they are just carbon.

A pile of burning diamonds.

Antonie Lavoisier did an experiment where he put a diamond in a sealed jar and focusing a colossal magnifying glass on it. The diamond burned up completely, but the mass of the jar did not change. Curiously, diamonds heated in jars from which the "phlogiston" (oxygen) (Lavoisier already knew phlogiston theory was wrong from other experiments, but did not use the word oxygen until 1778) had been depleted using charcoal would refuse to burn.

This led to the discovery of all sorts of important things about combustion and chemistry, such as the idea that diamonds were carbon and hints at the existence of oxygen as an element.

If you do not have a magnifying glass the size of a car but still want to see a diamond burn, you can heat a diamond until it glows with a handheld torch and either drop it in liquid oxygen or blow a puff of pure oxygen gas on it.EDIT: To stop the inbox flood, the phlogiston theory featured the idea that combustible objects contained a substance that would allow them to burn and be released into the air. It was thought that objects in a sealed container stopped burning because the air had become saturated with phlogiston. People had already noticed that burning metals gained mass, which led people to think that the theory had to be backwards and the substance that allowed combustion was part of air. This evolved into an understanding of oxygen

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