What is the smallest unit of matter that keeps an element's identity?

The atom. Split it and you no longer have the same element - what makes an atom gold rather than lead is nothing but the number of protons in its nucleus, 79 against 82. Everything the alchemists tried failed because they were doing chemistry, which only rearranges how atoms bond, and the answer was in the nucleus where chemistry cannot reach.

The name is a promise the word could not keep. Atomos is Greek for uncuttable, coined by Democritus around 400 BC as a philosophical argument that matter cannot be divided forever. When chemists in the nineteenth century adopted it they believed the same thing, and then the electron turned up in 1897, the nucleus in 1909, and the nucleus itself turned out to be made of protons and neutrons made of quarks.

You can now see individual atoms. A scanning tunnelling microscope, invented in 1981, drags a tip one atom wide across a surface and maps it - and IBM used one in 1989 to spell out its own logo in 35 xenon atoms, the smallest advertisement ever made.