The Dead Mathematicians Society: help Newton and Boole solve a maths puzzle

11 Jul 2016

Raphael’s School of Athens, featuring Pythagoras. The Dead Mathematicians Society was modelled after this (even if the name is a little Robin Williams)

In this week’s puzzle from the Irish Mathematical Trust, we sit with some dead mathematicians to help them solve a fun maths problem.

In the great, non-denominational, all-inclusive after-life, there are a lot of ways to pass the time.

Some people spend their time catching up on the TV they missed while they were still alive, others want to learn some new super-powered skills, while still others play the inexplicable perennial favourite, shuffleboard.

Some, though, just can’t break out of their cliques, gravitating to the like-minded.

Given their proclivity for mathematics, Euclid, Pythagoras, Newton, Euler, Gauss and Boole, unsurprisingly, found themselves drawn together and, after long aeons in each other’s company, set up a maths club – the Dead Mathematicians Society.

Every week, they meet in the same spot and hash out old maths problems. (After pooling their collective geniuses for long enough, they were even able to solve the bulk of the world’s unsolved maths problems.)

At the end of every meeting, though, the mathematicians liked to take turns setting each other brain twisters and puzzles – a nice, fun way to end a session.

As they’d been meeting for so long, though, they eventually ran out of puzzles to set.

One day, a child was walking past the group and saw them sitting around, looking miserable and not speaking.

“What’s wrong, guys?” the child asked. “Usually when I walk past here, you’re all delighted with yourselves. Why the long faces?”

“Well,” said Pythagoras. “We like to have some fun with maths every week, but we’ve run out of puzzles.”

“Well, lads,” said the child. “I’ve got a puzzle for you.

“Everyone in the world is assigned a number. Pythagoras, yours is -24. Newton’s is 13, Gauss’s is 27, Euclid’s is -20 and Euler’s is 9. So what’s Boole’s?”

The mathematicians sat around for a while, gazing into the middle distance, trying to figure out the solution.

First Newton got it, then Euler did. Gauss took a little longer, but he got there eventually, and so did Euclid. But, try as hard as he could, Boole just couldn’t figure out what his number was.

(To be honest, he was probably over-thinking it.)

Can you help him out? What is Boole’s number?

Scroll down to reveal the answer.

This week’s maths puzzle comes courtesy of Dr Gordon Lessells, lecturer in Applied Mathematics at the University of Limerick  who is actively involved in mathematics enrichment classes at UL and the Irish Mathematical Olympiad.

Maths: George Boole

George Boole, no doubt irritated by the fact that he can’t solve this problem. Image: Wikimedia Commons


The answer is -5.

The story continues.

“OK,” said Boole. “I have no idea. Drawing a total blank. Just tell me.”

“Well,” said the child, “it’s soooo simple… [the child has picked up a little bit of vocal fry from talking to the after-life’s teenage population] It’s all about number substitution.”

The child grabbed a piece of chalk that the mathematicians had been using earlier in the day to show off their theorems, and drew on the nearest flat surface:

Maths: number substitution chart

“It just uses number substitution. Every letter in your name corresponds with a number between one and 26,” said the child.

“Eh,” interrupted Boole, “then why do Euclid and Pythagoras have negative numbers?”

“I was just getting there,” continued the child, a little less kindly now. “As some of your numbers are negative, it’s clear that you have to subtract some of the letters, while adding others. As the rest of your group figured out, with a little experimentation, E – U + C – L + I – D = 5 – 21 + 3 – 12 + 9 – 4 = -20.

“The rest of them follow the same pattern: a – b + c – x + y, etc. So, do you know what your number is now?”

Finally, triumphantly, he crowed, “Eureka! 2 – 14 + 14 – 12 + 5. I’m -5! I’ve got it!”

And he did.

Main image via Everett – Art/Shutterstock

Kirsty Tobin was careers editor at Silicon Republic