He stood up slowly. “We’re like babies out here, Jeanie; each of us with our own playthings. If anybody seems to be interested in what we’re doing, and nods their head now and again, we assume they understand. At the Institute, you interrupt if you don’t follow an argument. But that’s not the way Earthside government runs. Nod, and smile, and don’t rock the boat — that’s the name of the game, and it will take you a long way. You’ve seen how well it works for Dr. Tallboy.”

“But if he doesn’t understand a thing, what will his report say? The whole future of the Institute depends on it.”

“It does. And God knows what will happen. I thought his background was physics or engineering, the way he kept nodding his head. Did you know his degree is in sociology and he has no hard scientific training at all? No calculus, no statistics, no complex variables, no dynamics. I bet the real quality of our work won’t make one scrap of difference to his decision. We’ve all wasted a week.” He sniffed, and muttered, “Well, come on. Tallboy will be leaving in a few minutes. We must play it to the end and hope he leaves with a positive impression.”

He was heading for the door with me right behind when McAndrew hurried in.

“I’ve been wondering where you two had gone,” he said. “Tallboy’s at the departure dock. What a show, eh? I told you we’d do it, we knocked him dead. Even without Wicklund’s work, we showed more new results today than he’ll have seen in the past ten years. Come on — he wants to thank us all for our efforts before he goes.”

He went bounding away along the corridor, full of enthusiasm, oblivious to the atmosphere in Limperis’ office. We followed slowly after him. For some reason we were both smiling.

“Don’t knock it,” said Limperis. “If Mac were a political animal he’d be that much less a scientist. He’s not the man to present your budget request, but do you know what Einstein wrote to Born just before he died? `Earning a living should have nothing to do with the search for knowledge.’ ”

“You should tell that to Mac.”

“He was the one who told it to me.”

There didn’t seem much point in hurrying as we made our way to the departure dock. Tallboy had seen the best that we could offer. And who could tell? — perhaps McAndrew’s enthusiasm would be more persuasive than a thousand hours of unintelligible briefings.

The mills of bureaucracy may or may not grind fine, but they certainly grind exceeding slow. Long before we had an official report from Tallboy’s office, the argument over Jan’s visit to Triton Station was over.

I had lost. She was on her way to Neptune. She had finagled a ride on a medium-acceleration supply ship, and anytime now we should have word of her arrival. And McAndrew couldn’t wait — Wicklund was still frustratingly coy about his new work.

By a second one of those coincidences that McAndrew insisted were inevitable, Tallboy’s pronunciamento on the future of the Penrose Institute zipped in to the Message Center at the same time as Jan’s first message from Triton Station. I didn’t know about her spacegram until later, but Limperis directed the Tallboy message for general Institute broadcast. I was outside at the time, working near the Hoatzin, and the news came as voice-only on my suit radio,

The summary: Siclaro’s work on kernel energy extraction would proceed, and at a higher level (no surprise there, with the pressure from the Food and Energy Council for more compact power sources); Gowers would have her budget reduced by forty percent, as would Macedo. They could continue, but with no new experimental work. McAndrew had his support chopped in half. And poor Wenig, it seemed, had fared worst of all. The budget for compressed matter research was down by eighty percent.

I wasn’t worried about McAndrew. If they cut his research budget to zero, he would switch to straight theory and manage very well with just a pencil and paper. But everyone else would suffer.

And me? Tallboy wiped me out at the very end of the report, almost as an afterthought: experimental use of the Hoatzin was to be terminated completely, and the ship decommissioned. There would be no expedition to Alpha Centauri or anywhere else beyond the Halo. Worst of all, the report referred to “previous unauthorized use of the balanced drive, and high-risk treatment of official property” — a direct knock at me and McAndrew. We had enjoyed free use of the ship under the previous Administration, but apparently Woolford had never thought to put it in writing.

I switched my suit to internal propulsion and headed back for the Institute at top speed. McAndrew knew I was outside, and he met me at the lock waving a long printout sheet. His mop of sandy hair was straggling into his eyes, and a long streak of orange stickiness ran down the front of his shirt. I guessed he had been at dinner when the report came in.

“Did you see it?” he said.

“Heard it. I was on voice-only.”

“Well? What do you think?”

“Horrible. But I’m not surprised. I knew Tallboy hadn’t understood a thing.”

“Eh?” He stood goggling at me. “Are you trying to be funny? It’s the most exciting news in years. I knew she’d find out. What a lass!”

I may not be as smart as McAndrew but I’m no fool. I can recognize a breakdown in communications when I see one. When Mac concentrates, the world isn’t there any more. It seemed to me odds-on that he had been thinking of something else and hadn’t registered the Tallboy decision.

“Mac, stand still for a minute” — he was jiggling up and down with excitement — “and listen to me. The report from External Affairs is here, on the future of your programs.”

He grunted impatiently. “Aye, I know about it — I heard it come in.” He dismissed the subject with a wave of his hand. “Never mind that now, it’s not important. This is what counts.”

He shook the printout, stared at part of it, and went off into a trance. I finally reached out, removed it from his hand, and scanned the first few lines.

“It’s from Jan!”

“Of course it is. She’s on Triton Station. Do you realize what Wicklund’s done out there?”

With Mac in this kind of mood, I’d never get his mind on to Tallboy. “No. What has he done?”

“He’s solved it.” He grabbed the spacegram back from me. “See, it’s right here, can’t you read? Jan didn’t get the details, but she makes it clear enough. Wicklund has solved Vandell’s Fifth Problem.”

“Has he really?” I gently took the paper back from him. If it was news from Jan, I wanted to read it in full. “That’s wonderful. It only leaves one question.”

He frowned at me. “Many questions — we’ll have to wait for more details. But which one are you thinking of?”

“Nothing you can’t answer. But what in Heaven is Vandell’s Fifth Problem?”

He stared at me in disgust.

I got an answer — eventually. But before I had that answer we had been on a rambling tour of three hundred years of mathematics and physics. “In the year 1900—” he began.

“Mac!”

“No, listen to me. It’s the right place to begin.”

In the year 1900, at the second International Congress of Mathematicians in Paris, David Hilbert proposed a series of twenty-three problems to challenge the coming century. He was the greatest mathematician of his day, and his problems drew from a wide range of topics — topology, number theory, transfinite sets, and the foundations of mathematics itself. Each problem was important, and each was tough. Some were solved early in the century, others were shown to be undecidable, a few hung on for many decades; but by the year 2000 most of them had been wrapped up to everyone’s reasonable satisfaction.

In the year 2020, the South African astronomer and physicist Dirk Vandell had followed Hilbert’s precedent, and posed a series of twenty-one problems in astronomy and cosmology. Like Hilbert’s problems they covered a wide range of topics, theoretical and observational, and every one was a skull-cruncher.