Glimpses of History – Part 3. Twentieth century

Glimpses of History

Part 3. Twentieth century

When the century opened its door,
HILBERT chose Mathematics’s core,
A definitive list,
Which those present insist
Was made up a few minutes before.

When HILBERT, who normally planned stuff
Got twenty-three problems to stand tough,
Then ev’ryone thought
His list was too short,
And his twenty-fourth problem was dandruff.

The Great and the Good worked at Graz,
There’s SCHR”ODINGER, murd’rer of cats,
KRAFT-EBBING drew curtains…
Let’s celebrate MERTENS,
Whose primes are worth more than one Satz.

No prizes for Maths? People say
That our chances were blasted away
-LER gave NOBEL a huff
By spooning around at midday.

“We know where the rationals are,”
Said BOREL, “and each shines like a star,
Marking out with their light
The unknowable night,
The continuum dark and afar.”

`Normal’ just meant U. D. for BOREL,
`Absolutely’, `entirely’ as well.
An age that’s less formal
Renormalised `normal’.
In the next hundred years, who can tell?

The set theorists labour like elves,
Forged treasures stacked up on the shelves,
Then RUSSELL begets
The set of all sets
Which do not belong to themselves.

Is History fated or cock-up?
Was the Moon landing real or mock-up?
Is Maths just a game?
Well it brought RUSSELL fame,
So get down to work, pull your sock up.

VIETORIS outlived many chaps.
He defined types of points, sets, and maps.
Not all still make sense:
A hundred years hence,
`Compact’ doesn’t mean `without gaps’.

When LITTLEWOOD first got the word
Of his Fellowship prize, was he stirred?
A two-lemma section
Ensured his election;
He sat down to prove Lemma the Third.

A habit of HARDY made men tense:
Repeating the end of a sentence,
Like a mission’ry who
In a cannibal stew
Continues to call for repentence.    [see preface to `Pure Mathematics’]

The face of their friendship was freckled
As LITTLEWOOD Hyde-d and Jekyll-ed.
A question from HARDY
Made LITTLEWOOD mardy:
He cried out, “I will not be heckled!”

RAMANUJAN’s powers still shone
When consumption was very far gone.
“Two ways to combine:
Cubes of ten and of nine,
Or else cubes of twelve and of one.”

In the earliest HARDY and WRIGHT,
Though the bound for divisors was right,
They were caught unawares
Over sums of two squares,
Where they might make a slight oversight.

At the fiftieth year jamboree,
Some critic asked RANKIN at tea,
“Could HARDY be cruel
Detecting a fool?”
“He was perfectly friendly to me!”    (1997)

BESICOVICH’s version of Maths:
Small area, very long paths,
With a many-point turn,
A canal boat, we learn,
Can reverse. Do not try this in baths.

BESICOVICH, upbraided at tea,
For his accent, replied scornfully,
“You talk so, but then
Hundred million men
In Russia say English like me!”

Find a to the n, all mod n.
If you get the same number, what then?
CARMICHAEL is blamed
For the numbers so named,
Which do it again and again.

The values the phi function took,
Each comes at least twice if you look.
But many have striven;
The answer’s not given
At the back of CARMICHAEL’s old book.

Der m”achtige HASSE-Bericht
Trug alles, das tief lag, ins Licht.
Dann kam es geflogen
Die Kohomologen.
Sie schalten’s ab. Jetzt sieht man’s nicht.

Herr ARTIN tritt nicht gern auf Bananen.
Er folgt’ nicht gew”ohnlichen Fahnen,
Er schafft uns trotzdem
Ein dynam’sches System
Mit quasi-ergodischen Bahnen.

For LANDAU the standard was `starred’,
And ev’rything had to be hard,
And `order of MAHLER’
Was used in his parlour
For someone who played the wrong card.

A device both obscure and unsavoury
Held the students of LANDAU in slavery.
On the day one got wed,
“Mark this lot,” he said.
The protest was futile and quavery.

“The zero of SIEGEL”‘s the phrasing,
But LANDAU had noticed the spacing.
Making zeros repel
Served LINNIK so well,
You must read it! It’s hard but amazing!    [IWANIEC’s comment on LANDAU]

When LANDAU was forced to give in,
SIEGEL took up his post at Berlin,
And wrote up the text
Of that paper signed `X’.
Whose were the ideas within?

The young VAN DER CORPUT wrote nice
Expositions, if seldom concise.
From nineteen-fortysix
He developed new tricks,
Such as publishing everything twice.    [the `Neutrix Method’]

You needed to be on your guard of
Academy Boss VINOGRADOV.
To improve his results
Got you sent to the vaults.
How different from HOOLEY at Cardiff.

VINOGRADOV was sure that his status
Was more than some Party dictator’s.
He replied without fear,
“You’re the idiot here,
To send my staff picking potatoes!”

Bilinear forms are the thread
Linking much VINOGRADOV has said.
And his tricks to call primes
Should be fixed for all times;
VAUGHAN mangled VON MANGOLDT instead.

VINOGRADOV was strong as a bear,
Maths, influence, every where.
With his days near their end,
He embraced an old friend,
Who got two broken ribs to repair.

PAUL ERD”OS, the infant sensation,
Resented LANDAU’s imputation,
And very soon found
How to turn it around:
“Well, do you know partial summation?”

It was Maths that filled ERD”OS’s life.
With a mother, who needed a wife?
When the time came to flee,
And MORDELL gave him tea,
He had not learnt to spread with a knife.

He knew Maths and so much besides,
Whom NOETHER as `Martian’ derides.
But HEILBRONN the paragon
Was also a polygon;
We have to admit his sharp sides.

“To call it `Large Sieve’ is a shame;
It’s a very unfortunate name.
We’ll discuss in the bar
What alternatives are,
And the old name will stick just the same.”    [IWANIEC’s comment on LINNIK]

The probabilist ALBERT RENYI
Wrote LINNIK’s `Large Sieve’ out more plainly.
As probabilist,
He was top of the list,
But his sieve is a little ungainly.

The problems that SIDON’s immersed in,
With diff’rences, started to worsen.
He’d cry, “Go away
Till a different day,
Come back as a different person!”

The Saturday worries of HAMMING,
On whether his punch cards were jamming,
Led to error correction,
A Maths Reviews section,
To websites, CDs, and to spamming.

“What ERD”OS and INGHAM have shown,
No mathematician alone
Could possibly get;
No two-element set,
Except for the one that is known!”

Most things about INGHAM were neat.
His papers were clean and complete,
But his lecturing gown,
That he wore through the town,
Had faded except at the pleat.

The French mathematical maquis
Scorned Maths that was clever or wacky.
But to father their work,
Took not ATAT”URK,
But a Greek hero, General BOURBAKI.

Though BOURBAKI-sts sought anonymity,
They taught indiscreteness and symmetry,
And Maths in their view
Was things that you do
With spaces of BANACH and limitry.

ANDRE WEIL had a joyless perspective,
But the joke that he spoke was infective:
“If the best things are free,
It is patent to me,
That the second-best things are projective.”

A distinguished exceptional set,
No visa at first could they get.
A pairing absurd as
Would STALIN have won if they’d met?

k k-th power sums disobey
Ill-fated Hypothesis K:
“Three fourths make a twelfth,”
Said MAHLER himself,

To a grad student in desperation
Said BATEMAN, “In your situation,
I humbled my pride.
`Young man, this is your dissertation!’ ”

“The first case is mine,” said MORDELL,
“WEIL did fields of numbers as well.”
He would rise without fail
If you said `MORDELL-WEIL’
From his doze in the corner to tell.

A student in days long ago
Brought DAVENPORT something to show.
With mounting distress,
He listened to “Yes,
Yes yes, yes yes, yes yes yes, No!”

If you’re junior to WATSON, then cower!
He is right at the height of his power.
“If there’s nobody next,
Then I stick to my text,
And go on for another half hour!”

MARGULIS’s reach is immense:
“Compact is the quotient, and hence…”
The work of MARGULIS
Makes DAVENPORT foolish,
And WATSON seem ev’rywhere dense.

He picks on a problem – it clicks,
ERD”OS of the myriad tricks;
Has mastered them all,
Though HALL has identified six.

PAUL ERD”OS, the best of our breed,
Knew a life that no other could lead.
A wandering scholar,
Who’d pledge his last dollar,
He lived ev’ry moment on speed.

“This conference sweeter than life
Must end; it was fleeter than life.”
Then ERD”OS would go
To some other show,
The rest home to meet with the wife.

There are proofs which can not be mistook:
They are leaves from GOD’s very own book.
All that’s known to the world
Is, its cover is pearled,
And ERD”OS is now free to look.    (1998)

So WILES has amazingly come
To FERMAT’s Last (or Lost) Theorem.
There are smiles of delight
To the left and the right;
How strange that the Great Ones look glum!    (1993)