Martin Gardner

I was given a Martin Gardner book as a birthday present

when I was 15. When I unwrapped it, I wasn’t particularly

pleased. A year later, as boredom set in over the

summer holidays, I picked it up again and got hooked –

just in time for the sixth form. Martin Gardner didn’t

consider himself a mathematician, but as a communicator

of mathematics and as an advocate of the pleasure

obtained from understanding mathematical ideas, I think

he was second to none. This session will discuss his life

and work and will include ideas for classroom activities

to help get your students hooked on maths.

Martin Gardner

1914 - 2010

WARNING Martin Gardner has turned dozens of

innocent youngsters into Math

professors and thousands of Math

professors into innocent youngsters

Persi Diaconis

Timeline

• 1914: Born Tulsa, Oklahoma – son of an oil

geologist

• 1929: Published first article, about a magic

trick, in the magazine of the Society of

American magicians

• 1936: Bachelor’s degree in Philosophy,

University of Chicago, Early jobs as

reporter/writer

• 1941-45: Yeoman in US Navy

• Late 1940s: Moved to NY, writer and designer,

Humpty Dumpty magazine

Timeline

• 1950 - 1979 Hasting on Hudson, NY, Euclid

avenue

• 1952: Married Charlotte Greewald (2 sons)

• 1956: First Scientific American ‘Mathematical

Games’ article published

• 1960: ‘Annotated Alice’ published – has sold

over a million copies

• 1941-45: Yeoman in US Navy

• 1979: Semi-retired, moved to Hendersonville,

North Carolina

Timeline

• 1981: Final Scientific American ‘Mathematical

Games’ article (almost 300 in total)

• 1993: First ‘gathering for Gardner event, now

held in every even numbered year – devoted

to Gardner’s writings in recreational maths,

magic, puzzles, and philosophy

• 2002: Returned to live in Oklahoma, near

family

• 2010: Died, aged 96

• 2013: Autobiography ‘Undiluted Hocus-Pocus’

published posthumously

Summary?

• Writer: (wrote more than 100 published books and

hundreds of articles on books on the subjects of

mathematics, skepticism, literature, magic, and

religion)

• Friends with, and admired by many of the great

mathematicians and thinkers of the 20th century,

including John Conway, Piet Hein, Roger Penrose, Carl

Sagan, M.C. Escher, Douglas Hofstadter, Stephen J.

Gould, W.H. Auden, Arthur C. Clarke, Isaac Asimov,

Richard Dawkins, Noam Chomsky, Salvador Dali

John Conway described him as “the most learned man I

have ever met.”

Summary?

• He was, I believe, the greatest communicator

of maths.

“I go up to calculus, and beyond that I don’t understand

any of the papers that are being written. I consider that

that was an advantage for the type of column I was doing

because I had to understand what I was writing about,

and that enabled me to write in such a way that an

average reader could understand what I was writing

abut. If you are wiritng popularly about math, I think it’s

good not to know too much math.”

Marin Gardner, 2004

Activity for KS3/4

Area dissection – links to Fibonacci

5

8

5

5 8

8

13

13

• Draw this square on squared paper

• Cut it up into 4 pieces along the lines

• Assemble the pieces into a rectangle

• What is the area of the square?

• What is the area of the rectangle?

• Explain

• Try with a different ‘Fibonacci triple’

• Can extend into ideas of

convergence and limits

Activity for KS3/4

Binary mind reading

• It’s a travesty that roman numerals are in the

mathematics NC but binary isn’t!

• This ‘trick’ fascinates students (it fascinated me)

• To explain it, ask students to draw up a table

with 2s, 4s, 8s, 16s and 32s columns and rows

for each number from 1 to 63, to enable them to

translate the numbers 1 – 63 into binary (great

revision of place value ideas that can really

help them to understand base 10, as well as

revealing the awesome power of binary)

Activity for KS3/4

Binary mind reading

• They can then use their table to make up their

own cards and try the trick out themselves

32 16 8 4 2 1

1 0 0 0 0 0 1

2 0 0 0 0 1 0

3 0 0 0 0 1 1

Etc. Etc. Etc. Etc. Etc. Etc. Etc.

61 1 0 1 1 0 1

62 1 1 1 1 1 0

63 1 1 1 1 1 1

Activity for KS3/4

Cyclic number

• The basis of the trick is that, as decimals,

sevenths are cyclic numbers

• Reciprocals of some other primes are also

cyclic – it’s worth Googling!

. . . . . .

. . . . . .

1 2 30.142857, 0.285714, 0.428571

7 7 7

4 5 60.571428, 0.714285, 0.857142

7 7 7

Activity for A level

Folding surprise

• Take a circle of paper

• Mark a point on it, not at the centre

• Fold the circle so that the perimeter of the

circle touches that point, then unfold to leave a

fold line

• Repeat many times, folding different points on

the perimeter to touch the point inside the

circle, building up an envelope of fold lines

Folding surprise

• What shape is the envelope of folds?

• Can you prove it?

Activity for A level

Interesting problems/puzzles

• Martin Gardner published many interesting

puzzles and problems

• These are 4 of my favourites

1. Guess the diagonal

5 5 D C

B A

How long is AC?

Interesting problems/puzzles

2. The repetitious number:

• Write down a 3 digit number.

• Repeat the digits to produce a 6 digit number.

• Divide it by 7 (don’t worry, they won’t be a remainder).

• Divide the result by 11 (no remainder again).

• Divide by 13.

• You have back your original number. Why?

Great for KS3, really understanding place value and

factorisation.

Interesting problems/puzzles

3. The early commuter: A commuter always arrives at his

local station at exactly 5pm, and his wife always arrives

at exactly 5pm to drive him home from the station,

always taking the same route. One day he is able to

leave work early and catches the train that will get him

home at 4pm instead. It’s a nice day, so rather than

letting his wife know, he decides to walk home on the

route she drives, so she can pick him up when they

meet. His plan works perfectly and he gets home 10

minutes earlier than usual. Assuming she always drives

at a constant speed and that she left just in time to meet

his normal train, for how long was he walking before

she picked him up?

Interesting problems/puzzles

4. Hole in the sphere

‘This is incredible problem – incredible because

it seems to lack sufficient data for a solution. A

cylindrical hole six inches long has been drilled

straight through the centre of a solid sphere.

What is the volume remaining in the sphere?’

We glibly talk of nature’s laws

But do things have a natural cause?

Black earth turned into yellow crocus

Is undiluted hocus pocus.

Piet Hein [Quoted at the start of Martin Gardiner’s autobiography,

entitled ‘Undiluted Hocus-Pocus’]