In 1657, Fermat challenged William Brouncker, of Castle Lynn in Ireland, and John Wallis to find integral solutions to the equations $$x^2 − 151y^2 = 1$$ and $$x^2 − 313y^2 = −1.$$ He ( Fermat ) cautioned them not to submit rational solutions because even the lowest type of arithmetician could devise such answers.

"An Introduction to Diophantine Equations, A Problem-Based Approach, Andreescu, Andrica & Cucurezeanu, Springer 2010"

Considering that Fermat used the qualification

**the lowest type of arithmetician**there must have been a ranking in the computational branch those days. Until at least WW2, a computer, was the job description of someone who did "computational work" in banking, insurance, trading, logistics and what have you. Jobs like that exist even now, think of the actuarial sciences, but most of them if not all require a degree in mathematics. I am not sure but I suppose that in Fermat's days there must have been people responsible for the basic addition and multiplication type of calculations. Fermat called them "arithmeticians, of the lowest kind".

I am speculating of course. Fermat could have been a terrible arrogant man looking down on the working class. Considering that he was not a mathematician himself but that he wrote, on his own initiative, letters to the great minds of his time says at least something of his self-image.

Link: My previous post on Fermat

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