Chapter 313: A Visit to the Institute for Advanced Study
The History of Number Theory is not a simple history book, although it contains some historical events of mathematics.
An excerpt from it, Shen Qi wrote as follows:
"The discipline of number theory originated in Greece, and the indefinite equations introduced by the great mathematician Diophantine made it a systematic theory. ”
"Indians and Arabs have struggled to maintain the system of equations in Diophantine so that number theory will not be buried in the dust of history. ”
"Greek, Indian, and Arab professional mathematicians have made great efforts in number theory, and the person who really made a broad contribution to number theory and gave great impetus to the discipline was a French amateur mathematician, Fermat. ”
Coming from a wealthy merchant family, Fermat was a lawyer by profession and was very keen on politics, at one time an adviser to the Toulouse parliament. ”
Although mathematics was nothing more than a hobby for Fermat, and he was able to devote only a small amount of his leisure time to the study of mathematics, he made the most top-notch contributions to number theory and calculus. ”
Fermat was one of the two inventors of coordinate geometry, and together with Pascal, he pioneered the study of probability theory, which began with a gamble in which Fermat lost. ”
Fermat came up with hundreds of conjectures in his lifetime, but he proved only one of them, and the proof was only a general idea, and it came to an abrupt end after half of the summary. ”
In contrast to Fermat, an amateur, the German professional mathematician Riemann devoted his life to mathematics. ”
"Riemann is not in good health and has a suspicious personality. ”
At the age of 33, Riemann developed the famous Riemann conjecture, married at the age of 36, and died of illness at the age of 40. ”
The author and his academic partners proved the Riemann conjecture and sorted out the theoretical system of prime distribution of 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 under "The following" are very valuable and belong to Shen Qi's academic originality, in which he published the complete version of the theoretical system of prime distribution of Riemann zeta functions for the first time.
For mathematicians, the 100-page professional exposition of the theoretical system of prime distribution of Riemann Zeta function is the biggest selling point of the book "History of Number Theory".
But this readership is small, if not scarce.
Therefore, Shen Qi did not expect "The History of Number Theory" to be a big seller, whether to make money or not is a trivial matter, and it is the wish of a famous mathematician to publish a mathematical monograph.
On the day when "The History of Number Theory" was officially released and sold in the United States, the whole United States was unusually calm, and there were no visions of lightning, thunder, and tornadoes sucking up the sea.
It will take some time for the sales data to come out, and Shen Qi maintains a normal mentality, he has completed one of his scientific research tasks in the Department of Mathematics of the University this year and published an academic monograph.
System: "New Achievement!The host publishes a mathematics monograph, and the basic reward is 500,000 points, multiplied by the coefficient of 2.0 for the main talent of mathematics, and the final reward is 1 million points. ”
Shen Qi returned to China to receive a national medal, published a book, and earned back the points of the scholar who had upgraded physics to level 10.
Shen Qi has been studying condensed matter physics for some time.
In the discipline classification of physics, condensed matter physics is classified as theoretical physics.
Condensed matter is a general term for solids, liquids, and forms in between.
Condensed matter physics is a science that studies the structure of condensed matter and the laws of interaction and motion between constituent particles, so as to clarify its properties and uses.
The research goals of condensed matter physics are very broad, even complex, and physicists working in this field account for more than half of the total number of people.
The length of condensed matter matter ranges from a few meters to a few nanometers, the time range involves a few years to a few femtoseconds, the energy involved ranges from a few thousand to a few nanometers, and the number of particles involved is 10^27~10^21, which is almost close to the thermodynamic limit.
Let's talk about specific applications in condensed matter physics, including high-temperature superconductors discovered in recent years, quantum transport in mesoscopic systems, photonic crystals, C60 molecules and solids, carbon nanotubes, giant magnetoresistance and giant magnetoresistance, etc.
A part of the condensed matter world is directly observed by the naked eye, and many of these structural details must be observed with the help of various microscopies, which naturally involves related experiments.
Shen Qi did not have the resources for physical experiments at hand, and the most valuable experimental instrument in their mathematics department was a high-performance computer to verify mathematical speculations with huge amounts of data.
If you have difficulties, find a master.
Shen Qi paced to the Institute for Advanced Study in Princeton, where he was preparing to visit Edward Witten.
The Institute for Advanced Study in Princeton is next door to Princeton University, and it has been two or three years since he came to Princeton, and Shen Qi has wandered many times in front of the bronze statue at the entrance of the Institute for Advanced Study building, but he has not entered it once.
The bronze statue is a bust of Albert Einstein, and the pedestal is engraved with Einstein's famous quote: "Imagination is more important than knowledge." ”
Shen Qi stared at Einstein, stunned and said to himself: "I have knowledge, I have no lack of imagination, but I don't have experimental equipment, Professor Einstein, please tell me, how did you make up the theory of relativity in your brain back then?"
"It's simple. Suddenly, a familiar voice came from behind him.
Shen Qi glanced back: "Edward, such a coincidence, I was about to go in to find you." ”
The man was Edward Witten, who said, "The supreme test of the physicist is to attain those universal fundamental laws, and then to deduce from them the whole universe." ”
Shen Qi looked at the bronze statue of Einstein and smiled at Edward Witten: "What you said is Einstein's version of reductionism, which reduces complexity to simplicity, and then reconstructs complexity from simplicity." ”
"So, do you understand?" asked Witten.
"yes, I see. Shen Qi nodded, and asked again: "Edward, is there any experimental equipment for condensed matter physics in the Institute for Advanced Study?"
"It seems that you don't fully understand how to deduce the whole universe. Witten beckoned and motioned for Shen Qi to follow him into the Advanced Research Institute building.
Professor Witten has the ability to reconstruct complexity from the simple, and he deduced the universe, but the problem is that no one praises him because no one else can understand Witten's universe.
Shen Qi understood part of the universe set by Witten, and with awe, he stepped into the building of the Institute for Advanced Study in Princeton for the first time.