If diamonds are just lumps of precisely-structured carbon, why don't they burn? Actually, they do. And proving that they do is one of the things that cost a famous scientist his life.
I wrote last week about Antoine Lavoisier, who died, in part, because he had mocked the scientific discoveries of someone who became one of the leaders in the French revolution. One of the charges leveled against Lavoisier — just before he got his head and body forcibly separated — was his aristocratic extravagance. He had done the one thing more profligate than setting money on fire; he'd set a diamond on fire. The fact that he had done it to prove that diamonds are carbon, and that matter is conserved in chemical reactions, carried no weight with the leaders of the revolution, but it does have some significance to us.
Diamonds don't burst into flame under normal circumstances. Fire, also called oxidation, involves pieces of a material combining with oxygen as they break off from the main body of the material. The process needs heat, and getting the right amount of heat and oxygen is key. Although diamonds can burn at temperatures reached by a regular welding torch, generally there isn't enough of a ready supply of oxygen in the atmosphere. Lavoisier heated a diamond in a flask of pure oxygen. It burned away to smoke. He then took another diamond, put it in a vacuum, and heated it to the same temperature. Nothing happened. He had demonstrated that diamonds were flammable carbon. He had also taken steps toward proving that mass didn't disappear when heated. It combined with oxygen and blew away as smoke.
People still do the burning diamond demonstration today. All it takes is a source of pure oxygen gas and a torch. As the diamond heats up, it will glow. Squirting little sips of oxygen gas at it allows it to burn in small increments. Then again, if you want to go all out, you can always drop the diamond in liquid oxygen. Suddenly, instead of one glowing stone, you have a fountain of burning diamond.