Amateur comes from the Latin amar which means to love. An amateur is someone who does something for pleasure rather than money. Sometimes people use it to mean a novice or someone who is unskilled but in this case the original meaning applies.

I think amateur in this case refers to non-professional / research mathematician with a PhD working at a University or a Research Institute. You still need to have some serious math chops to get this kind of result, it just isn't reflected in your official title or degree.

"Independent" might be a better adjective for someone like that.

If you're not doing it for profit, you're an amateur. Independent would suggest he could still doing math professionally but on a contract or otherwise unaffiliated basis.

Hmm, that is a definition of amateur; just as "professional" can mean you make a living from it.

However amateur often means - in British English - simply "low skilled" as professional can mean "formally carried out with high competence".

IIRC this guy or his associates dug up soil from a medieval burial site near Cambridge (England) to try and find a bacterial enzyme capable of breaking down 7-ketocholesterol (and hence potentially to cure artherosclerosis). Maybe not Indiana Jones but certainly ingenius and intrepid!