Excerpt
Prologue
Amphichiral Knot

They say a little knowledge can be dangerous.
But of course, we already knew that. Our minds might journey into the perfect, pure planes of mathematics, but we cannot live there. We are only human and no matter how we try, no axiom can shield against corruption, no theorem stand in place of morality.
In the dead of night, we smuggled that knowledge beneath our coats and ran, trailing chalk into the desert. We tried to hide what we knew and became fugitives; we tried to wield what we had learned and became outlaws. We used the knowledge we had fought for as a weapon, and became villains, turning ink to blood.
So you see, a little knowledge can be dangerous. But a lot of it can be deadly.
We learned that the hard way.
One
Iteration

Malago!
The shouts reached me over the sound of burning pages, the hungry gulps of flame consuming the university.
Malago, help!
My colleagues ran choking in the smoke, ripping the coats from their backs to try to beat out the pyre that licked at the library walls, reaching with their bare hands to save the precious texts even as their covers bubbled and hissed. While all around, masked attackers hooted and howled, putting torch to whatever they could find, daubing the walls with anti-pedagogist slogans in paint as red as the blood that pooled on the stones of the quad.
SCIENCE IS SIN
I staggered through the chaos in my nightdress, bare feet cut and bleeding, but there was nothing I could do; nothing I could say to stop the violence. The mathematics building was ablaze, the classrooms ransacked, astrolabes and orreries smashed to pieces on the flagstones. I dropped to my knees among the carnage, raking through it to save something, anything…
Metal clattered. A single tin.
THE NEWTON SET OF MATHEMATICAL INSTRUMENTS
COMPLETE & ACCURATE
A sob escaped me as I gathered it up. Those few simple tools, a mathematician's first, were now as guilty as a smoking gun.
There was a shout and an explosion of glass as a figure crashed through the window of the arithmetician's lounge, arms clasped around a bundle of papers. He staggered up, brown curls matted with sweat.
'Ferm!' I cried.
He turned my way. Too late I saw his mouth drop open in a warning, too late I saw the reflection of movement in my spectacles, an attacker looming behind me to strike…
I do not know how it happened. One moment the protractor was on the stones, the next it was in my hand and the next my hand was moving, the instrument arching in a perfect parabola to slice my attacker's throat. He dropped the club he had been wielding, blood spurting over his ill-fitting yellow jacket. Only then did I see how young he was, barely more than a boy, taught too soon to hate. I reached out but he stumbled away in fright and tripped, falling backwards into the flames…
I lurched awake.
My heart was pounding, back slick with sweat. For a moment I was sure I could still smell the acrid, tragic sting of leather and paper burning, and instinctively reached beneath the pillow. The protractor was there, as always. I drew it out. My fingers rested where they had on the first night I had wielded it, all those years ago.
Beside me, Dog let out a whine and thumped her tail in question. I set a hand on her head to still her, listening. Nothing. Just the dry hiss of the desert beyond the safehouse window. Just Miss Wang's sleeping breath and the faint, furtive tick of Reason's pocket watch in the next room. Without its steady gauging of seconds, time turned feral, measured only in gnawing hunger and thirst, in sundials made from sticks and bones and ghosts of schoolroom bells. I closed my eyes, trying to let it soothe me. Everything seemed quiet. So why was my neck crawling with ants?
I reached for my boots.
In the main room, the stove had burned down to embers, pulsing weakly through thick coats of ash. A figure slumped at the table, asleep on his watch. Fermat. His cheek rested on pages covered in a frantic, spider scrawl of calculations, drool blurring the symbols to uselessness. He still clutched the pen, his fingers wretched with ink, an empty whiskey bottle on the floor beside him. Gently, I pulled the blanket up around his shoulders, unbolted the door and stepped out into the night.
Beyond the shack, the badlands stretched, an unbroken sheet of paper in the moonlight, white to the horizon. Sometimes I wished I could make my mind like that, tabula rasa, with no trace of my sins.
Closing my eyes, I listened. Even here, so far from civilization, we were in danger. Greed had legs. So far, we had outridden it, but sooner or later, one of us would stumble. We were WANTED and that word acted like a spell, transforming us from human beings into bags of gold wrapped in flesh. My own bounty was now too large to be spoken aloud in respectable company. Little wonder. It was the sum of my transgressions, a decade of debt in the eyes of the Capitol: robbery, treason, arson. Arithmetic. Calculation. Murder.
Call it instinct, or a mathmo's nth sense, but abruptly I realised I was not alone. Someone was out here, watching my every move. I shifted the protractor in my fingers.
'Who's there?' I called.
The darkness answered. 'Malago.'
The hairs on the back of my neck rose. Only one person ever called me that. Only one person dared. The man in whose presence I had trembled as an undergraduate, the man who had taken the pen from my hand and replaced it with a gun. The man I had run from.
Princeps Mathematicum, we had called him. Prince of Mathematicians. The Cannon, the Capitol had named him since. The leader of the notorious Magnetic Association. The only mathmo in the Western States who had never been caught.
'Gauss,' I said. 'What are you doing here?'
He moved into the light and smiled. 'Malago, meine geehrte Schülerin, I'm here for you.'
