A Visit to the Institute for Advanced Study

The History of Number Theory is not simply a history book, although it does contain some events from the History of Mathematics.

An excerpt is provided below, written by Shen Qi:

"Number theory originated in Greece, and the Diophantine equations introduced by the great mathematician Diophantus made it a systematic theory."

"The Indians and Arabia painstakingly preserved Diophantus's system of equations, preventing number theory from being buried in the dust of history."

"Professional mathematicians in Greece, India, and the Arabia have made great efforts in number theory, but the person who truly made extensive contributions to number theory and gave the discipline a tremendous impetus was an amateur mathematician in France— Fermat."

"Fermat came from a wealthy merchant family. He was a lawyer by profession and very passionate about politics, once serving as an advisor to the Toulouse Parliament."

"Although mathematics was merely Fermat's hobby, and he could only dedicate a small amount of his spare time to studying it, he made top-level contributions to number theory and calculus."

"Fermat was one of the two inventors of Coordinate Geometry. He and Pascal pioneered the study of Probability Theory, which originated from a gambling incident in which Fermat lost everything."

"Fermat, but he only proved one of them, and even that proof was only a general outline, ending abruptly halfway through."

"Compared to Fermat, an amateur mathematician, the German professional mathematician Riemann devoted his entire life to mathematics."

"Riemann was in poor health and had a suspicious personality."

"At the age of 33, Riemann proposed the famous Riemann Hypothesis. He married at 36 and died of illness at 40."

"The author and academic partners have proven the Riemann Hypothesis and outlined the theoretical framework for the prime distribution of the Riemann zeta function, as follows:-"

Reζ'/ζ(s)=σ-1/∣s-1∣^2-∑ρσ-β/∣s-ρ∣^2+O(1/λ(s)+log(∣s∣+2))

{ρ1,1-ρ1,ρ2,1-ρ2,...,ρk,1-ρk,...ρn,1-ρn}

x=βk,γ=γk, x^2-x-γ^2+γk^2+βk-βk^2=0,γk(1-2β)+γ(2x-1)=0

ζ(s)=e^A+Bs∏∞n=1(1-s/ρn)(1-s/1-ρn)e^(s/ρn+s/1-ρn)

..."

The 100 pages following "below" are extremely valuable, representing Shen Qi's original academic work. In this book, he publishes for the first time the complete theoretical system of prime number distribution of the Riemann zeta function.

For mathematicians, the 100-page professional treatise on the prime distribution of the Riemann zeta function is the biggest selling point of the book "History of Number Theory".

However, this readership is small, even sparse.

Therefore, Shen Qi did not expect "History of Number Theory" to be a bestseller. Making money was a minor matter; publishing a mathematical monograph was the wish of a famous mathematician.

On the day that "History of Number Theory" was officially released and sold in the United States, the entire country was unusually calm, and there were no extraordinary phenomena such as lightning, thunder, tornadoes, or the drying up of the sea.

Sales data won't be available for a while, but Shen Qi remains calm. This year, he completed one of his research tasks at the Mathematics Department of Princeton University and published an academic monograph.

System: "New achievement! The host has published a mathematics monograph. The basic reward is 500,000 Academic Excellence Points, multiplied by the main mathematical talent coefficient of 2.0, resulting in a final reward of 1,000,000 Academic Excellence Points."

Academic points are accumulated over time. Shen Qi returned to China, received a national medal, published a book, and earned back the academic points he had earned by upgrading his physics level to 10.

Shen Qi has been studying Condensed Matter Physics for some time now.

In the classification of physics disciplines, Condensed Matter Physics is categorized under Theoretical Physics.

Condensed matter refers to solids, liquids, and states in between.

Condensed Matter Physics is the science that studies the structure of condensed matter and the laws governing the interactions and motions between its constituent particles, thereby elucidating its properties and applications.

The goals of Condensed Matter Physics research are very broad, even complex, and physicists working in this field make up more than half of all physicists.

Condensed matter involves lengths ranging from meters to nanometers, time ranges from years to femtoseconds, energy ranges from thousands of Kelvin to nanokelvin, and particle numbers ranging from 10^27 to 10^21, almost approaching the thermodynamic limit.

Let me mention some specific applications of Condensed Matter Physics, including the High-Temperature Superconductor discovered in recent years, quantum transport in mesoscopic systems, photonic crystals, C60 molecules and solids, carbon nanotubes, giant magnetoresistance and colossal magnetoresistance, etc.

Condensed matter is a part of the world of matter that can be directly observed by the naked eye, but many of its structural details must be observed with the help of various microscopic techniques, which naturally involves related experiments.

Shen Qi didn't have the resources for physics experiments. The most valuable experimental equipment in their Mathematics Department was a high-performance Computer Science, which was used to verify mathematical predictions involving massive amounts of data.

If you have any difficulties, ask your mentor.

Shen Qi strolled toward the Princeton Institute for Advanced Study, intending to visit Edward Witten.

The Princeton Institute for Advanced Study is right next to Princeton University. Having been in Princeton for two or three years, Shen Qi had lingered in front of the bronze statue at the entrance of the Institute for Advanced Study building many times, but had never gone inside.

This bronze statue is a bust of Einstein, with his Einstein quote inscribed on the base. "Imagination is more important than knowledge."

Shen Qi stared blankly at Einstein, muttering to himself, "I have knowledge, I have no shortage of imagination, but I lack experimental equipment. Professor Einstein, please tell me, how did you come up with the Theory of Relativity back then?"

"It's very simple." Suddenly, a familiar voice came from behind.

Shen Qi turned around and said, "Edward, what a coincidence, I was just about to go in and look for you."

The visitor was Edward Witten, who said, "The ultimate test for physicists lies in reaching those universal fundamental laws and then deducing the entire universe from them."

Shen Qi glanced at the bronze statue of Einstein and smiled at Edward Witten, "What you're describing is Einstein's version of reductionism, reducing complexity to simplicity, and then reconstructing complexity from simplicity."

"So, Qi, do you understand?" Witten asked.

"Okay, I understand." Shen Qi nodded, then asked, "Edward, does the Institute for Advanced Study have experimental equipment for Condensed Matter Physics?"

"It seems you haven't fully grasped how to deduce the entire universe." Witten beckoned, gesturing for Shen Qi to follow him into the Institute for Advanced Study building.

Professor Witten possesses the ability to reconstruct complexity from simplicity; he has deduced the universe. The problem is, no one applauds him because others cannot comprehend Witten's universe.

Shen Qi did understand part of the universe created by Witten. With a sense of awe, he stepped into the building of the Princeton Institute for Advanced Study for the first time.