Paul S. Bruckman and Number Theory

Paul and John at Patras, Greece, July 2008
Paul and John at Patras, Greece, July 2008

On the right is a picture of Paul Bruckman and myself. He is in the white shirt.

My friendship with Paul goes back some twenty years. We have met at a few Conferences and have socialized with him and his wife Lynn on several occasions in San Francisco.

I was first inspired to write to him about some problem of mine, knowing what a superb problem-solver he is … for about 40 years he has solved nearly all the problems set in the Fibonacci Quarterly, in both the Elementary and Advanced Sections.

My amazement and admiration for this led me to write a poem entitled “The Enigma”–The Man Who Does Them All. At the risk of embarrassing him, I am including this poem together with a brief introduction to Paul and his work.

The Fibonacci Quarterly is the official Journal of the Fibonacci Association, and it has been published regularly since 1963. It is devoted to the study of integers with special properties. I have been a member of the Association for some 35 years, and so have received and studied over 140 issues of the Journal.

A Nonsense Poem Addressed to Paul S. Bruckman

The following poem was inspired by a burst of correspondence between myself and Paul Bruckman in the late 1980s. It began with my sending him a copy of our recently published book* on Pythagorean Triples.

His reply was very complimentary of the book, and it initiated further correspondence in which we discussed our views on many things, including mathematicians, mathematical research, and our personal philosophies.


by J.C. Turner (21st April, 1990)

Who is this mysterious Paul,
The man who does them all?
The so enigmatico,
Supremo math’matico,
Prover unbeatable,
Rider unseatable?
There’s ne’er a one to top this Bruckman,
You’ll never meet a less unstuckman,
Is he some instrument of the Devil?

To my good friend (I hope!), professional actuary and amateur
mathematician extraordinary … Paul Bruckman, F.Q. and bar.

(His talk of mortality,
Might prove your fatality.
With Paul do not joust,
For he’ll sure poke you faust.)

Is he a brainy, brawny Texan,
In a great big straw-white hat;
Or a skin-rib, cut-jib, spawned from the Bronx’n,
Thin like a rake, and none the worse for that?

Was he born in West Virginia,
Whilst his Ma plucked wild white cotton;
Did his Pa ‘scape from Sardinia,
Leaving dark crimes best forgotten?

Did his forebears hunt the bison,
On the plains of Tomahawk?
Was he bought from Fortnum Mason,
Or brought by a flighty stork?

Did his Mam push a pram,
In South Alabam?
(Or was it a dray,
In old Santa Fé?)

Does he jog in a Walkman,
This enigmatic Bruckman?
And find his best solutions,
Whilst a-doing his ablutions?

Does he dunk his nuts in coffee,
Whilst he reads the morning paper?
Do his false teeth stick in toffee?
Does he lead his wife a caper?

Does he quote his favourite Dante,
To his loving, doting Auntie?
And play his bongos nightly,
In a nightgown most unsightly?

Is Paul an old swaggerman? **
A seedy, cloak-and-dagger man?
A Mick; or yet a Jagger fan?
A sot on gin and black-and-tan?

Who is this man called Bruckman?
Is he fat, a choc and tuckman?
Is he conceited, a real-live Yuckman?
Does he swear, a nasty Nixon f…man? (sorry about that!)

Who is this man of taxes and pensions,
Who bitterly claims so many abstentions,
From the men of Mamman, and business matters,
Preferring the egg-heads and Math mad-hatters?

Does he wear a pistol,
And gaze in a crystal,
When he’s acting the actuary?
Do his clients pay lots
for the schemes that he plots,
For their taxing sanctuaries?

Though I haven’t many clues on,
And confess much confusion,
I’ll continue to puzzle on,
I won’t put a muzzle on,
My musings and thoughts on,
My games and word sports on,
This man who’s not a truckman,
This man called Paul Bruckman.

There’s one thing I’m sure of,
I’ve caught the allure of,
His exciting presciences,
His multi-alliances,
And I know I’m a luckyman,
To know this Paul Bruckyman.

So, to end this patter,
Of schoolboy chatter —
Throw your hats to the sky,
Shout “Here’s mud in your eye”.
Sing “Hail to the glorious man called Paul”,
The lad from Seattle who does them all.


** To inform Paul Brucker-man,
A swaggerman’s a tucker-man,
Who rides on a kangaroo.
He hunts crocs in the night,
By a car’s head-light,
And sings to a didgeridoo.

N.B. ‘F.Q.’ means ‘Fibonacci Quarterly’, the Journal of The Fibonacci Society.
He has solved all the problems set in F.Q. for years, and years, and years … and years.

For more about Paul, go to Five Papers by Paul S. Bruckman

[ *A New Chapter on Pythagorean Triples, by A.G. Schaake and J.C. Turner,
pub. University of Waikato, Hamilton, New Zealand, 1989.]