It deals with a game that [Theodore] Roosevelt and I used to play at Sagamore Hill. After an evening of talk, perhaps about the fringes of knowledge, or some new possibility of climbing inside the minds and senses of animals, we would go out on the lawn, where we took turns at an amusing little astronomical rite. We searched until we found, with or without glasses, the faint, heavenly spot of light-mist beyond the lower left-hand corner of the Great Square of Pegasus, when one or the other of us would then recite:

That is the Spiral Galaxy of Andromeda.
It is as large as our Milky Way.
It is one of a hundred million galaxies.
It is 750,000 light-years away.
It consists of one hundred billion suns, each larger than our sun.

After an interval Colonel Roosevelt would grin at me and say: ‘Now I think we are small enough! Let’s go to bed.’

— William Beebe, The Book of Naturalists, 1944

To divide 8101265822784 by 8, move the 8 from the number’s head to its tail.

To multiply 1034482758620689655172413793 by 3, move the 3 from the tail to the head.

During the Russian revolution, the mathematical physicist Igor Tamm was seized by anti-communist vigilantes at a village near Odessa where he had gone to barter for food. They suspected he was an anti-Ukrainian communist agitator and dragged him off to their leader.

Asked what he did for a living, he said he was a mathematician. The sceptical gang leader began to finger the bullets and grenades slung round his neck. ‘All right,’ he said, ‘calculate the error when the Taylor series approximation to a function is truncated after n terms. Do this and you will go free. Fail and you will be shot.’ Tamm slowly calculated the answer in the dust with his quivering finger. When he had finished, the bandit cast his eye over the answer and waved him on his way.

Tamm won the 1958 Nobel prize for physics but he never did discover the identity of the unusual bandit leader.

— John Barrow, “It’s All Platonic Pi in the Sky,” The Times Educational Supplement, May 11, 1993

Suppose we illustrate. You put a ball on a billiard-table, and, holding the cue lengthwise from side to side of the table, push the ball across the cloth. Here, in a rough way, the ball represents the ship, the cue the wind, only, as there is no waste of energy, the ball travels at the same rate as the cue; evidently it cannot go any faster. Now, let us suppose that a groove is cut diagonally across the table, from one corner-pocket to the other, and that the ball rolls in the groove. Propelled in the same way as before, the ball will now travel along the groove (and along the cue) in the same time as the cue takes to move across the table. The groove is much longer than the width of the table, double as long, in fact. The ball, therefore, travels much faster than the cue which impels it, since it covers double the distance in the same time. Just so does the tacking ship sail faster than the wind.

— “Some Famous Paradoxes,” The Illustrated American, Nov. 1, 1890

A pleasant anecdote is told of Partridge, the celebrated almanac maker. In traveling on horseback into the country he stopped for his dinner at an inn, and afterward called for his horse that he might reach the next town, where he intended to sleep. ‘If you would take my advice, sir,’ said the ostler, as he was about to mount his horse, ‘you will stay where you are for the night, as you will surely be overtaken by a pelting rain.’ ‘Nonsense, nonsense,’ said the almanac maker, ‘there is sixpence for you, my honest fellow, and good afternoon to you.’ He proceeded on his journey, and sure enough he was well drenched in a heavy shower. Partridge was struck with the man’s prediction, and being always intent on the interest of his almanac, he rode back on the instant, and was received by the ostler with a broad grin. ‘Well, sir, you see I was right after all.’ ‘Yes, my lad, you have been so, and here is a crown for you, but I give it you on condition that you tell me how you knew of this rain.’ ‘To be sure, sir,’ replied the man; ‘why the truth is we have an almanac in our house called Partridge’s Almanac, and the fellow is such a notorious liar, that whenever he promises us a fine day we always know that it will be the direct contrary.’

— The Golden Rule, and Odd-Fellows’ Family Companion, Oct. 16, 1847

Here is a curious old story that is something like a puzzle: A crocodile stole a baby, ‘in the days when animals could talk,’ and was about to make a dinner of it. The poor mother begged piteously for her child. ‘Tell me one truth,’ said the crocodile, ‘and you shall have your baby again.’ The mother thought it over, and at last said: ‘You will not give it back.’ ‘Is that the truth you mean to tell?’ asked the crocodile. ‘Yes,’ replied the mother. ‘Then by our agreement I keep him,’ added the crocodile; ‘for if you told the truth I am not going to give him back, and if it is a falsehood, then I have also won.’ Said she: ‘No, you are wrong. If I told the truth you are bound by your promise; and, if a falsehood, it is not a falsehood, until after you have given me my child.’ Now, the question is, who won?

— Pennsylvania School Journal, March 1887

The first few powers of 5 share a curious property — their digits can be rearranged to express their value:

25 = 5²
125 = 5^{1 + 2}
625 = 5^{6 – 2}
3125 = (3 + (1 × 2))⁵
15625 = 5⁶ × 1²⁵
78125 = 5⁷ × 1⁸²

It’s conjectured that all powers of 5 have this property. But no one’s proved it yet.