I Know What Science Doesn’t

Chapter 008

"You absolutely have to do your doctorate in mathematics."

"I'll talk to the university and push through a special application. There's already a policy allowing someone with a physics master's degree to pursue a math PhD."

"If we handle it as a special case, you can still enroll in March. Staying in physics would be such a waste..."

George Monroe kept going, one earnest sentence after another. There was no mistaking the sincerity. He was not posturing, not making a joke, not testing the waters for sport. He genuinely believed he had just stumbled across a rare kind of talent and was scrambling to save it before the wrong discipline swallowed it.

Standing nearby, Kevin Shaw's face had already gone dark.

This was shameless.

Poaching a student in public, and doing it right in front of him, was almost impressively rude.

Off to the side, Brandon Brooks and Chris Fly were clearly enjoying themselves. A mathematics professor trying to poach a physics doctoral student was funny enough. A mathematics professor trying to poach that student directly from Kevin Shaw made it even better.

There was a certain malicious comedy to it.

Meanwhile, Daniel Hayes still had one hand trapped in George Monroe's grip. He knew the older man meant every word. That was exactly what made the situation awkward. But Kevin Shaw had genuinely treated him well, and there was no way he could simply jump ship to the math side now.

He said carefully, "Professor Monroe, thank you. I really appreciate the confidence. But I still want to study under Professor Shaw."

"You may not know this," he added, "but back at Frankenston University, Professor Shaw was already my doctoral adviser."

That made George Monroe blink. "You were already doing a PhD at Frankenston University?"

"For a little over a year."

Daniel Hayes answered calmly. "Some things happened, so I came here."

George Monroe still did not fully understand, but he did not press the matter. Instead, he suddenly released Daniel Hayes's hand and brightened with a new idea.

"Then there's another option. A second doctorate in mathematics."

"The university supports dual doctorates. You could do mathematics and physics together."

"It would be difficult, of course, but I don't think mathematics is the problem for you. It would be a real pity if you never earned the math degree..."

The moment he heard that, Kevin Shaw quietly let out a long breath.

A second doctorate in mathematics was a very different matter. The requirements for a dual-doctorate path would be high, naturally, but it did not threaten him in the same immediate way. At the very least, this was no longer outright poaching.

That alone spared him a deeper level of frustration.

Once the issue had been reframed, the atmosphere improved considerably. George Monroe stopped pushing the transfer angle, and the air in the room loosened at once.

Kevin Shaw seized the opening and asked about the research.

Daniel Hayes offered a brief explanation, but no matter how clear he was, he still did not carry the same authority as George Monroe did in this room.

So George Monroe took over almost immediately, and once he started speaking, the admiration in his face became impossible to miss.

"This student is genuinely extraordinary," he said.

"He transformed the third-order Kawahara-type equation and discretized it in a direct way. During the analysis, there's a critical step: approximate substitution-conversion."

"What he discovered is a very unusual rule for approximate substitution-conversion. Once that conversion is applied, the dominant terms in the third-order Kawahara-type equation begin to converge rapidly after the expansion reaches a certain scale."

"As that rapid convergence sets in, the computational burden required for full-coverage calculation drops sharply. Put more simply, after the transformation, the equation can be computed directly by machine."

"The key lies in the approximate substitution-conversion."

He kept explaining, now speaking partly to the others and partly because he himself was still impressed by what he had just verified.

"This rule turns complicated terms into simpler ones, and the checked results remain extremely close. Many other equations or systems of equations could benefit from the same logic in a range of cases. The applied significance here is tremendous."

After finishing the explanation, he immediately turned back to Daniel Hayes and asked the question that had been bothering him the most.

"How did you even think of making the substitution that way?"

"How did you come up with a rule like that?"

He genuinely could not understand it.

To study a pattern like this, one first needed a large number of correct substitution-conversion forms to compare. It was like looking for a law in a sequence of numbers: you needed the numbers before you could analyze the pattern. So where had those correct forms come from in the first place?

For a brief moment, Daniel Hayes did not know how to answer.

The truth was impossible to explain. Because he could identify correct substitution-conversion forms almost instinctively, he had been able to list a large number of them and work backward into the pattern. But saying that aloud would help no one.

So he gave the only answer he reasonably could.

"I ran into the problem, started thinking about how to solve it, and then wondered whether an approximate substitution could be done this way."

"That's exactly it!"

George Monroe slapped his thigh and almost shouted in excitement.

"That's how it is. A great deal of research depends on inspiration, that flash of intuition."

"Often the difference between genius and ordinary people is exactly that one flash."

"I would never have thought in that direction. My instinct would have been to assume the problem simply couldn't be solved that way, and I would never have kept pushing."

Daniel Hayes felt he was being praised far beyond what was comfortable.

On the other side of the room, Kevin Shaw, Brandon Brooks, and Chris Fly had begun quietly discussing the experiment again.

Now that George Monroe had confirmed the research was real, they could use the new method to recalculate the precursor-study data. Even small numerical changes could have enormous consequences for the final conclusions.

Kevin Shaw naturally supported the idea.

So did Brandon Brooks. If the precursor-study conclusion was going to determine the direction of everything that followed, then they had to be certain it was sound. There was no room for a hidden mistake at the foundation.

Chris Fly was the one in the most awkward position. His group had been responsible for the calculation and data-analysis work, and now those results were effectively being torn down and scheduled for recalculation from the ground up.

Still, there was nothing useful he could say against it.

If a new method promised greater accuracy, what argument was left? And if the recalculation eventually proved that the earlier experimental conclusion had been wrong, then perhaps the blame would not fall squarely on him after all.

After a moment, he let out a sigh and said to Kevin Shaw, "Your student's mathematics is seriously strong, if he can produce work like this."

Then, predictably, he twisted the conversation into a joke.

"How about loosening your grip and letting him go to math after all?"

"Or if he stays in physics, let him study under me. My side focuses more on experimental testing and computational analysis. That should suit him too."

Kevin Shaw swept a hand through the air with a dark expression. "Not a chance."

That ended that.

Soon afterward, Brandon Brooks, Kevin Shaw, and Chris Fly jointly decided to recalculate and reanalyze the precursor-study data.

The project team held a formal meeting.

Everyone involved in the project was called in: associate researchers, doctoral students, everyone. There were more than thirty people in all, and all of them were to participate in the data-calculation and analysis effort. The Applied Electromagnetics Lab shifted almost immediately into a much busier rhythm.

Compared with the others, Kevin Shaw was relatively free. His responsibility lay in experimental design and execution, and only a smaller portion of the new work fell directly on him, mostly tasks connected to confirming experimental data. He still had no PhD students formally under his wing, and even the associate researchers who worked around him all had their own assignments.

But he did have one important job left.

He needed to bring Daniel Hayes formally into the project team, and he also invited George Monroe to assist with the computational side.

That gave Daniel Hayes and George Monroe a shared area of work: using the new method together to compute the third-order Kawahara-type equation arising in the experiment.

Formally joining the project was not something that could be handled with a casual verbal nod.

There was a contract to sign, and there was a confidentiality agreement as well.

What Daniel Hayes received was the standard agreement for a doctoral student entering the project. Kevin Shaw's name appeared as the supervising adviser. The immediate advantage was simple enough: he would begin receiving the project stipend ahead of time.

"It averages around three to four hundred dollars a month," Kevin Shaw explained. "Nothing dramatic, but it helps with living expenses."

"Also, your paper can be filed under the project name. Review fees and publication charges can be reimbursed, and once it's published, there'll be a project bonus attached to the result."

"It's not a lot of money, but it still helps."

Daniel Hayes signed the contract and the confidentiality agreement without hesitation.

That made him, officially, a member of the project team.

After the team meeting, the recalculation and analysis of the precursor-study data began in earnest.

Daniel Hayes was assigned a doctoral workspace. It was basically an office shared by several PhD students, with desks, computers, and enough room for everyone to pretend they had private territory when they clearly did not.

Three other doctoral students worked there with him.

The first was Samuel Lowell, a third-year PhD student under Brandon Brooks.

The second was Ethan Pike, also one of Brandon Brooks's doctoral students and also in his third year.

The third was a woman named Claire Lang. Her short hair and square-framed glasses gave her an easy, composed presence. She was a second-year PhD student under Chris Fly.

In terms of original enrollment year, Claire Lang and Daniel Hayes had once belonged to the same cohort. But since Daniel Hayes had restarted his doctoral track, and was also four years younger than she was, calling her "senior" was not exactly unreasonable.

She was the most lively of the three and immediately joked, "At last, there's a junior here who's younger than I am."

"Call me senior."

Daniel Hayes played along at once. "Hello, Senior."

"Good."

Claire Lang answered with a grin.

Samuel Lowell and Ethan Pike, however, were clearly on the same wavelength with each other. They acknowledged Daniel Hayes only with the most perfunctory gesture. Even their names had been introduced by Claire Lang, not by themselves.

Since they were not making an effort to talk, Daniel Hayes did not force anything either. He simply sat down at his place and began organizing his things.

The two men exchanged a glance and almost simultaneously curled their lips in faint disdain.

The reason was simple.

They disliked him.

More specifically, they disliked the fact that he had openly questioned the validity of the precursor-study conclusion.

To them, that was ridiculous.

They had spent more than a year on the project. They had participated in the design, the research process, and the analysis behind the precursor study. They had real confidence in the result. It was not just another result, either. It was the biggest success the project team had produced in half a year, maybe the only success with enough substance to show anyone.

Now this newcomer had effectively implied that it might be wrong.

Wrong?

What kind of joke was that?

The two of them leaned together, pretending to discuss work while actually whispering to each other.

"The team really decided to recalculate all the precursor-study data?" Ethan Pike said with a quiet click of the tongue. "The analysis was done three times already, and every result matched. Professor Brooks only agreed because of Professor Shaw's face, right?"

Samuel Lowell kept his voice low. "I heard there's some new math result involved. Supposedly his."

He tilted his head slightly in Daniel Hayes's direction.

"What I don't get is how a physics PhD student is supposed to have a math result strong enough to affect our experiment."

"Maybe it's really just because of Professor Shaw," Ethan Pike said. "And maybe because some math professor likes him a lot. I heard there's a professor on the math side who thinks very highly of him."

"Then why doesn't he just go study math?" Samuel Lowell gave a small dismissive snort. "All he's done is increase our workload with work that probably means nothing."

"Can't be helped."

"These next couple of days are going to be awful..."