Because arithmetic is completely solved and boring, duh.
There was a time when it was at least a little bit interesting, and many mathematicians were actually quite good at it.
There was a time when it was at least a little bit interesting, and many mathematicians were actually quite good at it.
Richard Guy developed a single-scale nomogram based on elliptic curves in 01953: https://www.jstor.org/stable/3609499
His explanation is wonderfully simple; quoting the beginning: "Since the equation x³ + ax + b = 0 has zero for the sum of its roots, the x-coordinates of the three intersections of the line y = mx + c and the curve y = x³ + px + q add to zero." It may be entertaining to attempt to derive the rest of the nomogram from that sentence and the use of logarithms before consulting the (one-page) paper.
A nice advantage of Guy's contrivance over slide rules is its facility with squares and square roots. On a conventional Oughtred slide rule you can easily enough read off the square root of a number on the A or B scales by reading across the hairline to the D or C scales, respectively; but if your square had been computed on C or D, you are out of luck. Guy's nomogram has some similar limitations, but you can in general easily take the square root of any point on it.
What is the fastest way to multiply two integers? Prove there is no faster way.
Do the same for division.
There. That will keep any mathematician busy for a while.