The Heart of Numbers pulsed, its gold and shadow halves swirling like a storm trapped in glass. Mark's Seal burned, the Numen from the cubic equation still thrumming in his veins. Lyra's hand was on his arm, her plea—break it—ringing in his ears. The chamber's walls cracked, equations spilling like water, and the ancient voice spoke again: "Take the Heart, or break it. Choose now."
Mark's chalk trembled. Breaking the Heart meant defying the Tower, maybe losing everything—his Seal, his chance to change Numina. Taking it meant power, but at what cost? Lyra's brother had chosen, and now he was gone.
"Why break it?" Mark asked, voice hoarse.
Lyra's eyes were fierce. "The Heart's a trap. It binds you to the Tower, makes you its puppet. My brother thought he could control it. Now he's part of it—those scholars, those shadows. I won't let that happen to you."
The Heart pulsed, and a new problem appeared, its symbols sharp as knives:
Solve: 1/x + 1/(x + 1) = 2
Mark's mind raced. Combine the fractions: common denominator is x(x + 1). So, (x + 1 + x)/[x(x + 1)] = 2, or 2x + 1 = 2x² + 2x. Subtract: 0 = 2x² + 1. No real solutions—discriminant negative.
"No real solutions," he said.
The Heart dimmed, and the voice growled: "Correct. But the Tower demands more."
Lyra's problem appeared:
1/(x – 1) = 3
"x = 4/3," she said, quick and sure.
The Heart flared, but the chamber shook violently. Cracks spread, and the scholar reappeared, his robe now a storm of numbers. "You resist," he said. "But the Heart will have its due."
Mark's resolve hardened. "We're done with your games." He turned to Lyra. "How do we break it?"
Her eyes widened. "Solve its final lie. The Heart's power is an equation—unstable, infinite. Find it, and we can shatter it."
A massive problem materialized, its symbols spiraling into infinity:
Solve: ∑(1/n²) from n=1 to infinity
Mark froze. Infinite series? He'd heard whispers of such things—Numina's scholars called them the "songs of eternity." Lyra nodded. "It's the Basel problem. The sum converges to π²/6."
"Pi squared over six," Mark said, trusting her.
The Heart screamed, and Numen exploded, knocking them back. The cores cracked, light and shadow spilling out. The scholar vanished, and the chamber began to collapse. Lyra grabbed Mark's hand. "Run!"
They sprinted toward a glowing exit, the Heart's fragments raining behind them.