Yes, diamond can be burned. The most common form of burning in everyday life is carbon combustion. In carbon combustion, carbon atoms break their bonds with each other and with other atoms (which requires energy) to form bonds with oxygen atoms (which releases even more energy than first required) (https://wtamu.edu/~cbaird/sq/mobile/2013/06/27/when-does-the-breaking-of-chemical-bonds-release-energy/) . The net extra energy released in this reaction can then go on to rip more carbon atoms free of their non-oxygen neighbors, thus continuing the reaction, or the energy can escape as heat and light. Carbon bonded with oxygen makes carbon dioxide and carbon monoxide, which are the waste products of combustion. They drift away from the fire as gases. Since biological organisms, and the fuels derived from biological organisms, contain a lot of carbon, much of the burning that goes on around us is carbon combustion. This includes camp fires, candles, car engines, and gas stoves. Pure diamond consists only of carbon atoms bonded into a dense, strong crystal lattice, so diamond can also undergo carbon combustion. In fact, Antoine Lavoisier first determined that diamond is made out of carbon by burning it and showing that the combustion product was carbon dioxide. The book Diamond Films and Coatings (http://books.google.com/books?id=0-xTAAAAMAAJ) by Robert Foster Davis states, "In 1772 the French chemist Antoine L. Lavoisier found that the products of diamond combustion behaved as, and most assuredly were, solely carbon dioxide..