are roots of x3 minus 6x2 plus 14x minus C equals 0.”
She removed a clean sheet of paper from a drawer and wrote several equations equaling zero. “And it would have been easier if you’d found the constant term P first. Like this.” She wrote out several more equations determining the roots of the numbers. “Then you can identify a, b, c as roots of this.” She wrote x3 − rx2 + ½(r2 − s)x + [½r(3s − r2) − t]/3 = 0 and tapped the paper with her pencil.
She turned the page to show him how she’d worked it out. His eyes flashed with self-directed anger. “That’s not what I did.”
“I see that. Fortunately, there is often more than one way to solve a problem.”
Lydia ran her finger over the scribbles and cross-outs that constituted his work. When she came to the last page, a black circle ringed the solution he’d reached. Lydia looked at the number 0 with a curious combination of dismay and elation.
Schooling her features into an expression of impassivity, she turned to look at him. He stood right behind her, his hands loose on his hips, his expression still dark as he stared down at his messy work.
“You’ve got it,” she said.
His gaze went to hers, his eyebrows lifting. “I beg your pardon?”
“You solved the problem.” Lydia tapped her pencil on the page. “The sum of the fourth power of the numbers is zero.”
“It is?” Northwood blinked with surprise.
“Yes.”
“You’re sure?”
“Positive. Congratulations.”
“I’ll be damned.” Northwood shook his head, a grin breaking across his whiskered face. He slapped his hands together in victory. “You’re not putting me on, are you?”
“Of course not.” Lydia couldn’t prevent another smile, her disappointment over losing the locket yet again fading underneath a sudden rush of pure pride. In him.
Northwood chuckled, his fatigue dissipating with his well-deserved satisfaction. He ran his hands over his face and through his disheveled hair.
“And you wrote that.” He shook his head. “Good lord, woman, you’ve got a sharp mind, though I admit to occasionally believing you’d given me an unsolvable problem.”
“I wouldn’t have done that.” Lydia gathered the papers and slipped them into the desk drawer. The secret place in her heart knew she would always treasure them. “I do play fair, Lord Northwood.”
“You not only play fair, but you also play well.”
Lydia closed the drawer and stood, turning to face him. Apprehension twisted through her as she realized that his solving the problem meant that, once again, she owed him an undetermined debt.
He looked at her, his gaze intent on her face as if he were trying to see beneath the surface. Her hand curled around the back of the chair.
He continued looking at her, scrutinizing, assessing. “Women very rarely receive an education in advanced mathematics.”
“True.”
“So how did you?”
A black cloud threatened at the edge of Lydia’s consciousness. She pushed it aside, refusing to allow it to darken her pleasure over Northwood’s victory, over his admiration of her abilities.
“My grandmother,” she confessed. She rubbed her finger over a crack on the surface of the desk. “She was… I told you that my mother became quite ill when I was just a girl. But even then I had a fascination with numbers. My grandmother recognized my aptitude and convinced my father to hire a mathematics tutor. Mr. Sully. He taught me for about four years, everything from algebra to geometry and basic calculus. Then when my mother’s illness worsened, my father sent me to boarding school so I wouldn’t have to contend with her condition.”
“Did you have to put mathematics aside then?”
“On the contrary. It wasn’t part of the curriculum for girls, but again my grandmother insisted that the headmistress bring in a special tutor for me. My father paid an extra fee to ensure I had at least two sessions per week. Mr. Radbourne this time. He wasn’t as amiable as Mr. Sully, but he was brilliant. Neither one of them ever treated me as some sort of abomination. Without them—without my grandmother and my father—I never would have sought to explore my intellectual capabilities.”
“Did you continue studying with tutors after boarding school?”
“I went to Germany, actually, when I was fifteen.” Her chest tightened. She stared at the floor, at the intricate pattern spreading through the worn carpet. “Mr. Radbourne knew of a mathematician at the University of Leipzig. After I took several exams to prove my competence, he agreed to become my professor.”