Quote: Discover the beauty of humanities and mathematics
Is math boring?
We should look at the problem from another Angle.
In a way, mathematics is like poetry: concise, concise, abstract… Mathematics and the humanities are not completely separate. In mathematics, we find a similar “beauty” to poetry.
Take a humanistic poem as an example — the desert smoke straight, long river falls yen.
The poem depicts a majestic and magnificent landscape of the desert.
Geometrically speaking,”The desert“Can be regarded asThe plane.”Solitary smoke“Perpendicular to the groundA straight line(Figure 1).
The second sentence regards the long river as a straight line and the setting sun as a circle. “Long River falling yen” is a circle cut in a straight line (see Figure 2).
The contrast between the two figures is clear, simple and clear, both rigid and soft.
The natural scene will be lost in the waves of history,
The white-haired fishermen on Jiang Nagisa will all pass away,
Only the beauty of abstraction will be immortal!
“The desert smoke straight, the river falls yen” is precisely the geometry of the highly condensed, humanities and mathematical beauty together here, has a shock through the ages of artistic charm!
It is a pity that many people ignore the beauty of mathematics for the sake of examination.
To make up for this regret, the quantum school, together with 43 professors and experts in the field of mathematics, published the Beauty of Formulas. Each formula has a mathematical picture, so that more people can appreciate the beauty of mathematics.
01:1 + 1 = 2
discoverer ？
Discovery time?
Formula diagram
In the center of the illustration, the ancient Egyptians caught three fish from the Nile. The disposal of the third fish proved to be the biggest problem.
What the ancient Egyptians did with the third fish is unclear, but the ancestors opened the door to mathematics when they realized that 1+1=2 after they had the concept of quantity.
Seemingly simple but the most primitive seeds of mathematics, gave humans the ability to transcend other races in higher dimensions.
In the long river of the rolling waves of history, the seed of mathematics began to take root and sprout…
1+1=2, one of the cornerstones of human civilization.
02: Pythagorean Theorem
Discoverer Pythagoras, Shang Gao
It was discovered around 500 BC
Formula diagram
In the illustration, a surreal eye is staring at two small squares below it. After filling with water, their combined amount of water is equal to the amount of water injected into the larger square of the right triangle formed by their perpendicular sides, thus visualized the derivation of the Pythagorean Theorem.
Below it is the Pythagorean tree, which proved that for all right triangles, a²+b²=c². The upper right corner of the illustration is the oracle bone inscriptions of shang and Zhou dynasties. In shang and Zhou dynasties, your son Shang Gao also proposed “Three strands, four strings and five”.
A ²+b²=c² is the first time in human history that “number” is combined with “form”.
Fermat’s last Theorem
discovererfermat
It was discovered in 1637
Formula diagram
In the center of the illustration is the time hand, turning a time disk spanning 358 years.
To the left of the disk is Fermat, the “king of amateur mathematicians” whose “Fermat’s Last Theorem” kicked off the 358-year disk of time, leaving behind the famous aphorism “I have found an excellent proof for this, so I won’t write it if I can’t.”
Many mathematicians failed to solve “Fermat’s Theorem” in the process of decryption, but created many new mathematical theories, so “Fermat’s Theorem” is also known as “the goose that lays golden eggs”.
Sitting on the broken egg to the right of the disk is Wiles, who ended the intellectual relay in 358, but the golden Egg saga continues. The elliptic curve, for one, has made a big difference in asymmetric cryptography and has been applied by cryptographic punks to bitcoin, making it mathematically unbreakable “mathematical gold.”
04: Calculus
discovererNewton, Leibniz
It was discovered in 1684
Formula diagram
In the illustration, Achilles, the son of Neptune, tries to catch up with a short-legged turtle.
According to zeno’s paradox, Achilles could never catch up with the turtle.
Newton, on the left, throws an apple, as opposed to Leibniz, who throws a binary. Between apples and binary is the famous calculus formula.
Both Newton and Leibniz are credited with the discovery of calculus, but after their deaths they were tied together by the Newton-Leibniz formula after a long battle over who discovered it first.
The advent of calculus led to the subsequent revolutions in science and technology.
The Law of Universal Gravitation
discovererNewton
It was discovered in 1687
Formula diagram
The earth was firmly bound to an apple, and it was Newton who connected the two.
Newton formulated the law of gravity, and gravity became one of the fundamental forces of the four forces.
Newton’s law of gravity sealed the deal, and he taught us that the laws that govern nature and the universe are simple.
At the end of the 19th century, the law of gravity exposed its limits, its unreachable shades of gray.
But gravitation, like a chasm from the apple tree to the sky, splits the darkness and brings light to mankind. Newton was like Prometheus who stole fire. He gave man a spark that would start a prairie fire.
06: Euler’s Formula
discoverereuler
It was discovered in 1748
Formula diagram
Euler through konigsberg seven bridge, the seven chic bridge across praeger river connects four areas, everyone try not to repeat back to its starting point through seven bridge failure, just in the right eye blindness of euler its artful into geometry problem, prove route doesn’t exist, which opened a new branch of mathematics, graph theory and geometric topology.
Euler’s formula, e^ PI I +1=0, is perfect.
Euler’s formula, known as “God’s formula”, had a far-reaching influence after it was put forward. Moreover, Euler worked hard all his life, and his scientific legacy was like shining stars. Even though Euler was dead, the stars would never be extinguished.
07: Galois Theory
discovererGalois
It was discovered in 1832
Formula diagram
The man on the right fires, the bullet passes through the quintic equation, and the man on the left falls.
Above is a struggling woman, and the two are clearly fighting over each other.
The fallen man, 21-year-old Galois, died in a duel related to a passionate love affair. On the eve of a duel he knew he would die, Galois wrote a 32-page paper. In 1843, his work was confirmed and published, and the mystery of the quintic equation was lifted.
The concepts of “group” and “domain” introduced by Galois’ theory successfully opened the door of the glorious palace of modern group theory and opened the curtain of modern mathematics.
08 Riemann Hypothesis
discovererRiemann
It was discovered in 1859
Formula diagram
Riemann ascended the steps to the complex and wondrous edifice of mathematics, from a higher dimension, with a key in his hand, to the door of mystery.
The mathematical edifice was built from a thousand redundant mathematical propositions based on Riemann’s Riemann conjecture, and Riemann held a key that could easily unlock the mysterious door.
But the building built on the Riemann conjecture is not unbreakable, if the Riemann conjecture is confirmed, the building will exist forever, otherwise, the building will collapse in an instant.
Second Law of Thermodynamics 09: Second Law of Thermodynamics
The discoverer, Clausius
It was discovered in 1854
Formula diagram
The illustration is full of death, decadent atmosphere, can not be dispersed.
This is what the law of entropy means: entropy increases forever.
The inflated corpses in this picture are surrounded by the very universe in which we live. The moment the light came on, the Big Bang appeared. From the moment of the Big Bang, the universe has become an old house that no one has cleaned, and over the years, dust has accumulated on the ground. This is entropy.
The law of entropy drives humans to despair. We think we are on our way to becoming God, yet we remain as helpless as a barefoot child in the face of increasing entropy, powerless to cope with the universe’s eventual demise.
The universe is destined to die.
10: Maxwell’s equations
discoverermaxwell
It was discovered in 1865
Formula diagram
An electromagnetic field appears, but more like a steady stream of light into the universe.
As for the relationship between electricity and magnetism, predecessors have gone through numerous thorns before making the road slightly smoother.
Coulomb, Auster, Amperes, Faraday… Failed to find a perfectly uniform description.
In the end, Maxwell miraculously completed this feat — with his unique mathematical language, summarized the major laws of predecessors, established electromagnetic differential equations, the electric field and magnetic field perfectly integrated together, unified the entire electromagnetic field.
Since then, any electromagnetic phenomenon in the universe can be explained by these equations.
God said let there be light, and maxwell’s equations were born.
11: Mass-energy equivalence
Discoverer Einstein
Discovered in 1905
Formula diagram
Two soaring mushroom clouds are clearly visible from the atomic bombs dropped by the United States on Nagasaki and Hiroshima in World War II.
After the explosion, there was nothing but ruins. On the lower left of the inset is a destroyed city, broken, mutilated, with no survivors.
When the mushroom cloud lifted, death quietly looked at everything, in her eyes, everything was so normal, quiet.
Before Einstein came up with the equation of mass and energy, people thought of mass and energy as two parallel lines that did not interfere with each other. But when Einstein wrote down the equation of mass and energy, energy and mass became one entity — mass and energy. It seems simple, but it can describe a world ranging from atoms to the whole universe. A grain of dust, also contains the enormous energy that human beings can not imagine.
This is the formula. Humans have opened Pandora’s box.
12: Schrodinger Equation
discovererschrodinger
It was discovered in 1926
Formula diagram
This is our macro world on the right, and the hydrogen atom on the left is our micro world.
Schrodinger’s cat connects the two. The cat is going from the macro world to the micro world.
Schrodinger developed the theory of the wave function, but the equation became the Copenhagen school’s weapon, pointing to Einstein.
In order to demonstrate the absurdity of quantum mechanics, Schrodinger proposed “Schrodinger’s Cat” thought experiment, which has become the biggest controversy in physics in the 20th century.
This cat, which does not belong to Schrodinger, walks between life and death and shuttles through the parallel world, its track is mysterious and unpredictable.
13: Dirac Equation
discovererDirac
It was discovered in 1928
Formula diagram
To the left is a tower of Babel, in the light of our physical world.
The darkness on the right was like a black sea ripple, signifying the fathomless world of antimatter.
The emergence of antimatter in the dark world makes the tower of Babel in the physical world totter.
And in between is a path that separates the two worlds into the sky, which may lead into the antimatter world, and even find a portal into the dark matter world.
The Dirac equation, which united special relativity and quantum mechanics, led to the momentous conclusion that electrons could have negative energy values, opening up a new world of antimatter roaming the universe.
Antimatter and matter are like twins, but they are incompatible with each other. Once they meet, they annihilate. They are like the left and right sides of the painting, one side bright and the other dark, but no one knows what lies behind the antimatter world on the dark side.
14: Yang-Mills Gauge Field Theory
discovererYang Zhenning, Mills
Discovery date: 1954
Formula diagram
In the composition of the Young-Mills equation, the “god” in the middle is bringing the “four forces” together.
“Gravity” on the left, “charge force” on the right, “strong nuclear force” on the top, “weak nuclear force” on the bottom.
Einstein had hoped to unify the universe with a formula, but it failed to do so until his last moments. The burden falls on the normative field theory.
Yang – Mills equation stands on the shoulders of predecessors, later derivation and correction, become the mainstay of normative field theory.
With the discovery of the Higgs particle, the canonical field theory unified the three forces of nature and approached the grand unified theory.
Once humans achieve the “unification of the four forces”, they may truly become gods — randomly combining and changing particles, creating unprecedented forms of matter, controlling the number of dimensions of space, and eventually becoming masters of the universe.
15: Shannon Theory
discoverershannon
It was discovered in 1948
Formula diagram
Shannon was like an acrobat, juggling four balls on a unicycle and the Penrose Steps.
He started from the “beacon fire smoke” castle, and gradually moved towards “network communication”.
Shannon’s formula not only brought mankind from the industrial age to the information age, but also made mankind go faster and faster on the road of long-distance transmission of information and communication.
After Shannon wrote the Shannon formula, people left a limit, and then people have been racing to chase in it, 1G, 2G, 3G, 4G, 5G… People’s lives are also changing rapidly due to changes in communication methods.
That’s why shannon is placed on the Penrose Steps in the composition — chasing the limits of Shannon’s formula, which never ends.
B-S Equation (Black-Scholes Equation)
discovererBlake scholes
It was discovered in the 1970s
Formula diagram
In the composition of the B-S equation, the crumbling financial building is in the middle.
The B-S equation was once the backbone of Wall Street, but when the edifice collapsed, no one could help.
The B-S equation was once described as the most expensive, worth up to $1 trillion. But “human nature”, this formula is not perfect, the 2008 financial crisis became the last straw.
So the bull’s head falls under the crumbling financial edifice, the bull market is gone, and all one can do is jump off the b-S equation that has made so much money.
There’s nothing wrong with the B-S equation, there’s always someone abusing it. Mathematics can calculate the trajectory of the economy, but not the madness of human nature.
17: Trajectory Equation
discovererThe structure,
It was discovered in 1881
Formula diagram
The muzzle in the center of the gun looks like a black hole, pointing directly at the heart of the girl. The young man on the left shot the gun, but the bullet passed the girl on the right probably because he raised the muzzle by 3CM.
Guards who used to guard the Berlin Wall fired, killing the young man who crossed the wall. The young man in the picture raised the muzzle of the gun by 3CM and saved the life of the girl on the right.
That’s the beauty of ballistic equations.
You must execute the order to shoot, but you should have the conscience to raise the muzzle by 3CM.
18: Hooke’s Law
Discoverer Hooke
It was discovered in 1678
Formula diagram
Charlie Chaplin in Modern Times turns a nut on a giant cog-wheel, and everyone is a screw.
The familiar dial numbers visible through the gear gap are the symbol of a mechanical watch.
Behind the illustration are factories and chimneys belching smoke, symbolizing the first industrial revolution.
The development of mechanical watches is the epitome of the industrial revolution, mechanical watch behind the precision, can not do without the gear and balance between the delicate gossamer, and the time secret gossamer can not do without Hooke’s law.
Chaos theory
discovererlorenz
It was discovered in 1963
Formula diagram
A butterfly is kneeling on a whale as it swims east from the western Pacific Ocean.
This beautiful butterfly flaps its wings as hurricane after hurricane forms on the right side of the Amazon macrophylla.
As an ancient Chinese saying goes: A miss is as good as a mile.
Chaos is the essence of the world. The butterfly effect is just a typical chaotic system.
Our world is chaotic and disordered, and just as we find it difficult to describe accurately the shapes of clouds, mountains, and coastlines in geometry, we cannot find laws that describe the irregular world.
20: The Kelly Criterion
discovererkelly
It was discovered in 1956
Formula diagram
Right in the middle of the illustration is the familiar playing card, in which the character is replaced by Kelly.
After playing cards is a gambling plate and dice, dice drilled out on one side of the hands clutching money, the eyes of a man, on the other side of a skull. The message is obvious — gambling, by chance, is a slippery slope.
On top of poker sits a wealth formula, the Kelly formula, worth trillions. Gambling is not a game of chance, it’s a problem of math. But the gambler never learns this and still plunges into the casino.
Kelly’s formula tells us that once you enter a casino, you’re a gambler. And the only rule to win, there is only one – don’t bet.
Bayes’ theorem
discovererThe bayesian
Discovered in the 18th century
Formula diagram
The future is a cyberpunk city of electronic chips and wires.
An artificial intelligence robot is standing in front of a mirror, pressing one hand on the mirror and asking itself “Who am I?”
The development of artificial intelligence is inseparable from the support of Bayes’ theorem. Although bayes’ law was not accepted at first, it has become an iron law in the WORLD of AI over the past 200 years.
One question we might want to ask ourselves is: if Bayes’ formula were really combined with A.I., would it work out whether it was a person or a machine to get the “who am I?” answer?
22. The Three-body Problem
discovererHilbert
It was discovered in 1900
Formula diagram
Newton, in a red robe, was walking in space, with three spheres circling around him.
With all kinds of known and unknown forces and other factors interfering in the void, it’s hard to work out the equations of motion for these three spheres.
Newton had solved the two-body problem mathematically, but faced with the three-body problem, even if he was a true wizard and alchemist, he might not be able to do it.
We might wonder, did the light particle civilization that destroyed trisolaran hit one of its stars because they figured out trisolaran motion?
2: Orthotropic Theorem for Orthotropic problems
discoverergodel
It was discovered in 1931
Formula diagram
A barber prepares to cut hair, but claims he only cuts hair for everyone in the city who doesn’t cut his own. Does he have to cut his own hair?
In addition to the illustration, a man raises a knife to the barber who is getting his hair cut in the painting, but in fact we cannot tell whether the man with the knife is in the painting or out of the painting, that is, the existence of the man cannot be proved to be true or false in this system.
This is Godel’s incompleteness theorem: even the world’s self-evident axioms are incomplete.
Godel’s incompleteness theorem opens up a new way: when facing an incomplete system, please jump out of the system; When faced with a proposition that cannot be determined within an axiomatic system, please find a new mathematical tool or scientific experiment to determine it.
24: Elliptic curve equation
Discoverer Wiles
It was discovered in 1995
Formula diagram
A ghost ship sails at sea.
Captain Satoshi Nakamoto is standing at the bow, but will soon disappear.
Ghost ships will automatically navigate the seas, powered by virtual currency systems led by Bitcoin, Ethereum and Libra.
The traditional financial world is on fire behind the ship, and only a new digital currency system can survive. Around the ghost ship, there are numerous “peeping eyes” floating in an attempt to pry into the crypto currency’s secrets.
The elliptic curve equation plays a key role in bitcoin, which is the cornerstone of the currency. Without elliptic curve equations, there is no security for Bitcoin.
The elliptic curve equation is what saved Bitcoin from the NSA’s backdoor scheme.
Yang Zhenning: “The beauty of formula” concise like poetry
In an interview with Bill Moyers in 1988, Yang said:
Poetry is condensed thoughts, formula is condensed poems!
The brevity and precision of physical formulas have something in common with poetry,
You can write very complex ideas in a few lines.
Physicists like Newton, Maxwell, Einstein,
The structure of matter and the macroscopic universe are expressed in a few formulas,
To turn a very complicated phenomenon into a few equations,
Simple, precise and clear, with extreme beauty.
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