On the other side of the Earth.
It was night time at the Princeton campus, only a few library rooms were still lit.
Inside a library room, Vera placed a stack of theses on the table. She found a particular line of calculations and spoke.
“… Line 11 on page 27, there’s a problem with the formula.”
She hadn’t changed much over the past three years. The only difference was that her short ponytail had now reached her arm.
If she were wearing a long skirt, one might even mistake her for a real princess. Unfortunately, she often wore teenage-looking clothes, which made people mistake her for a high school visiting student…
“Oh Jesus… My God, you’re even more strict than my PhD supervisor…” Molina rubbed her eyebags and grabbed a pen from the table. She stretched her back and stood up.
She didn’t like pulling all-nighters, and sitting there all night hurt her shoulders and back. Even though she was one of the younger lecturers, she was still getting quite old.
At least she was when compared to Vera…
Vera smiled awkwardly as she said, “What do you mean, Sophie Morel is way worse than me.”
Sophie Morel was Molina’s PhD supervisor. The two had worked on the Riemann hypothesis for a long time. After losing the 2018 Nobel Prize, Sophie gave up on the Riemann hypothesis and began researching other areas of study. Surprisingly, Sophie had been doing quite well.
Molina, on the other hand, was still stuck on this age-old question. Even though she went from a PhD student to a Princeton University lecturer, her desire to solve this question was still there.
As for how she ended up working for Vera, it was a long story.
All in all, right now, the two were in the same research project group and had the same goal— solve the Riemann hypothesis.
“No, Vera, you’re too humble. That coward could never prove Kakutani’s fixed-point theorem so beautifully. She could never study a problem so meticulously…” said Molina. Molina scratched her head and felt irritated. She said, “Damn it, I should have thought of the Odlyzko–Schönhage algorithm a long time ago.”
“Bingo, the Odlyzko–Schönhage algorithm,” Vera said softly. She wrote down two lines of calculations on a piece of paper and said, “After we correct the algorithm, we can prove that 40% of the non-trivial zero points is on the critical line… Congratulations, Molina, you discovered a method other than Levinson’s algorithm that proved Corney’s critical line theorem.”
Vera was trying to make Molina feel better by congratulating her.
However, Vera wasn’t sure if Molina felt better at all.
It took them a month to come up with this idea, and another two months to test this idea. However, in the end, their result was already proved by someone in the 1990s.
The critical line that divided the non-trivial zero points of the z function was still at 40%. If anyone could increase this percentage, they were likely to win the next Fields Medal.
However, even after so many years, no one was able to defeat this dragon.
“This is meaningless…” Molina sighed and said, “Maybe Mathematics Chronicle will accept our thesis.”
Vera gave her a look of encouragement and spoke.
“I think they will consider it. After all, we found another use for the Odlyzko–Schönhage algorithm.”
Unlike other fields, mathematical research wasn’t completely a result-oriented field. Even if someone didn’t produce a beautiful result, as long as the proof process was interesting, it might be published. Not to mention that even though Mathematics Chronicle wasn’t managed by Princeton anymore, it still had a more “relaxed” attitude regarding Princeton submissions.
However…
It was unlikely for them to publish in large journals such as Annual Mathematics.
“Maybe…” Molina rubbed her messy hair and said, “I think we should change our mindset. A while ago, I found Sir Atiyah’s notes, and I think his research is interesting.”
Vera’s mouth was wide open.
“Molina…”
Molina said,” What?”
Vera said in a serious manner, “You should really take a break.”
This might be disrespectful toward Sir Atiyah, but long before Atiyah passed away, people had been trying to use his notes, all to no avail.
“Don’t worry about me, I’m doing great.” Molina rubbed her forehead and said, “Actually, you’re right, I think I should take a break.”
Anyone who studied Sir Atiyah’s notes must be going a little haywire.
Vera sat next to her, and a moment of silence passed before she asked, “Why… are you so determined on solving the Riemann hypothesis?”
Molina replied sarcastically, “Just like how you’re determined on getting that guy?”
Vera blushed, and she hesitated for a bit and looked at the thesis on the table.
“I… I’m not as determined as you. It’s just that, he was the one who helped me when I needed help the most.”
Molina: “But that was many years ago, right?”
Vera nodded in silence.
She was well aware that it was many years ago.
She didn’t know if Lu Zhou still remembered what she looked like.
But she remembered exactly what he looked like…
“I feel the same.” Molina smiled and grabbed the empty mug on the table as she said, “Mathematics saved me.”
Vera looked at her with a puzzled look.
“But why Riemann hypothesis?”
“That’s a story for another day.”
Molina stood up from her chair, but because of her extreme fatigue, she struggled to maintain her balance. Fortunately, Vera stood up and supported her.
“Thanks.” Molina grabbed the chair and smirked as she said, “If he doesn’t want you, I’ll marry you, sis.”
Vera’s face turned bright red, and she said, “Sorry, I don’t… swing that way.”
Molina pouted and smiled.
“Just kidding.”
Moline picked up the thesis on the table and quickly walked away.