“And the cube is the seven-twelve unity because it has twelve foundations in the Bible,” Odom continued, “twelve edges for the twelve apostles, the twelve tribes of Israel, the twelve months of the year. It has seven axes of symmetry for the seven days of creation, the seven days of the week, the seven early churches. And it has nine planes of symmetry, for the nine hours of the crucifixion. So it’s full of Biblical meaning.

“When I was very young, growing up,” he went on, tangentially, “I used to salvage cardboard boxes from dumps and wrap them in coloured crepe paper. I thought the box was so beautiful. I just admired the box for its simplicity and symmetry.”

Finally addressing the origins of his golden-ratio theorems, Odom said he was drawn to geometry after seeing a 1960s exhibition of Buckminster Fuller’s models. “That’s when I was struck by the beauty of mathematics. It was more than alphanumeric utilitarian scribbling. It was beautiful things that you could see and touch.”

Conway pulled from his paper bag the folding puzzle: two cubes comprised of smaller cubes in red and blue, hinged together. The trick was to fold the pair of cubes so that they display identical red-blue patterns on all faces. Conway can do it in “about half a second,” though he confessed the puzzle took him twenty years of thinking to invent.

“You should manufacture it and get it into classrooms,” said Odom, refusing to take a try. He changed the subject to a patent he holds on a variation of tic-tac-toe. “Hollywood Squares should be paying me royalties,” he said. “I won’t go into it, but if you ever want to play tic-tac-toe, a better way to play it is with all Xs or all Os. There is less chance of a stalemate.”

“When do you get a point? ” Conway queried.

“When you make a row; the last X to make the row gets the point for the row.”

“And if you make several rows at once? ”

“You get multiple points.”

Conway grabbed his ever-present Sharpie marker and sketched on a piece of paper his version of a similar game, magic squares, only played on a hexagonal grid and with numbers instead of Xs and Os.