Page 39 of The Secret of Secrets

“And exponentials, apparently,” Gessner said, clearly unsettled. “Okay, Professor, no more hints for you.”

“And on that note,” Langdon said, standing brusquely, “I think it’s a good time to call it a night.”

“Ah, Father says the party’s over,” Gessner said, getting to her feet, leaving most of her vodka tonic behind. “Katherine, I’ll see you in the morning. Eight a.m. sharp at Crucifix Bastion.”

We’ll see, Langdon thought.

As Katherine stood, she drained the remainder of her absinthe in a single swallow. Langdon calculated he now had approximately three minutes to get her upstairs before the concoction fully hit her.

They said their goodbyes, and as Langdon helped Katherine down the hall in the direction of their suite, he chided himself for tolerating Gessner for so long tonight. He had met plenty of self-important academics, but Brigita Gessner took arrogance to an entirely new level.

An Arabic tribute to an ancient Greek with a Latin twist? Seriously?

Langdon wished he’d been able to decipher Gessner’s “ingenious passcode” on the spot, if only to blunt her unbearable self-importance. But the moment had passed. Forget it, he urged. Who cares?

When they entered their suite, Katherine disappeared into the bathroom to get ready for bed. Langdon paced the living room, knowing he was too wound up to go to sleep. As much as he wanted to forget his encounter with Gessner, his irritation over her smug superiority had awoken his competitive spirit. His analytical mind was already churning, looking for a way to unpack Gessner’s riddle.

Isolate each piece, he thought. An Arabic tribute…

Langdon knew there were no Arabic letters in an alphanumeric alphabet, so he was fairly certain Gessner was referring to the other Arabic alphabet—numbers—the mathematical language popularized by the Arabs over a thousand years ago.

Gessner’s passcode must be a number.

“An Arabic tribute…” he puzzled aloud, “to an ancient Greek.”

Logically, if Gessner’s passcode was a number, then her “tribute” would be numerical, so it therefore followed that the ancient Greek in question was probably associated with mathematics.

The three most famous mathematicians of ancient times were all Greeks.

Their names had been emblazoned in Langdon’s brain after his prep school math teacher Mr. Brown informed the class that their school’s ubiquitous acronym, “PEA,” was not an abbreviation for Phillips Exeter Academy as everyone believed, but rather a secret tribute to the three titans of early mathematics—Pythagoras, Euclid, Archimedes.

So, which one might Gessner be referencing? Langdon worked his way through the list.

Pythagoras: Pythagorean theorem, theory of proportions, sphericity of the earth.

Euclid: Father of geometry, conic sections, number theory.

Archimedes: Archimedean spirals, the number pi, areas of circles.

Langdon paused.

“Pi,” he declared loudly.

Katherine called from the other room. “That’s a great idea! Call room service. I’ll have a piece too!”

Different pie, he thought, chuckling as he went into the bedroom and helped Katherine woozily into bed. After kissing her good night, he stepped back into the living room, extracted a piece of paper and a pen from the rolltop desk, and sat down on the couch, overtaken now by a compulsive desire to finish what he had started.

The solution to Gessner’s puzzle was far from clear, but Langdon had just realized that the spelling of pi—arguably the most famous number in history—was intriguingly close to that of PSI.

Gessner said her passcode was PSI…encrypted.

Langdon sensed he was on the right track.

3.14159, he thought, jotting down pi’s most common form.

The number pi could certainly be described as a tribute to an ancient Greek, and it also was expressed in Arabic numerals, which meant it satisfied two of Gessner’s three requirements.

An Arabic tribute to an ancient Greek.