To most mathematicians, valuing intuition is not a new idea. While one of the most distinguishing qualities of mathematics is its rigor, to focus on this qualit

To most mathematicians, valuing intuition is not a new idea. While one of the most distinguishing qualities of mathematics is its rigor, to focus on this quality misses the big picture. Henri Poincare, arguably the greatest 20th century mathematician, said it best: "It is by logic we prove, it is by intuition we invent." This theme is echoed in many of his writings about creativity in mathematics. Turing's argument is beautiful and elegant, undoubtedly one of the gems of modern mathematics. However, the reason you don't see the intuition behind Turing's argument taught is that there is too much material to cover in a general theoretical computer science course. You need to be able to master the known material, to stand on the shoulders of giants, to make new advances in the discipline. This may not necessarily be the best way to encourage creativity and insight in computer science, but the hope is that interested students will delve deeper (like the author) and discover insights for themselves. Lastly, at least among many mathematicians, Turing may be up there with Euclid among the demigods of mathematics, but there are those that lie still higher, people like Gauss and Euler who have yet to be matched in terms of mathematical output and impact.