One now finds indeed approximately this number of real roots within these limits, and it is very probable that all roots are real. Certainly one would wish for a stricter proof here; I have meanwhile temporarily put aside the search for this after some fleeting futile attempts, as it appears unnecessary for the next objective of my investigation.
Bernhard Riemann, Ueber die Anzahl der Primzahlen unter einer gegebenen Groesse. 1859
He looked up after reading it at the lady. She was staring directly at him in a slightly disconcerting fashion.
“I am bewildered. I had thought I was working on an astronomical problem, and here it is, solved. I know that politics often link with science, since navigation and war often rest on astronomy and physics, but this seems, alarmist.”
“He is assured absolutely in what he says. He has asked me to accompany you to London.”
“Since the letter is authentic, I accept what he says, even if I am not sure how to take it. But how am I to know who you are, and whether d’Arrest intends it?” Suddenly he stopped, he recognized her as d’Arrests young cousin, who he had last seen some years ago before she had bloomed to womanhood. The dress was ill fitting – as his eye began to understand, and worn, because it was not hers. She was borrowing it from someone else, perhaps an aunt or her mother, having had no such “proper” attire. The pieces fell into place. “Maugerite. I had not recognized you.”
She handed him a second note, clearly intended for the event that he accepted the first letter. She managed a wane smile, and her face brightened, glad that she had been remembered. “Enclosed you will find sufficient funds for train tickets to Calais, travel papers that I have procured through my own channels, and tickets thence to London. Also included are letters of introduction, should you find them necessary. Marguarite you will find an excellent traveling companion, with many skills of her own. She is also able enough in astronomical calculation to act as an assistant there, but it is advisable you treat her with the deference which is appropriate.”
And he counted out the money carefully. Between this and what he had secured in Berlin, at least this would not be among their immediate concerns. He thought for a moment, and had an idea. He handed over almost all of the bills to her, keeping only the gold and silver coins. “I’m entrusting you with our travel arrangements.” He did this for the simple reason that there was no better way to find if someone was trust worthy than to trust them. He had often listened at length to people, and found, repeatedly, that after they had talked themselves out, that their designs would be revealed. If she meant him badly, the temptation of using the money quickly would be overwhelming, and he had enough friends to deal with the consequences.
Aside from that, he had to admit that there was a fine blush to her cheeks, a lovely cascade blue to her eyes, and the idea of a woman savant struck him with a deep curiosity.
- - -
The hours that would pass would find them first in that kind of technical conversation which men of a particular discipline engage in to show their dexterity. She accorded him due respect, but not the kind of empty deference that someone has who does not understand. She was clearly more than a secretary, had spent some time before the observing piece, and while clearly no virtuoso of the instruments as he was, neither was she hollow in her understanding. When it came to discussion of photographic developments, he had to admit that she was more capable than he. It was a startling moment, and one which changed his perception by one step farther still.
The night came, and they were able, with some difficulty, to change arrangements, as they went through one of the seemingly innumerable changes of coach. Each time finding a way to stand together, in the end, she, while her German was worse, explained that he was escorting her to Paris on the instructions of d’Arrest. Auwers could only fumble in such circumstances, and somehow the combination of her bright glance, poor but confident German, and lilting voice made it through. He was duly impressed.
The changed again at night at the French border, they watched carefully as baggage was moved. And she commented on how silly this was, and that someone should use the same tracks and let them change engines. He chimed in agreement, noting that unification – of knowledge, trade and money would be the great project of their generation. She made reference to his astronomy project, at which he actually managed a smile beneath his thickening beard.
It was greying dawn as they approached Paris, though it was hard to tell that they were approaching anything, since there was merely a thickening of the inhabitation. The conductor came for them and he found that she was already awake.
“Billets, si vous plait, madamoiselle, monsieur.”
She provided both of the tickets, spoke a rapid stream of French, and then explained to him that she had told the conductor that they needed a taxi to the hotel, and a porter before Arthur’s brain had even truly snapped to consciousness. The crowd and the noise however revived him, as did that uncomfortable feeling of sticking to the inside of ones suit. He stood up, she straightened his tie, settled his top hat and inspected him. Her face was quite close, and he could see the slight blush of red on her cheeks, and the careful inspection in her eyes, without being clearly aware of what it meant. He could feel the faint whisp of her breath, like an echo, rather than truly smell it. She hummed something, he did not know the tune, until he recognized it as a Chopin waltz rather belatedly.
Himself settled, she stepped back, there was an instantaneous feeling of the air rushing between them, though of course only a little bit stirred. But he felt far away, as if a great light had opened up, and he saw it from a distance in her. She led and he followed outwards, taking his walking stick and papers with him.
- - -
They came into a vast cavernous noise, with bodies pressed everywhere, but the porter arrived and they were almost ushered into a waiting horse and coach. He felt it was a blur, he hand never traveled with such precision, and had always felt himself almost lost. Clearly there was at least one thing he could learn from her, and that was how to accomplish this. Apperantly she had arranged for two rooms in a small hotel, and looking at him declared.
As they clattered along in the carriage, she turned to him directly and asked.
“So who believe you?”
He did not even hesitate. “I believe d’Arrest’s numbers, and nothing else. Everything else is conjecture, worry, fear, and imbalance. The numbers are correct. Louis is probably right that there is a great project of the age, and that I will have to take great risks for it, and that less evolved individuals may attempt to stop it, and that it will bring confusion to many, even many who are very wise. But believe? I believe, says Kant, in the stars above me, and the order within me.”
She smiled. “Do well you will. We have much to find out.”
We. Hrrrm. We. Another time, another place to ask.
“You said something about seeing Paris?”
“No Paris another time, you rest you must.”
And that was that. The building they were taken to was of some age, perhaps 200 years, with tall but small rooms, and narrow windows that opened outward. She closed her door behind her saying “Well sleep!” He had thought to wander out and test what French he had learned from d’Arrest, but as soon as he reached the room, he had thoughts of nothing but sleep. He undressed, gave himself a sponge bath and was again asleep, this time comfortably, withing a few minutes. The last thing he recalled was realizing that the simplest solution to the Mercury problem was that it had been…
He would have to work it out more strictly, but there was certainly a simple answer...