Mythbusters attempted to replicate the 'death ray' and was not successful. It's highly likely that the death ray is a myth

Technically, Archimedes was an engineer and mathematician. I don't think "scientist" existed as a category at the time (wikipedia mentions him as science and the section on scientist mentions that indeed the concept didn't exist in classical antiquity).

Archimedes was notable for having developed an approach like calculus for discovering the areas of conic sections.

https://en.wikipedia.org/wiki/Archimedes

Interesting. From your link:

Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity.

As I mention above, I also mention above that the link to "scientist" says the concept doesn't apply to classical antiquity.

Shrug.