[The Euclidean algorithm is] the granddaddy of all algorithms, because it is the oldest nontrivial algorithm that has survived to the present day.
I remember that mathematicians were telling me in the 1960s that they would recognize computer science as a mature discipline when it had 1,000 deep algorithms. I think we've probably reached 500.
The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.
I decry the current tendency to seek patents on algorithms. There are better ways to earn a living than to prevent other people from making use of one's contributions to computer science.
An algorithm must be seen to be believed.