Henry Smith was a mathematician of the 19th century who worked mainly in number theory. He especially did important work on the representation of numbers by various quadratic forms. We have discussed how even in something seemingly settled, like Joseph Lagrange’s theorem that every natural number is representable as a sum of four squares, new questions are always around—especially when one considers complexity.

Today Ken and I want to discuss a private slip of forgetfulness, and how often others may have done the same.

For a variety of reasons we recently were thinking about one of the most basic questions in linear algebra: the solvability of

$latex displaystyle Ax = b, &fg=000000$

where $latex {A}&fg=000000$ and $latex {b}&fg=000000$ are fixed and $latex {x}&fg=000000$ is to be determined. Over a field there is a polynomial time algorithm that determines whether there is a solution and finds one if there is. The…