"Hmm..."

Leaning forward, he made a small correction to the computations on the blackboard, flicking a small amount of white dust away with his little finger, then stepped back. Equations filled almost the entire six by twelve foot slate-gray area with mathematical conundrums, exercising his mind to fullness and giving him much pleasure. Such calm cerebrations were to be valued in today's hectic world filled with the clatter of cabs and the sound of tradesmen going about their business, all of it overlaid with the smell of coal smoke and steam.

Overall, he rather approved of the march of technology, as it showed the primacy of the mind over the whims of nature, but at times it was vexing in its din. With time, he hoped, mankind would fathom how to bring about change without the attendant noise and smell. It would be something he personally would find most pleasing.

Idly he thought that perhaps when he had finished this current project, and set the other machinations he was contemplating into action, it might be a diverting pastime to resume his research into the work of that Babbage fellow, who had produced such brilliant concepts in the field of computational machinery. He had been well ahead of his time and sadly limited both by industrial capability and financial concerns. Nearly twenty years of improvement to the mechanical arts might well have rendered the first consideration moot, while he himself had much more financial acumen and therefore could personally fund the construction of a machine built to Babbage's designs.

It seemed worthy of further consideration, if only due to the ability of such a mechanism to automate some of the current mathematical drudgework he was laboring at, possibly achieving in minutes what took him days to do manually. Such an eventuality would be most helpful, and he could see some fascinating developments that could result from so vast an improvement in calculation speed.

Pausing to make a note in his diary so he would remember that line of thought later, he put it back on his desk then resumed ruminating. The greater picture hinted at by the equations in front of him was slowly coming into focus, but still most of it eluded him despite his best efforts.

Bernhard had proposed a hypothesis which was fearsomely complex even for this field, he once again decided as he slowly wrote another line on the board, then went back half a dozen places and changed some terms. It was an entertaining challenge, one worthy of his own abilities, and one that at some level he rather thought might even be beyond him. Still, it was fascinating, and a good diversion from day to day life. The purity of the calculations required and the opportunity to lose oneself in the realm of raw thought for extended periods was relaxing in a way that few other things were.

Some time later, as he was sitting on the edge of his desk yet again studying the blackboard, attempting to resolve a number of apparently mutually contradictory suppositions, there was a polite tap at his door. At first he ignored it, hoping that whatever person desired his attention, be it student or faculty, would after a while decide to bother someone else. Unfortunately the knock came again, which made him sigh a little, put the stick of chalk he'd been rolling between his fingers down on the desk, then move to answer the interruption.

With any luck he could persuade his undesired caller to leave promptly and get back to work before the train of thought he'd been following faded. It was most irritating when that happened.

Pulling the door open somewhat more roughly than good manners would allow, a sharp query on his lips, he abruptly found himself staring, shocked.

"Excuse me Professor Moriarty. It's an honor to meet you, sir. I've been quite enjoying your latest work but I believe I've found a mistake with your calculations and I was wondering if I could impose upon you for a clarification." The figure in the corridor outside his room was, it was fair to say, not one he was expecting to lay eyes on.

James gaped a little at the woman standing there smiling at him. Her dress sense was impeccable, he absently mused, noting the quality of the material and the pure artistry in the tailoring, showing a keen eye for fashion and a considerable level of wealth to afford such finery.

Her sartorial choices, though, somewhat paled into insignificance when one took notice of the fact, which he couldn't deny despite his surprise and disbelief, that she was apparently reptilian in nature rather than the much more common human. He could see no signs of it merely being elaborate makeup or some inventive application of the theatrical arts, the scales appeared to be entirely real, as did the tail which he could see near her feet. Feet that were bare and bore talons the like of which he thought would make one of the great cats somewhat envious.

Her glowing yellowish eyes, a reptilian pupil in each fixed on him, seemed to radiate calm interest and a certain sly amusement at his shock.

He opened his mouth to say something, couldn't quite work out what to say, closed it again, then looked rather helplessly both ways down the corridor. Possibly he was hallucinating? He had been working very hard recently after all, and a fever of the mind wasn't entirely impossible, although he liked to fancy he was above such things. A corroborating opinion as to what precisely was standing in front of him would be welcome at this point, even if it came from one of the shaven neanderthals commonly known as students that infested the place.

Annoyingly, for once there was no other person present, so he could only proceed on the basis of what his eyes were telling him.

"I apologize if this isn't a good time," she added, a distinct accent of the colonies present in her voice, alongside something he suspected came from much further afield. "I could come back later if it would be more convenient for you."

Deciding that good manners would substitute for comprehension for the moment, until he could come to some understanding of whatever was genuinely happening, James replied, "My apologies for staring, Miss…?"

"Saurial," she replied, holding out a hand, which he noted also bore sharp talons on the fingertips, but was otherwise very human appearing despite the scales, with long graceful fingers. He took it and bowed very slightly.

"James Moriarty, at your service, Miss Saurial. Your appearance was, I confess, something of a momentary shock. I apologize once more for my rudeness."

"Don't worry, it doesn't bother me, Professor," she replied with another smile, good humor in her voice. "It happens a lot." She held up a book in her other hand which he instantly recognized. "I found your book fascinating and very well written. It's highly enjoyable. However, like I said, I did spot a point where I think you may have made a small error, and as I was in the area, I hoped I could discuss it with you. If you have time, of course, I wouldn't want to interrupt."

"You've read my book?" he asked, even though she'd just told him that, feeling somewhat blindsided.

"Yes, I've been following your career with interest for some time," she nodded. "Your treatise on the binomial theorem was excellent. I spent some time tracking down other shorter works of yours for my personal library, and when this was published I immediately bought it."

"I see," he said, only partially truthfully. Coming to his senses, he stepped back and to the side. "Please come in, Miss Saurial."

"Thank you, Professor," she replied, entering his room. He closed the door and turned to see her studying the blackboard with her head cocked to one side. "Ah. Interesting. You seem to have got a lot further with this than most people have managed so far."

He looked from her to the board and back. "You can follow the maths?"

"Yes, it's fairly straightforward," she told him, moving closer to the board and scanning the equations. "I believe you may have missed a term here, and these eigenvalues are wrong," she added a moment later, indicating one section of the equations. "Do you mind?" The humanoid and well dressed lizard glanced at him.

Somewhat numbly he shook his head. She picked up a piece of chalk and with rapid precise strokes wrote a new series of formulae on a blank section of the board, while his eyes steadily widened at the implications.

"Good god," he whispered in awe, moving over to stand a few feet from the blackboard, intently studying what she'd written there. "I see… Brilliant. Absolutely brilliant. I missed that entirely. And if this is correct..." James stepped sideways, to inspect one of his original long series of symbology that few others on the planet could understand. "...this is wrong, it should be four over pi times the square root of x..." He made some quick changes. "Which further implies this entire section cancels out."

"Correct," she responded, sounding pleased.

He continued to change his equations, new paths opening in his mind as he saw places he'd been sticking at for weeks fall away like melting snow. It was almost dizzying, the sudden alteration from imponderable problem to possible solution. Half an hour later, having entirely forgotten about his unusual visitor, he stood back and examined the result of his reworking almost the entire board. "Astounding," he breathed. "It is not quite complete, but this is far, far closer to a general proof of the hypothesis than I thought I would manage in my lifetime." James shook his head in wonder, then turned to Saurial, who was watching with a small smile on her face.

"Yet again, I must apologize, my dear. I fear I succumbed to the call of the intellectual pursuits to the exclusion of manners. Would you care for some tea?"

"That would be very nice, thank you," she replied politely with a nod.

Going over to his tea service, he lit the alcohol burner under the pot of water he kept ready, then prepared two cups. "I suspect that you are visiting from somewhat further afield than, for example, Devizes," he said, glancing at her with interest. She laughed gently.

"Yes, I'm not local, I have to admit," she smiled. "My family does get around though. We like traveling and meeting people. And, where possible, helping out. We're quite good at that."

"You appear to have a considerable mathematical bent," he noted.

"It runs in the family," she nodded, taking a biscuit from the plate he held out. "I thoroughly enjoy this sort of thing. If you like, I could show you some of my own work. I've made some interesting discoveries in the field of multidimensional array theory, as an example."

"I would be most intrigued to see it," he replied with keen interest.

"Great. Oh, before I forget..." She held up the book again and smiled in a manner that was rather more toothy than he was accustomed to, but winsome nonetheless. "Would it be imposing too much to ask you to sign this?"

James Moriarty smiled back. "Not at all, my dear. Do you know, you're the first person to ever ask that of me? It would be my pleasure." He took the book from her and opened it to the frontispiece, accepting the slightly odd and remarkably high quality pen she handed him as well. "And while we wait for the water to boil, I would be interested to see where you believe I made an error. I was under the impression that I'd covered all eventualities in my original work."

Many years later, Professor Emeritus Moriarty, noted polymath and inventor, often spoke with great fondness of an old acquaintance of his who was even better at mathematics than he was, something his students tended to take with a pinch of salt. As they did his descriptions of her as a lizard woman. However, none of them were ever of a mind to publicly disagree with him, since his reputation tended to ensure people were at least polite and tolerant of his peculiarities.

After all, he had almost single-handedly brought the Mechanical Information Age into being, which counted for a lot.

That Holmes fellow who sometimes wrote in the Times was clearly not entirely all there, although no one could deny he was a remarkably gifted investigator. Why he had an apparent fixation on Moriarty no one could fathom, but brilliance didn't deny eccentricity.

Since they were British they allowed it in good humor, and merely snickered under their breath while going about their business.