The task that motivated Atanasoff?s construction of the first electronic digital computer has a mathematical legacy going back thousands of years, and it remains the fundamental operation by which computers are measured; solving systems of linear equations. This is sometimes misconstrued as a "special purpose" form of computing, but is actually as general in application as is any basic block of source code involving the four arithmetic operations +, -, ?, and ?. Systems built for this function share many architectural features; 70 years after Atanasoff conceived the ABC, ClearSpeed is building hardware for the solution of the exact same type of calculation, but trillions of times faster. The quest for linear solvers has motivated some of the most important innovations in computing history.