The Mathematician who Challenged Rome

By Francesco Grasso

The story of the long battle between Rome and Carthage (264 - 146 BCE) tends to neglect the role of a third city, a city that was at least as prosperous as Rome, and was possibly even superior in its heritage and culture.

It was Syracuse, the pearl of Magna Graecia, a beacon of civilisation and military power that found itself - unfortunately for her - an ally of Hannibal at the wrong time. A course of action that Rome never forgave.

Despite being overpowered by her enemy in terms of men and arms, Syracuse resisted the siege of the Roman fleet and legions for two years, from 214 to 212 BCE, thanks largely to the remarkable inventions of Archimedes, one of the most brilliant scientists of all time.

If misfortune (and the Syracusans themselves) had not prevented Archimedes from taking full advantage of his brilliant inventions, that long siege might have had a different outcome. This novel recounts the world of the eminent mathematician, and describes his fascinating discoveries and how they were deployed during the historic face off.

• Language: English
• Publisher: BadPress
• Release date: Feb 21, 2019
• ISBN: 9781547568703

Book preview

Syracuse, The Agrigentine Gate, 679 ab urbe condita (74 BCE)

The man brandished his ash walking stick and made his way through the brambles which, tangled into a thorny curtain, concealed the tombs. The warm wind blew a cloud of fine dust into his jet-black eyes, and now and again he wiped his brow and ample forehead with a piece of white linen.

What are you looking for, Marcus?.

The man’s twitchy lips barely moved.

A headstone.

Baffled, the woman stared at her husband. She made as if to join him, then realised that beyond the shelter of the shade projected by the walls built by Dionysios the heat cut her breath short. She hesitated. She beckoned to a servant, a tall, scrawny, coloured young man, who came running with a parasol.

Marcus Tullius!, she exclaimed indignantly. Are you telling me that you have brought me for a walk in a necropolis, a city of the dead?.

The man pointed to the tombs in the moat, slabs of stone emerging from the undergrowth that was dotted with purplish berries.

A necropolis in ruins, he specified. The Syracusans do not lavish devotions on their dead.

My mother used to say that from their gravestones, the dead stare at those who survive them as if calling them to account..., the woman observed.

The man laughed. He was short and stocky, with a strong neck and arms, and calloused fingers.

It’s not the dead we need to fear, Terentia, but the living.

The woman shook her head. She was tiny and curvaceous, her rebellious hair barely held back by a riot of ribbons and hairpins.

Well, what do you find so remarkable about all these cobblestones? Apart from the heat, I mean....

The man spread his arms out wide.

Terentia, your lamentations are an offence to the gods. Look around; isn't this a magnificent sight?.

The woman followed her husband’s gaze. To the west, the countryside paraded a succession of olive trees, orchards, wheat ready for harvesting, and rows of vines clinging to the sides of the hills. To the north, the towers of Euryalus Castle rose up against the clear sky. Far away, dimmed by the distance, rose the buttresses of lava rock of Mount Etna. To the east, beyond the city walls, her eyes met the sea and the gentle contours of the Plemmirion promontory. To the south, she could see the Cyane wetlands, lush with ferns and papyri. The crickets were chirping, and the air was warm and full of the scents of summer.

Pleasing, for sure, replied Terentia, her voice marked by a trace of petulance, but I prefer the city of Rome, our Urbs.

The man paid her no attention. Follow me, wife of mine. You won’t be disappointed. He cut down more brushwood with his stick and walked among the tombstones. The woman, albeit reluctantly, ordered the servant to shade her as she followed him.

What’s this, Marcus? One of your investigations? Are you looking for proof against that...? What’s his name? Verres?.

The man twisted his lips while being careful to dodge the thorns that his cane pulled away from the undergrowth.

I'm not wearing the quaestor's toga today, Terentia. If anything, I am wearing the drapes of a scholar. Of the historian. Among these stones, rests one of Rome's greatest adversaries. A Greek who at the time of the Punic Wars defended this city from the Roman legions. Since we arrived in Syracuse, I have asked a thousand times to visit his tomb. No one, alas, recollects exactly where he is buried.

The woman raised an eyebrow.

He can’t have been the hero you say he was if his fellow citizens have forgotten him.

The quaestor shrugged his shoulders.

Sometimes, Terentia, to achieve immortality, it is not enough to accomplish great deeds; someone needs to tell posterity about them. It’s a wrong that, at least in this case, I want to put right.

Are you looking for the tomb of this enemy of Rome? And how will you recognise it among so many tombstones?.

The poets say that he made arrangements that his tombstone be engraved with the successes for which he wished to be remembered.

A trophy?, ventured the woman, suddenly intrigued. A crown? A golden sword?.

Sword?. The man laughed. I don't think he ever held anything deadlier than a wax scraper.

But you said he protected Syracuse from the legions of Rome.

Exactly so. But he didn't think that that was his greatest achievement. On the contrary, he considered that his greatest achievement was... Here it is!.

Once again, the woman, dutifully, followed the direction of her husband’s pointed finger. Like a hedge, a scrubby patch of blackthorn encircled a small stele. Carved at the top, she saw the figures of a cylinder and a sphere.

What does it mean?, she muttered, bewildered.

The quaestor ordered the young black man to force a passage through the undergrowth. He then turned to his wife, again.

The man whose tomb I seek is Archimedes. Have you ever heard of him?.

The woman frowned. I small wrinkle appeared between her painted eyebrows.

"I think so. Give me a lever and I will move the world... or was it Atlas? I’m never sure with Greek myths".

The man laughed again. Not contemptuously, but as someone enjoying a long-awaited pleasure.

Archimedes was a very talented mathematician, Terentia. More important than Pythagoras, Euclid, and Eratosthenes. He was a scientist and a philosopher; he did not want to the remembered for vanquishing legions but for having discovered the ratio between the volume of a cylinder and the sphere inscribed within in it.

Then, almost unable to stop himself, he pushed to one side the servant who was still swinging his sickle. He approached the tombstone and ran his fingers over the marble stone, half-closing his eyes to better savour the solemnity of the moment.

Marcus?.

What is it, Terentia?, he snapped, curtly, piqued by her interruption.

I have some bad news for you.

What?.

This is not the tomb you are looking for. There’s a name carved down here. But it’s not Archimedes. The woman spelled out the letters, D-I-N-O-S-T-R-A-T-O-S if I am reading it right.

The quaestor gave a start.

Are you sure?.

The woman protested.

I don’t speak Greek as well as you do, husband, but permit me to know the Greek alphabet.

The man knelt beside his wife. He tore away a handful of grass exposing the base of the tombstone. He created some shade with his hands and squeezed his eyes tight until they were two narrow slits.

It’s an epigram.

"A what?".

A funeral ode.

Do you mean one of those verses that the person who builds a tomb dedicates to the deceased?.

Exactly!.

I didn’t know that the Greeks, too, had this custom.

We were the ones who learned it from them, I'm afraid. The Greeks say, ‘In Hellas, we have already brought to perfection all that the gods have granted man the power to invent’.

Modest, Terentia commented, sarcastically.

The quaestor observed with irritation the cracks that the humidity had inflicted on the stone.

We’ve been fortunate, he observed. A few more years and these letters would have eroded. I believe we are the last to be able to read them.

The woman tapped her index finger on the signs carved into the stone.

Hurry up and translate them then.

Humouring her, the man assumed the rhetorical tone that was already making his public speeches famous in Rome, the Eternal City.

May the earth enfold you gently, master / as the cylinder encloses the sphere / in the embrace whose perfection you measured. / This is the wish of Dinostratos / the humblest of your disciples, the most faithful of your servants.

Sombre words, the woman remarked.

Pious, too, added the quaestor. This ‘Dinostratos’ must have been very attached to his master.

How do you know?.

"Well, the stele demonstrates it. Archimedes died in dramatic circumstances; it can’t have been easy to arrange his burial.... The man assumed a pensive expression. I must admit, I am envious".

Envious?, the woman repeated, questioningly.

The quaestor hinted at the young black man mooching lazily, a vacuous gaze in his eyes, and his sickle dangling from his hempen belt.

If I were to perish suddenly, my servants would grab what they could, and bugger off. None of them would dream of providing for my funeral.

The woman caressed her husband’s shoulder, tenderly.

Don't distress yourself, my sweet lord. It will certainly not be a servant who will honour you; that far-off day, I will write in your memory the most poignant funeral ode that Rome has ever heard - since the time of Romulus.

Moved, the quaestor allowed his wife to wrap her arms around him. However, in the years that followed, amid the thousands of wars, conspiracies and odious betrayals that marked his political career, he often wondered whether the vow Terentia had made to him on that sweltering day at the gates of Syracuse had been a promise, or rather a threat.

––––––––

The Romans were so uninterested in mathematics that Cicero's act of respect in cleaning up Archimedes' grave was perhaps the most memorable contribution of any Roman to the history of mathematics.

George F. Simmons

Ancient Syracuse Map

Roman siege camp, 541 ab urbe condita (212 BCE)

Marcus Claudius Marcellus looked with indifference at the man the centurion Agrippa had dragged in chains into the consular tent. Without hurrying, he finished checking the military dispatches leaving for the Peninsula, then turned to the prisoner in a benevolent tone, surprisingly at odds with the ferocity that, for days, the victors of the long siege had been showing to the vanquished.

You’re the assistant of Archimedes, they tell me. What’s your name?.

Dinostratos, the man replied, despondently. But I was just his servant.

The centurion yanked at the chain, brutally, forcing the prisoner to fall to his knees. He then leaned over him, and growled into his ear:

Do you dare contradict the consul, you dog? Do you want a taste of the whip? If the consul says you’re the assistant of Archimedes, you say, ‘Yes Sir, I am’. If he says you’re a horse, you neigh and beat your hoofs. If he says you’re a fish, you eat worms and stink in the sun. Is that clear?.

The Dux of the Roman Army solemnly raised his right arm. The centurion slackened his grip on the prisoner's chain.

You said ‘I was’, Marcellus observed in a conciliatory fashion. So, you already know your master is dead.

You killed him, Dinostratos ventured to say, expecting the centurion to retaliate again. However, the Roman appeared to be flattered by his correction. Dinostratos read satisfaction in his sharp face, almost as though he had given him some credit.

I didn’t want him to die, Hercules is my witness, the consul declared frankly.

No?.

Marcellus shrugged his impressive shoulders.

I ordered him to be brought before me. But he refused to obey. An act of pride; he would have done better to acknowledge defeat and, finally yield to the authority of Rome.

The authority of Rome?. The prisoner shook his head. "My master was barely aware of your siege. I don't think he could tell the difference between a Roman miles and a Syracusan hoplite. Or that he was interested in understanding the difference".

Marcus Claudius Marcellus frowned, his ample forehead furrowed with wrinkles.

Are you saying your master was crazy?.

With difficulty, Dinostratos rose to his feet. He was barefoot, scruffy, his clothes torn, and had a bad wound to his shoulder which was badly concealed by clotted blood. His black eyes were clouded by his suffering. He was not yet thirty years of age, but the burden weighing on his soul made him look like an old hunchback.

My master was a genius, he replied softly, in a tone not born from pride, but from the despondency of one who has lost everything. He lived in a world which is not the one that belongs to us imperfect human beings. His mind flew high, beyond the heights of Olympos.

Why did he insult the legionaries, then?.

The prisoner shook his head.

He did not intend to. When your men came to fetch him, he answered as he would have to anyone - a general or a king - distracting him from his thoughts. He was not arrogant, consul, he was simply acting like someone who in intellect is closer to the gods than to humans.

The centurion’s mouth twisted as he beat the prisoner once again.

I’ll tell you one last time, dog. Do not contradict the consul!.

Marcus Claudius Marcellus sighed.

Leave us alone, Agrippa.

The centurion hesitated for a split second, a flash of confusion in his eyes the colour of the River Tiber before Roman discipline took over. He beat his fist against his breastplate and left the tent.

The consul proffered a pitcher to the prisoner. Dinostratos drank greedily as the blood pouring from his swollen lips changed the colour of the water.

Hercules is my witness, I hate violence, the Roman declared, although sometimes it is my duty to inflict it.

So, we deserve what you are visiting on us?.

The Roman, agreeing, nodded grimly.

Rome cannot allow herself any weaknesses, Greek. Not now, with Hannibal at our gates.

In agony, Dinostratos touched his ankle, now reduced to a deep wound by the iron chain.

I understand. You need to flaunt your victory.

Just as he pronounced the syllables, he knew instinctively that he had overstepped the mark. If the centurion had still been there, he thought, he would certainly have laid his hand on his whip. But the consul, surprisingly, stretched out his lips revealing his teeth.

"You are an insolent Greek. But you are right. Yes, I will strip Syracuse of her treasures and I will take them to Rome as booty. I will drag your very gods, with their simulacra, as slaves to the Forum. I will celebrate the greatest triumph since the times of Curius Dentatus. After so many defeats, the Roman people will be uplifted. This is why I need you".

Me?, echoed Dinostratos, bewildered.

The greatest treasure of this city is the brilliance of Archimedes, everyone knows. I intended to yoke your master to my chariot and display him as a slave. But the gods have ordained differently. I will have to make do with taking his works to Rome.

Dinostratos knitted his eyebrows.

You mean his treatises? In that case, you should halt your legionaries from their looting. I saw them. They were having fun throwing papyruses onto a fire while his corpse was still warm.

Papyruses? Do you think that as booty I want to parade rolls of dried leaves?. Marcellus laughed. By Hercules, only a Greek could conceive of such nonsense! No, I intend to take to Rome marvels that leave the Senate open-mouthed, magical objects that will impress the people, something... ...magnificent that will put your rivals in the shade, the prisoner interjected. I understand.

The consul stretched his lips again, this time intimating a threat rather than a smile.

You’re right again, you impudent Greek. Well, why should you not say it? I want to humiliate Quintus Fabius Maximus, whose celebrated military campaigns have never conquered more than one village, and that conceited Publius Cornelius Scipio, whose only success is to have survived Cannae.

"That’s why you destroyed the sphaeristerium?", Dinostratos asked in a subdued tone.

The what?.

The device that simulates the movement of the Moon and the planets, the prisoner explained.

Oh! The glass and silver globes, Marcellus confirmed smugly. It's apparatuses just like that I'm talking about. Expensive and sophisticated, evocative and mysterious. I'll set it up on the Palatine and make the heads of all those Roman patricians spin.

Your men have taken it apart, Dinostratos protested, They have gutted it like barbarians. I don’t know if it can be rebuilt.

"You will rebuild it, the consul hastened to add, in a tone that did not invite a reply. And then you will teach me how to use it. As you will with those accurate stone-throwing lithoboloses, the manus ferrea, and the other war machines we will take to Rome".

Despite being aware that the consul was deaf to his protests, Dinostratos shook his head again.

You are asking me the impossible, Sir. I am merely a servant, I have already told you.

Contemptuously, Marcellus cut him short.

I understand that you mean to protect yourself, but it is pointless. I know for certain that you were the assistant of Archimedes for years, that you knew him better than anyone else. You will do what I order you to if you want to live.

Dinostratos lowered his head struggling to gather his thoughts, which were still shaken by the smell of fires, the cries of looting, and the sight of the gladii which the legionaries, in the frenzy of the free-for-all amid the blaze of the flames, were burying in the bodies of his fellow-citizens.

He shut his eyes, drew a deep breath and made up his mind. I can tell you about my master, consul, he said, raising up his head, Everything I can remember. All his teachings, every anecdote. That meagre fragment of Archimedes' mind that I was able to understand. And retain.

That will suit me, Marcellus agreed, pleased with himself.

But I want something in exchange.

The Roman was taken aback.

You will have your life, Greek. How dare you expect more?.

Dinostratos shrugged.

My life has no value. You know that well. I demand something else.

Marcellus snorted.

You are in no position to bargain, loser. But your brazenness amuses me. So, tell me - what’s your price?.

I want the name of the person who betrayed us.

The Roman puckered his lips.

What are you talking about? There was no betrayal. You surrendered.

I am not talking of the last defenders of Ortygia, consul. They were a handful of survivors without food or arms. I refer to when you took the Epipolis. It is said that a man from Syracuse opened the gates of the tower of Euryalus to you. Is that so?.

Marcellus laughed.

You’re as crazy as your master, Greek.

He was an aristocrat insisted the prisoner. It was the squint-eyed noble called Periphas, was it not?.

The consul stopped laughing. His face became pensive. He sat down on his tripod and invited Dinostratos to do the same.

Tell me about Archimedes, Greek. Tell me how he fought in the siege. If I am satisfied with what you say, I will grant you the reward you seek.

There are two different stories, Dinostratos clarified. My master in peacetime, and my master at war. I can tell you both. But I won’t be brief.

Marcellus filled his pitcher with wine.

We have all night.

––––––––

"You have often heard that the city of Syracuse is the greatest of the Greek cities,

and the most beautiful of all. It is so, O judges".

Marcus Tullius Cicero, In Verrem, II,4,117

Ortygia, 227 BCE

"Too frail! What’s up, are you ill? Why should we take you, you runt? We need sturdy slaves here!".

The ‘welcome’ I received into the house of Archimedes was not exactly a show of Syracusan hospitality. In my memories, I see myself standing straight, naked with my head bent undergoing a serious inspection by Theonia, my master’s youngest sister. I already knew that since the death of her husband she had dedicated herself to presiding over the private life and the domestic affairs of her famous brother. But I did not know that within those walls decorated with nymphs and painted dolphins she was a tyrant of whom Dionysios himself would have been terrified.

I must admit, moreover, that, at that time, my appearance justified Theonia's cynicism. I was just thirteen years of age but looked younger. I was a heap of bones protruding from a huge bush of unkempt hair. I remember staring at the splendours in the villa, accustomed as I was to the damp hovel dug into the caves under Neapolis, which was crowded with families of my own stock that I shared with my mother, two brothers, six sisters, some fleas, rats, the cold and hunger.

As I was saying, Theonia checked my teeth, knees and nails thoroughly. She then took a lit torch to my face and clicked her fingers by my ears.

He can see and hear perfectly well, my father, or rather, the creep who the day before had presented himself at the caves as such, reassured her. May Zeus strike me if I had ever seen him before he took me with him promising that he would ‘set me up for life’.

Theonia ignored him majestically. She weighed half of the money my father had asked for and, without concealing her disapproval, dropped the coins onto the mosaic floor. The creep hurried to pick them up, muttered something incomprehensible and disappeared.

Mighty Athena, have you perhaps robbed me of my mind?, Theonia grumbled. What a great idea to take this useless being into my home! Now I'll have to find him a clean robe!.

I would have thrown myself onto my knees to thank her, but at that moment I felt too intimidated. My new mistress was middle-aged, just a little over three cubits tall, with a dour expression, and flabby flesh that hung in rolls from her chin to her elbows. She had hair the colour of Mount Etna, a whiskery mouth, fingers like the claws of a