At the 1961 Solvay conference on physics, Abdus Salam overheard this conversation between Richard Feynman and Paul Dirac:

Feynman extended his hand towards Dirac and said: ‘I am Feynman.’ It was clear from his tone that it was the first time they were meeting. Dirac extended his hand and said: ‘I am Dirac.’ There was silence, which from Feynman was rather remarkable. Then Feynman, like a schoolboy in the presence of a Master, said to Dirac: ‘It must have felt good to have invented that equation.’ And Dirac said: ‘But that was a long time ago.’ Silence again. To break this, Dirac asked Feynman: ‘What are you yourself working on?’ Feynman said: ‘Meson theories’ and Dirac said: ‘Are you trying to invent a similar equation?’ Feynman said: ‘That would be very difficult.’ And Dirac, in an anxious voice, said: ‘But one must try.’

“At that point the conversation finished because the meeting had started.”

(Abdus Salam, “Physics and the Excellences of the Life It Brings,” in Ideals and Realities: Selected Essays of Abdus Salam, 1987.)

This is brilliant: University of Hull chemist Mark Lorch has combined the periodic table with London’s classic Tube map to create an Underground Map of the Elements.

“My son loves trains. So I came up with a train related twist to an inspection of the periodic table. We sat and cut up a copy of the table and then rearranged each element as a ‘station’ on an underground rail system. Each line represents a characteristic shared by the elements on that line.”

More details at the Guardian and at Chemistry Blog.

Construct squares outwardly on the sides of triangle ABC, and make a triangle of their centers. Now the centers of squares constructed inwardly on the sides of that triangle will fall on the midpoints of the sides of ABC.

(Due to Luxembourger mathematician Joseph Neuberg, 1840-1926.)

A thought experiment in probability by Leonardo Barichello: Two people are stranded on an island with only one banana to eat. To decide who gets it, they agree to play a game. Each of them will roll a fair 6-sided die. If the largest number rolled is a 1, 2, 3, or 4, then Player 1 gets the banana. If the largest number rolled is a 5 or 6, then Player 2 gets it. Which player has the better chance?

Writing in the north of England in the early 8th century, the Venerable Bede described a Roman system of finger counting:

1 = the little finger bent at the middle joint
2 = the ring and little fingers bent at the middle joints
3 = the middle, ring, and little fingers bent at the middle joints
4 = the middle and ring fingers bent at the middle joints
5 = the middle finger only bent at the middle joint
6 = the ring finger bent at the middle joint
7 = the little finger closed on the palm
8 = the ring and little fingers closed on the palm
9 = the middle, ring, and little fingers closed on the palm
10 = the tip of the index finger touching the middle joint of the thumb
11 to 19 = the actions denoting each numeral from 1 to 9 plus that of 10
20 = the thumb tucked between the index and middle fingers, so that the thumbnail touches the middle joint of the index finger
21 to 29 = the actions denoting each numeral from 1 to 9 plus that of 20
30 = the tips of the thumb and index finger touching and forming a circle or ring
40 = the thumb and index finger standing erect and close together
50 = the thumb bent at both joints and held against the palm
60 = the index finger closed over the thumb
70 = the first joint of the index finger resting over the first joint of the thumb, which is held nearly straight
80 = the tip of the index finger resting on the first joint of the thumb
90 = the thumb bent over the first joint of the index finger

The signs for 100, 200, 300, and so on are the same as 10, 20, 30, but made by the right hand; and the signs for 1,000, 2,000, 3,000 and so on are the same as 1, 2, 3 but made by the right hand. “To add two numbers, one simply signed the first, then made the mental arithmetical calculation and reproduced the gesture corresponding with the correct sum,” writes Angus Trumble in The Finger: A Handbook (2010). “The process was cumulative; to add a further number to the sum of the first two, you proceeded to represent the gesture corresponding with the new total, and so on. Likewise, the task of subtraction merely threw the whole system into reverse. It was perfectly clear to anyone observing you carry out these separate procedures whether the job in hand was one of addition or subtraction.”

Trumble says that at the end of the 19th century Wallachian peasants were discovered to have preserved a few methods of digital multiplication and division that had been preserved throughout the Roman empire. Here’s one.

Choose one of these cards and fix it clearly in your mind. Then open the answer box.

Suppose you want to hang a picture by a string that’s attached at two points on the back of the frame. How can you arrange the string on two nails such that the picture will fall if either nail is removed?

One solution is above. I don’t know who first asked the question; I first saw it in Mathematical Mind-Benders, by Peter Winkler, who got it from Giulio Genovese, a mathematical graduate student at Dartmouth, who’d seen it in more than one source in Europe.

But it opens up a surprisingly rich discussion — see the paper below for some entertainingly complex variants.

(Erik D. Demaine et al., “Picture-Hanging Puzzles,” Theory of Computing Systems 54:4 [2014], 531-550.)