Cosma’s review of Stephen Wolfram, linked to below, says that:
Wolfram refers incessantly to his “discovery” that simple rules can produce complex results. Now, the word “discovery” here is legitimate, but only in a special sense. When I took pre-calculus in high school, I came up with a method for solving systems of linear equations, independent of my textbook and my teacher: I discovered it. My teacher, more patient than I would be with adolescent arrogance, gently informed me that it was a standard technique, in any book on linear algebra, called “reduction to Jordan normal form”, after the man who discovered it in the 1800s. Wolfram discovered simple rules producing complexity in just the same way that I discovered Jordan normal form.
I’m in no sense of the word a mathematician, but I too made a “discovery” in my teenage years, and found out years later that I wasn’t alone – Samuel Beckett, since we’re already talking about him, describes the technique in Watt. In Beckett’s words:
In another place, he said, from another place, he might have told this story to its end, told the true identity of Mr Nackybal (his real name was Tisler and he lived in a room on the canal), told his method of cube-rooting in his head (he merely knew by heart the cubes of one to nine, and even this was not indispensable, and that one gives one, and two eight, and three seven, and four four, and five five, and six six, and seven three, and eight two, and nine nine, and of course nought nought).
In other words, each single digit number has an unique cube, and if you know this cube, and do a bit of memorization (e.g. that the numbers 0 to 9 have cubes between 0 and 729, that 10-20 have cubes between 1000 and 8,000, and so on), you can derive the cube roots of quite large sounding numbers very easily (as long as they’re whole numbers). For example, to figure out the cube root of 103,823, the final digit is a 3, which means that the final digit of the cube root is 7, and since 103,823 is between 64,000 (the cube of 40) and 125,000 (the cube of 50), the cube root has to be 47.
I’m presuming that if this trick occurred to me and Beckett independently, it must be common knowledge, but haven’t seen it written up anywhere else. I’d be curious to know if someone else (Martin Gardner???) has described it.