Chapter 1949 - Advanced Mathematics

Today marked another session for teaching Feng Shan discrete mathematics. Set theory, graph theory, mathematical logic, Boolean algebra, group theory... culminating in automata theory—Feng Nuo hadn't mastered these subjects well in the original timeline. He'd even failed abstract algebra back then, and now, more than a decade later, attempting to resurrect this knowledge and teach it to someone else proved excruciatingly difficult.

But however difficult, he had to grit his teeth and teach it himself. Though several other transmigrators with computer science backgrounds existed in the Executive Committee, he could hardly dispatch Feng Shan elsewhere for instruction. First, his own professional competence would be seriously questioned. Second, Feng Nuo genuinely suspected their abilities in this domain might not exceed his own. And third, sending Feng Shan alone to receive one-on-one tutoring from some pudgy IT otaku transmigrator... Feng Nuo quickly shook his head, banishing the unpleasant image from mind.

In the end, he'd devoted several weeks to gnawing through several undergraduate-level discrete mathematics foundation courses, then considered the sequencing and structure of these courses to prepare a training program.

A few days prior, Dr. Zhong had visited and proposed a new card-reading mechanism and an independent digit wheel scheme driven by electric/escapement forks. The new digit wheel scheme would enable the tabulating machine to perform multi-digit number statistics while ensuring carry accuracy.

He'd also proposed that card tops and bottoms should feature positioning holes, like 80-column printer paper perforations. Using a pair of pressed rollers as the card-contact mechanism, with metal contacts arranged on the rollers—this would ensure proper card hole alignment with contacts through the positioning holes at both ends. Since the card would be in rolling contact with the rollers, subject to pressure and slight friction rather than scraping against contact-area mechanisms, it would benefit both card and contact longevity. This would avoid the embarrassing situation where frequently tabulated/queried cards were extremely prone to damage—like what occurred during last month's intensive tabulating machine tests.

While they were deep in discussion, Feng Shan had been waiting at the door all along. Zhong Lishi found this peculiar and, upon inquiring of Feng Nuo, learned he'd already initiated private discrete mathematics lessons for Feng Shan, and this was scheduled class time. So Dr. Zhong sat in with great interest to observe one of Feng Nuo's lessons.

Unexpectedly, after attending the class, he became quite animated. Not only did he lavish praise, but he also declared this an important exploration in higher education for the new timeline, requesting that Feng Nuo organize his thoughts and related materials for preparing these courses. Finally, Dr. Zhong emphasized that current higher education must integrate cutting-edge topics in scientific and technological restoration when establishing majors, asking Feng Nuo to bear this point in mind when sharing his experience—he stressed the characters for "science and technology" very heavily.

It indeed held true that Feng Shan was among the very few naturalized citizens with access to higher education level material. From this perspective, Feng Nuo's work was genuinely exploratory. As for whether this pace suited ordinary naturalized citizens' abilities, he didn't intend to consider that. For at least the next twenty or thirty years, only the brightest naturalized citizen prospects would have any chance of accessing higher education. Each would be the elite of the elite, and basically no need existed to worry whether they could keep pace. Take Feng Shan—her knowledge absorption speed and ability was astounding. If she didn't understand something, she would study and contemplate it day and night. This was nothing like when Feng Nuo was in college, where recreation came first and studying second.

This astonishing receptivity made Feng Nuo's preparation for these more theoretical courses extraordinarily arduous. Often, each class hour required 7-8 hours of preparation. Certain theorems he simply couldn't prove had to be glossed over or temporarily skipped; occasionally they could even be assigned as homework—perhaps she could understand the proofs herself.

Interspersed with all this were endless other annoyances. A typical example was the conventionally established names of theorems.

In slightly advanced mathematics and physics subjects, theorems and formulas named after people were ubiquitous, and explaining their origins presented major problems. This issue wasn't obvious in the Executive Committee's current national school basic education and no systematic solution yet existed. However, the several transmigrators teaching Feng Shan calculus were already complaining bitterly, and had mentioned it to Feng Nuo repeatedly during "academic exchanges." Now Feng Nuo was experiencing this annoyance himself.

Complete renaming was obviously impossible—the transmigrators were generally muddle-headed about these theorems and formulas to begin with. If names were changed beyond recognition, these disciplines would probably be lost entirely. So the Executive Committee's general policy was to claim as extensively as possible that these people were all "Australian sages." The Truth Office had issued a general guideline requiring that "professional terms with personal names that cannot be changed" should, wherever possible, claim those resembling Chinese names actually were Chinese people.

But no transmigrator possessed the energy to systematically sort this out—most of the principal transmigrators in education were actually just elementary and middle school teachers by background, which also explained why Dr. Zhong was pushing so vigorously to bring higher education under the Science and Technology Ministry system. Consequently, the several transmigrators teaching Feng Shan advanced mathematics would often improvise on the spot.

One time, Feng Nuo heard Feng Shan mention that the lecturing transmigrator had told her that Lagrange was Mongolian; Euler's original surname was Ouyang and he was a descendant of Ouyang Xiu; Cauchy was the third of four brothers, and he also had a second brother who was a criminal detective... Feng Nuo was immediately furious and nearly took his student to confront them.

But now he himself could only begin improvising. Today he planned to claim that Cantor's surname was Kang, and Russell's surname was Luo.

As for why some names were peculiar and didn't resemble Chinese ones—fortunately the Truth Office's "Great Song Australian Provisional Capital Historical Guidance Notes" with its "Guidelines for Explaining Foreign Personnel Names in Various Materials" document provided guidance, so there wouldn't be any slip-ups.

Feng Shan, Qian Yuzhi, Li Jianai, and two young transmigrators from the Academy were now seated before the small office blackboard.

After news of his systematic teaching of discrete mathematics foundation courses was spread by Dr. Zhong, the Academy specifically assigned two young transmigrators with "mathematical talent" to attend these courses. This suddenly made Feng Nuo realize that he'd been cooped up in the machine room so long that he'd had too little contact with naturalized citizens. And he himself was also a "Doctor"—at this level, in the future transmigrator empire, there should be at least three or four schools of thought named after him. It would be such a pity if there were no successors.

So he thought of Qian Yuzhi and Li Jianai, these two recent graduates. Though their backgrounds were somewhat lacking—one from a vocational school, one from the Liberal Arts Academy—they were still rare talents properly cultivated through the timeline's formal education. He began contemplating taking on two disciples.

They weren't very old, so molding potential should still exist. Moreover, Li Jianai was quite perceptive and could be cultivated toward software theory; Qian Yuzhi was also diligent and might be able to learn something about system architecture and applied technology. He had Feng Shan catch them up on some upper primary and middle school courses in her spare time, and whenever he taught Feng Shan, he tried to have them sit in as well. But Feng Nuo knew in his heart that discrete mathematics remained far too premature for them—for the most part, it would resemble playing music to cows.

Reality wasn't far from Feng Nuo's estimate. After attending this class, Li Jianai felt her brain was in complete chaos.

She and Qian Yuzhi also now addressed Feng Nuo as "Teacher." Feng Nuo even mentioned that after the New Year, he would discuss with the Tiandihui about possibly officially transferring them over. Qian Yuzhi remained somewhat confused, not comprehending the significance, but Li Jianai recognized this as an excellent opportunity.

Being transferred to a transmigrator's side and becoming a transmigrator's "student"—this kind of status was the best prospect outside of becoming a transmigrator's "life secretary"!

However, after attending several classes, she understood that being this kind of student wasn't so easy. And now the classes the teacher gave them separately were the so-called "different kind of mathematics."

This mathematics was indeed strange—it didn't involve extensive calculation. After a class, the blackboard was covered with odd scribbles. Senior Sister Feng Shan explained those characters resembling pinyin were called Latin letters, just without tones; there were other characters resembling ghost drawings, called Greek letters; and there were numerous, numerous other symbols she'd never encountered before.

That was one thing, but initially the content still seemed comprehensible, and it didn't even employ the decimals, fractions, and multi-digit multiplication and division that she found somewhat difficult. One time the teacher earnestly explained that among 13 people, at least two must have been born in the same month, and she nearly laughed aloud—this counted as mathematics?

But then the teacher immediately assigned homework: "101 Fubo Army soldiers stand in a row. Then at least 11 soldiers can be made to step forward and form a line arranged by height from shortest to tallest, or form a line arranged by height from tallest to shortest."

She was immediately stumped, having no idea how to even approach the problem. Fortunately, Senior Sister Feng Shan couldn't solve it either, to say nothing of that dummy Qian Yuzhi. They all looked at the teacher, who proved this proposition in mere minutes. Afterward, Li Jianai devoted an hour to reviewing her notes before finally understanding the proof.

Another time, the teacher explained that a Pseudo-Ming map could be colored with at most 5 colors to distinguish all provincial administration offices, and proved it cleanly and decisively. Under their admiring gazes, Transmigrator Feng seemed to get slightly carried away, claiming that actually he could also prove that 4 colors would suffice—it's just that this blackboard was too small to write the proof on.

But recently, what the teacher taught had become increasingly outlandish. During class, she only felt like she was lost in clouds and mist, and after class she couldn't remember much. In this class, she only vaguely recalled the teacher discussing something about a barber who did or didn't shave himself. He also seemed to claim the set of natural numbers was a countably infinite set. What a joke—if it's infinite, how can it also be countable? The instructor at the training class had stated that the Executive Committee's power was infinite, and when some trainees asked what infinite meant, the instructor answered that infinite meant having no end, being too many to count. The teacher also concocted some nonsense about natural numbers and integers being equally numerous—anyone who'd been to primary school knew that integers clearly had many more negative numbers than natural numbers!