# 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

Because MITTAG-LEFF

-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

Both HADAMARD, ERD”OS.

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,

Blew LITTLEWOOD, HARDY away.

To a grad student in desperation

Said BATEMAN, “In your situation,

I humbled my pride.

RADEMACHER replied,

`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;

Neither, SARK”OZY, HALL

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)