Howard Aiken on the uses of computers, 1955:
If it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincide with the basic logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered.
Update: Some people have read the quote above and thought Aiken was ignorant of the work of Turing et al. I assumed he was speaking in terms of what was practical rather than what was possible, which is apparently correct.
Thanks to Anatoly Vorobey in the comments below, I found a paper that goes into more background. From that paper:
Aiken’s theme in the lecture … was that a machine designed primarily for scientific use was far from ideal for business computing. … For example, scientific computing (Aiken pointed out) involves relatively small amounts of data and complex processing, whereas business computing involves large amounts of data and relatively shallow processing.