The British science journal *Physics World* once held a reader poll to select the "greatest formulas." The ten formulas that made the list ranged from the universally known 1+1=2 to the famous E=mc² ; from the simple formula for the circumference of a circle to the complex Euler formula. These formulas are not only the crystallization of the wisdom of mathematicians and physicists, but also a concentrated manifestation of human civilization. Each formula has profoundly influenced the transformation of human society and even shaped human thought.
Some of these formulas may be familiar to you, while others may be less so. As human beings, it's essential for us to understand these formulas and the history of human thought. Today, we've compiled these ten famous formulas from the internet and are sharing them with you:
Formula for the circumference of a circle
Founder: Ancient people
The mathematical expression of the beauty of nature. Currently, humanity has achieved a precision of 10 trillion digits for pi . If we use a 35 -digit precision value of pi to calculate the circumference of a circle that could enclose the solar system, the error would be less than one millionth of the diameter of a proton. Nowadays, most people calculate pi to test the computing power of computers, or simply out of interest.
Fourier transform
Founder: Jean -Baptiste Joseph Fourier
Any irregular signal can be represented as an infinite superposition of regular sine waves. It is a very important method in the field of digital signal processing. In short, regarding the impact of this formula, without it there would be no electronic computers as we know them today.
de Broglie equations
Founder: Louis Victor de Broglie
Louis de Broglie argued that all matter possesses both particle and wave properties; in other words, all matter, including humans, can be viewed as a wave. Humans exist not only as matter but also, in a sense, as a wave. Many concepts in high school physics related to optics are closely related to this. This matter-wave equation expresses the relationship between wavelength, energy, and other factors. De Broglie was awarded the Nobel Prize in Physics in 1929.
1+1=2
This formula needs no name, no translation, and no explanation.
Schrödinger equation
Founder: Erwin Schrödinger
In quantum mechanics, the state of an object cannot be described using displacement, velocity, etc., as in classical mechanics. Instead, it can only be described as a function of a physical quantity. This physical quantity is no longer a definite value, but a probability distributed over time. Every microscopic system has a corresponding Schrödinger equation. The significance of the Schrödinger equation in quantum mechanics is the same as the significance of Newton's second law in classical mechanics.
The Schrödinger equation is the most widely used and influential formula in the world's atomic physics literature. Schrödinger was awarded the Nobel Prize in Physics in 1933 for his outstanding contributions to quantum mechanics .
Mass-energy equivalence
Founder: Albert Einstein
The mass-energy equivalence equation profoundly reveals the relationship between mass and energy. Before this, people undoubtedly believed that mass and energy were separate entities with no connection. It was the discovery of the mass-energy equivalence equation that led to the explosions of the atomic and hydrogen bombs. More importantly, this equation completely overturned humanity's conventional thinking and propelled the progress of human civilization.
It seems that no scientific formula has ever had such broad significance. It was proposed in 1905, a " miracle year " in physics , by a young man named Einstein. That same year, he also published "On the Electrodynamics of Moving Bodies" —commonly known as the special theory of relativity.
Pythagorean theorem
Founder: Pythagoras
(Some believe that the Pythagorean theorem already existed in my country during the Shang Dynasty and have been proven.)
The Pythagorean theorem (3-4-5) is deeply ingrained in the minds of every human being. It is one of the most important mathematical theorems discovered and proven in early human history (recorded in ancient Babylonian texts dating back to around 3000 BC), and one of the most important tools for solving geometric problems using algebraic thinking. The Pythagorean theorem has approximately 400 proofs, making it one of the mathematical theorems with the most possible proofs.
Newton's Second Law
Founder: Isaac Newton
Newton's second law is the core of classical physics. It applies to all aspects of our daily lives, and all the fundamental equations of motion can be derived from it through calculus. It marks the beginning of true physics research. Without Newton, human civilization would have spent a much longer period in darkness.
Euler's formula
Founder: Leonhard Euler
Euler was one of the most prolific mathematicians in history, and the scholar with the most publications across various fields ( including all branches of mathematics, as well as mechanics, optics, acoustics, hydraulics, astronomy, chemistry, medicine, etc. ) . The 18th century is known in mathematical history as the " Euler Age . " Born in Switzerland, Euler lost sight in his right eye at age 31 and became blind in both eyes at age 59. Despite this, he was optimistic and possessed an astonishing memory and concentration. The ingenuity of Euler's formula lies in its conciseness; it incorporates the most fundamental mathematical terms— e , i , and π— into a single expression, while also including the crucial mathematical and philosophical concepts of 0 and 1 , all connected by a simple plus sign.
Gauss once said, " A person who sees this formula for the first time and does not feel its charm cannot become a mathematician. "
Maxwell's equations
▲ Integral format
▲ Differential form
Founder: James Clerk Maxwell
This theory organically unifies electric and magnetic fields into a complete electromagnetic field, establishing the electromagnetic field theory. Without this theory, modern civilization would not exist. This set of formulas integrates Gauss's law for electricity, Gauss's law for magnetism, Faraday's law, and Ampere's law.
A more modest assessment is: " Generally speaking, any electromagnetic phenomenon in the universe can be explained by this set of equations. " Later, Maxwell predicted the existence of electromagnetic waves from this set of formulas using only pen and paper calculations.
Don't we always like to make up stories, like how Einstein was inspired by a certain stimulus in his childhood to study hard and serve his country ? In fact, that stimulus was this set of equations you see here. It was precisely because this set of equations perfectly unified the entire electromagnetic field that Einstein always wanted to unify the gravitational field in the same way, and to put the two forces, macroscopic and microscopic, into the same set of formulas: the famous " Grand Unified Theory " .
