Mathematics Research Institute, rooftop.
Lin Ke sat helplessly by the conference table, while the mathematicians sat upright in front of the table.
The mathematicians hadn’t really fought; when Lin Ke was launched into the air, they quickly pulled him back, each like a small child who had made a mistake.
However, Lin Ke wasn’t angry.
Compared to the deceptive experts and professors from his previous life, the mathematicians here were pure and simple.
"Actually, regarding rational numbers and irrational numbers, I think of it this way..." Lin Ke didn’t waste time and went straight to the calculations.
"The distinction between rational and irrational numbers is as follows: I believe the key point is that a rational number can be written as a finite or an infinite repeating decimal, while an irrational number can only be expressed as an infinite non-repeating decimal!"
As soon as he finished speaking, the mathematicians collectively fell into deep thought.
To differentiate based on whether it’s repeating or finite?
After careful consideration, it’s an undeniably discernible classification.
"All rational numbers can be written as a ratio of two integers, whereas irrational numbers cannot be written as a ratio of two integers, and the scope of these two is different. The rational number set is an extension of the integer set. The four operations—addition, subtraction, multiplication, and division—are unimpeded in the rational number set."
"Rational and irrational numbers are both what I collectively refer to as real numbers, and complex numbers outside of real numbers I call imaginary numbers; real and imaginary numbers together form complex numbers..."
Lin Ke spoke rapidly, expounding on the concept of "numbers."
Complex numbers, real numbers, rational numbers, integers, fractions, odd numbers, even numbers...
A logically rigorous classification hierarchy of numbers slowly unfolded in the eyes of the mathematicians.
This is a complete and practicable mathematical system!
Generally speaking, structured systems do not form top-down in the beginning.
In science, progress is often made in bits and pieces—some research here, some research there—until these findings coalesce into a cohesive system.
Then, from this more comprehensive system, previous omissions are discovered.
Take the periodic table of elements, for example.
It wasn’t as if the concept was proposed from the start and experiments began from hydrogen.
Rather, elements were discovered sporadically, and from there, the patterns were discerned.
Mathematics is similar.
Someone studies positive integers, leading to the discovery of negative integers, decimals, and so on, gradually constructing one of the towering edifices of mathematics.
Science is bottom-up.
Hence, when Lin Ke proposed a complete classification concept top-down, the mathematicians were astonished.
Their formidable minds immediately began various intellectual collisions, and the conference room fell into a magical storm of ideas.
"Integers, prime numbers, analytic functions..."
"This is one of the cornerstones of mathematical disciplines!"
"I feel that each classification can extend into its own discipline!"
"Not only that, within each classification, a legend might be born!"
The mathematicians discussed excitedly.
At this moment, Juli River also inquired of Lin Ke.
"Mr. Lin Ke, you mentioned to me before a word that sounded something like... ’π’?" Juli River may not remember other things clearly, but she recalled matters of mathematics distinctly.
"π?" Lin Ke nodded: "I realize you haven’t yet invented something like a compass for drawing circles, and π comes from the method of inscribing polygons to approximate a circle..."
Lin Ke began to explain π and used elements in the air to outline the shape of the Greek letter "π".
π is the ratio of a circle’s circumference to its diameter.
In his previous life, π was represented by the Greek letter π and was a mathematical constant widely found in mathematics and physics.
π is also the ratio of a circle’s area to the square of its radius, crucial for precisely calculating the circumference, area, and spherical volume of geometric shapes.
In calculus, π can be strictly defined as the smallest positive real number x that satisfies sinx = 0.
But in Naseng, there wasn’t yet the concept of a circle constant.
Thus, Lin Ke would be the one to propose it.
In theory, Naseng and the previous life are entirely different universes.
But mathematics, being a discipline concerning pure numbers, remains unchanged.
Physics, chemistry, biology, history, astronomy—all these things might change with variations in universe, galaxy, or planetary laws.
Under certain conditions, one plus one equals two—not three, regardless of the universe.
However, something like physics and chemistry might radically alter with even a slight change in universal laws.
Therefore, mathematics is the foundation of science.
In his previous life, irrational numbers were defined as infinite non-repeating decimals.
Of which, the most representative was the constant π.
Why did so many in the previous life attempt to prove π’s periodicity?
For instance, on August 17 of year 2x21 in the previous life, a Swiss researcher used a supercomputer, taking 108 days to calculate π to 62.8 trillion decimal places, and it was still found to be infinite and non-repeating.
At present, this is a never-ending digit.
But if someone ever proves that π is periodic or finite, mathematical algorithms will collapse from the ground up, affecting every scientific discipline.
For example, higher mathematics founded on calculus and limits relies on the method of inscribing polygons as its base.
The same goes for physics—equations like the general relativity’s gravitational field equations will pose issues, as will Coulomb’s law.
Various conservation theorems would fail, and the scientific edifices built over nearly four centuries since Newton’s era would need to be restructured, rewriting all of human history.
Hence, when Lin Ke proposed π, Juli River’s eyes emitted a terrifying gleam.
Before her, a circle outlined by white light appeared. In a moment, it was inscribed with thousands of lines dividing it equally.
Moreover, this number kept increasing, filling the circle with lines in just a dozen seconds, segmented into countless sections.
Juli River’s abnormal state drew the attention of other mathematicians, who all turned to look.
Meanwhile, Juli River’s aura grew more intense, and the white light in her eyes became increasingly astounding.
Lin Ke and others remained unmoved, watching from their spots, as many researchers from the Mathematics Research Institute were attracted by Juli River’s aura, and countless elements in the small space surged towards her.
In Juli River’s glowing eyes, a symbol appeared—"π"!
Juli River shouted softly, and the infinitely segmented circle before her dissipated. Her body, however, began to float.
Lin Ke raised an eyebrow: "Is this... a breakthrough?"