Ryan had never felt so nervous in his life, but when he passed under the ancient stone archway he knew at once in his heart he had made the right decision. The ground was solid with no trapdoors in sight and when the Oracle was also sure, he had the rest of the ECHO team march beneath the arch just to make sure.
Another lengthy trudge through a tunnel with their heads full of thoughts of escape, and they reached a spiral staircase built into the rock, twisting down into the darkness until the stone steps eventually vanished from view. They looked heavy and solid, but where they led was another question. The thought of stumbling and falling over the edge into the abyss made Hawke and the others debate the sanity of not finding another route.
“There’s no other way,” Ryan said. “This is it. This is the pathway to the second gate. The tablet was clear.”
Hawke pulled a glow stick from his pack. He bent it in the middle, cracking the vial inside and mixing the hydrogen peroxide and diphenyl oxalate until a warm amber light began to glow. He dropped it down into the void, and watched with the rest of his team as it fell through the air and disappeared. “Anyone hear it hit the bottom?”
“Not me,” Lea said.
“Nor me,” said Ryan.
“Then it’s a drop of literally hundreds of meters!” Lexi said.
“We’ve been through worse,” said Reaper.
“Yeah, think of all those hours trapped in a pressurized aircraft cabin with Ryan,” Scarlet said, this time offering the young hacker a wink.
He returned the favor by blowing her a kiss. “Thanks, darling.”
“Hey, that’s my line!”
“Enough talking!” Absalom said. “And more walking. Get going down the steps, now!” He slid the bolt on his compact machine pistol and raised it until it was pointing at Hawke’s face. “You go first, hero.”
Hawke lifted his hands in mock surrender. “Hey, take it easy, mate. I can take a hint just like anyone else.”
With the rest of ECHO behind him, plus Qasim at the back, he started down the steps, acutely aware of the lack of any rail or rope, carefully selecting his footing before moving onto the next step. One slip and it was all over, and he hadn’t come this far to die on the final furlong.
With only the artificial lights from their flashlights and glow sticks, they moved carefully in the darkness as they followed the curving steps down into the depths of the earth. After a few minutes of walking in circles down the spiral steps, Hawke called out from the front of the line. “I see the glow stick now — it’s faint but definitely there.”
Lea peered down over the steps and squinted. “Why is it so pale?”
“Probably under water,” he said. “Let’s keep moving.”
They reached the bottom another quarter of an hour later. Hawke had been right — there was a pool of water around the bottom of the steps and the glow stick was at the bottom now, covered in silt.
“Look!” Ryan pointed into the dark, sweeping his flashlight across another chamber, much bigger than the first. This time there were seven archways, each adorned with its own intricately carved symbol on the keystone.
“It’s the second gate,” Ryan said. “Another tablet and another riddle.”
The Oracle shoved him closer to the wall with the stock of his weapon. “Read it.”
Ryan closed his eyes and counted his rage away before turning his attention to the next tablet. “It’s similar to the first, but harder… much harder.”
“What is it?”
“It’s mathematical, I think. Do you agree Professor?”
Qasim leaned in and peered at the carvings. “I think so, yes. These are numerals, and that means this is out of my field.”
Lea looked at Ryan, her eyes heavy with hope. “But not out of your field, right Ry?”
Ryan scratched his chin, before he could reply. The Oracle walked forward again, flanked by his Athanatoi guards. “You had better hope not, Bale.”
“I can do it, I think,” he said with a heavy sigh. “But it’s not going not be easy. “I think we’re looking at something to do with ring theory.”
Lexi laughed bitterly. “What is it with these guys and damned rings?”
Hawke rubbed his eyes and stared at Ryan in the gloom. “Ring theory, mate?”
He nodded. “In maths we have something called algebraic structures.”
“And here we go again,” Scarlet said, turning to Salazar. “Got a cigarette?”
“Shut your mouth.”
“Fair enough.”
“Algebraic structures?’ Hawke asked.
“It’s hard to explain to…” he changed tack when he saw the look on Scarlet’s face. “It’s a tricky subject. Let’s just say that there are various structures such as lattices, fields, groups and rings. It gets more complex still with vector spaces but we don’t have to go there now.”
Scarlet sighed in mock disappointment. “Damn it.”
Ryan shot her a glance. “Fine, so ring theory is the mathematical study and analysis of ring structures, and one of the unsolved mathematics problems we have is the Köthe conjecture.”
The Oracle sighed. “I’m growing impatient and so are my men. If this is a delaying tactic, you should know I will start executing your friends one by one, starting with him.” He nudged his chin at Zeke.
Absalom grabbed the Texan and hauled him out of the group, forcing him to his knees and putting a gun at his temple.
“You have three minutes.”
Ryan was aghast. “Three minutes to solve the Köthe conjecture?”
“Two minutes, fifty-five seconds.”
“But the greatest mathematical minds have been trying to solve this for nearly one hundred years!”
“Two minutes, fifty seconds!”
Ryan blinked in the darkness. “Will someone please hold the sodding light up at these symbols!”
Reaper whipped his flashlight up on the wall and Ryan started mumbling under his breath as his eyes scanned the ancient carvings.
The young hacker clamped his eyes shut as he struggled to work out the problem. “The nil radical is the sum of all potential nil ideals…”
“Is he speaking in Ryanish again?” Scarlet asked.
Lexi shrugged. “I have enough trouble understanding him when he speaks in English.”
“But if the ring hasn’t any nonzero nil ideals then does that mean it hasn’t got any nonzero nil one-sided ideals?”
He was staring at Lea now, his eyes wide open again, but he wasn’t seeing her. He was staring right through her into the middle distance. Suddenly he stopped muttering and spoke out loud. “That one.” Ryan pointed to the fifth door from the left. “We go through that one.”
“How do you know?” the Oracle said.
“If I tried to explain it you would never understand.”
“An insult to my intelligence… not very wise.”
“It’s the truth.”
“Fine, but once again, you go first.”
Ryan looked defiant. “No problem. I’m telling you the truth.”
“I’m kind of nervous about what we’re going to find now,” Lea said.
“Tell me about it,” said Ryan. “The fact this civilization had thought of and solved the Köthe conjecture hundreds of thousands of years before we did does not fill me with confidence.”
Ryan walked down the fifth tunnel and when he was safely through the others followed him — like before, first the ECHO team and then the Iraqis and then finally the Oracle and his Athanatoi guard.
When Hawke finally reached Ryan, he found the young man staring wildly across another chasm, his eyes mesmerized by something on the far side. He followed his gaze and realized instantly what had transfixed his friend: the entrance to the Citadel was right in front of them, at the far end of a bridge crossing the chasm.
From behind in the tunnel, he heard Lea’s voice.
“Is that light up ahead?” Lea asked.
“Come and see,” said Hawke.
“There shouldn’t be any light down here.”
“Just come and see!”
She exited the tunnel and gasped. “Oh my God…” her voice was barely a whisper. “I’ve never seen anything like it before!”
“I know.”
“What are those hole around the outside?” she asked.
“Keyholes,” Ryan muttered. “For the idols.”
“What’s the delay?” the Oracle barked, pushing his way past Qasim and Zeke. “Why have we stop… oh my God!”
As he stared at the vast circular portal, he knew immediately that they had found the Citadel. “Get the idols out,” the Oracle snapped. “It’s time to enter them into the locking mechanism.”
Absalom padded over to Hawke and ripped the bag carrying the idols from his shoulder. Dumping it on the floor, the monk carefully unpacked the idols Eden had shipped from London and walked with them over to the circular gate.
The Oracle fixed his gaze on Ryan. “You! Insert these idols in the correct holes and unlock the third gate.”
Ryan and Qasim studied the symbols above each of the holes and then started inserting the idols one by one. When the last one had been slotted into place, a heavy sigh emanated from the circular portal and the round portal clunked open in a cloud of dust.
“Looks like we made it,” Hawke said.
Lea held his hand. “I always knew we would.”
“Very touching,” the Oracle said cruelly. “Now you can be the first to go inside.”
Hawke and Lea exchanged a glance. “If we don’t make it,” he said.
She raised her finger to his lips and silence his words. “We’ll make it.”
As the Oracle cocked his submachine gun and yelled at them to get moving, Hawke and Lea stepped through the circular entrance and disappeared into the dust.