Comrade!

[Dear comrade, feeble English letters cannot save the Soviet Union. Only the ultimate computing power can make your ideals a reality!]

[Mission issued: Study "Mathematical Analysis" and master one new point of knowledge!]

[Warning: Americans are right beside you. Stay highly focused and do not expose yourself!]

[Time limit: 35 minutes.]

Qi Hao's pen-spinning hand stopped. He glanced at the English teacher, who was passionately lecturing from a "College English" PPT, and hesitation appeared in his eyes.

The American the system mentioned couldn't be... the English teacher, could it?

Only a few years had passed since the Beijing Olympics, and enthusiasm for learning English was growing across the country. Naturally, the university hadn't missed the opportunity.

The university had increased the number of English classes for several majors.

Even the basic mathematics major was no exception.

Qi Hao, a freshman at Rongcheng Radio and Television University, had thought a mathematics major would have fewer English classes, but now it seemed he had been mistaken.

Qi Hao had just been through the baptism of military training and had barely started classes when he was bound to a Soviet Academic Overachiever System.

He did like the Soviet Union, but more precisely, he liked the era that had once embraced humanity's lofty ideals, the spirit of that time, and the people who refused to yield for their ideals. Even now, he still couldn't understand Brezhnev.

Qi Hao didn't have a drop of old Soviet blood in him. He preferred the taste of hot pot under the red flag and ice-cold Weiyi soy milk to borscht and vodka, and he had no idea how the system had picked him.

Was it because of my good looks?

Qi Hao thought the system had excellent taste.

The system seemed to come from the Cold War era. It had judged learning English to be corruption by capitalism's sugar-coated bullets and taken the teacher reading out relative clauses at the lectern for an evil American.

The system now required him to enter a state of absolute concentration and study mathematics right under the English teacher's nose.

There was so much to complain about that he didn't know where to begin, but a line of text appeared before him and forcibly suppressed Qi Hao's urge to lie flat.

[Mission rewards: Personal panel unlocked, 10 mathematics subject experience points, and 1 random treasure chest.]

As a young man of the new era who had read countless novels, he knew all too well what those words meant.

In a basic mathematics major where GPA was life and securing a postgraduate recommendation depended entirely on outcompeting everyone else, crushing the competition on intelligence alone was practically hell difficulty. But having a cheat was a different story.

Experience points and a treasure chest were within reach. He'd be letting himself down if he didn't grab such easy freebies.

It's just mathematical analysis. I've got nothing to lose by trying.

He got straight to it.

Qi Hao decisively pushed "College English" forward and pulled "Mathematical Analysis" from his desk drawer, the book that struck fear into the hearts of countless freshmen.

The first chapter was on sets of real numbers and functions.

For students fresh out of high school, where they solved problems by plugging numbers into formulas, the Dedekind cut at the start of mathematical analysis was quite difficult. Fortunately, the teacher had covered part of it in the last class, so Qi Hao could just about work through it and follow the system's absurd instructions, relying on the key points he'd noted in the book and the scraps of knowledge he hadn't yet forgotten.

In any case, the mission only required him to master one new point of knowledge.

To avoid attracting the teacher's attention from the lectern, he had to keep his movements to a minimum while concentrating all his mental energy on the book before him.

Something wonderful happened.

Perhaps reading a math book in English class was too thrilling, or perhaps it had triggered a student's instinctive rebelliousness. Qi Hao found that his concentration had improved, and his usually somewhat restless mind was unusually clear.

In the classroom, the English teacher was reading example sentences with relative clauses in her accented English. Her voice reached him muffled, as though through a layer of water.

Qi Hao could hear her, but the words didn't enter his mind. His entire attention was fixed on the text before him.

Let Q be the set of rational numbers, divided into two nonempty subsets A and B, such that every element of A is less than every element of B...

When they studied real numbers in high school, the teacher had brushed past them with a simple, "Real numbers are points on the number line. Just remember that." No one had asked why, and no one had cared how the square root of two was constructed from the world of rational numbers.

But this felt different.

Qi Hao felt the abstract definitions forcibly pulling his thoughts forward.

He continued working through the derivation according to the definitions in the book.

He began applying them to an old friend he'd known since middle school but had never truly understood: the square root of two.

Let set A contain all negative rational numbers and all positive rational numbers whose squares are less than 2. Let set B contain all positive rational numbers whose squares are greater than 2...

Qi Hao's pen stopped.

His brain began racing as he searched for the boundary.

Could you find a largest number in set A?

For example, 1.4?

No, 1.41 was greater, and its square was still less than 2.

No matter how close to the edge a number in A was, there would always be a rational number greater than it that still belonged to A.

Likewise, there would never be a smallest rational number in set B.

The logic of Dedekind's proof was to abandon the traditional concept of numbers altogether and define the partition formed by A and B as a whole to be a new number, an irrational number.

To verify the theory, Qi Hao picked up his rollerball pen and wrote a series of expressions on his scratch paper.

He began checking the three basic conditions of the partition one by one and found that, without needing to use the lengths of line segments in geometric figures at all, he could establish the continuity of real numbers on a purely algebraic level, relying only on the classification and comparison of rational numbers.

This was the process of establishing a rigorous theory of real numbers.

The conclusions he had memorized in high school had become basic axioms and set operations he needed to master in university.

When Qi Hao finished writing the final step of the derivation on his scratch paper, a voice sounded in his mind.

[Mission complete!]

[Comrade, by consulting the textbook, you have gained a preliminary understanding of the definition of the Dedekind cut and achieved a new understanding of real number theory.]

[Mission rewards: Personal panel unlocked, mathematics subject experience +10!]

His personal attributes panel then appeared.

[Name: Qi Hao]

[Academic level: LV1 (ordinary person)]

[Subject proficiency:

Mathematics: LV1 (115/500)

Physics: LV1 (110/500)

Informatics/computer science: LV1 (90/500)

Biochemistry: LV1 (80/500)

Engineering: LV1 (80/500)

Materials science: LV1 (70/500)

Energy science: LV1 (60/500)

Linguistics: Chinese LV1 (120/500), Russian LV1 (0/500), English LV1 (110/500)]

[Treasure chests available to draw: 1]

There really was a standard-issue panel.

Qi Hao examined the numbers carefully, wanting to understand his current situation.

Nine years of compulsory education, plus three years of high school spent grinding through countless Five-Three workbooks and mock exams, were worth a mere hundred-odd mathematics experience points by the system's standards?

The conversion was terrifying.

On second thought, Qi Hao understood just how deep the 500-point gulf between LV1 and LV2 was.

It seemed the academic depth of advanced mathematics was on a completely different level from the formulaic elementary mathematics taught in high school. Dreaming of leveling up by relying on what he'd learned in high school was delusional.

Looking further down, he saw that physics and English were both a little over 110, which fit his actual level as a science-track college entrance exam student.

As for that conspicuous Russian experience value, surely he wouldn't have to learn Russian in the future?

But on closer thought, this was a Soviet system from the Cold War era.

In Big Brother's logic, Russian was the vehicle of truth, while English could only stand aside.

Worse still, that fighting nation was famous in the world of mathematics for not playing fair!

Demidovich, Zorich, Fikhtengolts... Which of these Russian mathematicians who had made such illustrious names for themselves in the history of mathematics and physics wasn't a ruthless figure who had repeatedly ground science and engineering students around the world into the dirt?

If this lousy system suddenly went crazy one day and forced him to tackle the original Russian edition of "A Course in Differential and Integral Calculus"...

Forget it. I'll cross that bridge when I come to it.

As a contemporary university student with extremely stable emotions, Qi Hao's approach was to take things as they came.

Still, complaints aside, once Qi Hao had fully worked out how the panel functioned, he couldn't help getting excited.

He knew all too well how valuable this panel was!

What was the most despair-inducing part of studying?

You could spend a month sitting in the library and fill a thick stack of scratch paper, only to remain completely stumped by a single proof. That sense of futility, of effort potentially adding up to nothing, was enough to drive any hardworking ordinary person to despair.

But now, the system's data panel had solved that problem.

As long as he worked through derivations, read books, and studied seriously, his experience points could steadily rise.

That meant he could get feedback throughout his studies!

Although Qi Hao's university was a 985 university, it was known for its computer-related majors, while its mathematics major took a back seat.

To put it more bluntly, finding a job after graduating from the mathematics department was a hellish battle royale that made people question their lives.

Outsiders always had a rosy stereotype of mathematics departments. They thought math students were all brilliant experts who could graduate and go into quantitative finance on Financial Street or join a major internet company, earn a million a year in no time, and reach the pinnacle of life.

But that applied to financial mathematics and quantitative majors.

Qi Hao studied applied mathematics. To put it nicely, it was a versatile foundational discipline; to put it bluntly, it was stuck in the middle, neither here nor there.

Want to do data analysis at a major company?

Students from 985 universities in top-tier cities, such as Tsinghua and Peking University, had more experience. Why would HR hire him?

Then how about becoming a math teacher?

Sorry, he hadn't attended a normal university, nor did he have a background in education.

The better public schools in first- and second-tier cities were now all focused on graduates of teacher-training programs, and even master's and doctoral graduates from Tsinghua and Peking Universities were competing fiercely for positions.

If he wanted to teach, he could either go to some backwater county town and compete with thousands of people for a position with an official staffing quota, or go to an after-school tutoring institution. But someone like Qi Hao, with no competition experience, wasn't in demand at those institutions either.

During his first week at university, he had heard an upperclassman complain about employment prospects. Qi Hao came from an ordinary family and had a younger sister, and not wanting to waste his tuition, he had recently been considering changing majors.

But now, he seemed to see hope.

As he pondered how to use the system, Qi Hao suddenly heard the clear sound of footsteps beside him.