Preface In the previous post, I mentioned that I was inspired by Archimedes' "Give me a fulcrum" and found a fast learning route for linear algebra. Some readers were very interested in Archimedes himself, so today's post is dedicated to this "scientist closest to a god," and to what he truly inspired in me.
The Scientist Closest to a God — Archimedes If one were to pick the ceiling of ancient human intelligence, Archimedes would absolutely rank first.
The scientific community has long held a widely recognized assessment: before Newton was born, no one in the world could match Archimedes in wisdom.
He lived in ancient Greece over 2,200 years ago, yet he grasped the rudiments of calculus, calculated pi precisely, and invented all kinds of ingenious machines. While others were still looking at the world through experience, he was already explaining the world with formulas and laws.
He is the most legendary all-around genius of ancient Greece — Archimedes.
In 287 BC, Archimedes was born in Syracuse on the island of Sicily. He came from a family of scholars and was obsessed from childhood with mathematics, geometry, astronomy, and physics. As a young man he traveled to study in Alexandria, inherited Euclid's geometric system, and yet single-handedly pushed ancient Greek science to the pinnacle of the classical era.
The line we have all heard — "Give me a fulcrum, and I shall move the earth" — comes from Archimedes. Many people think it is merely an inspirational quote, but it is in fact a solid physical theorem.
In Learn Linear Algebra in Three Days, I wrote down this learning route: use the definition of a vector as the fulcrum to leverage the whole of linear algebra. The inspiration for that sentence comes precisely from Archimedes. What he leveraged was the earth; what I want to leverage is that course that gives countless people headaches.
Archimedes was the first person in human history to systematically discover the principle of the lever and the principle of buoyancy, directly laying the foundation for all of statics and fluid mechanics.
The household story of the "crown mystery" further demonstrates his terrifying powers of observation.
The king suspected that a craftsman had replaced gold in the crown with silver, and no one at court could tell true from false. Archimedes thought hard for days to no avail. Then, while taking a bath, he saw the water continually overflowing as his body submerged, and in a flash of inspiration he discovered the law of buoyancy.
He ran out of the bath naked shouting "Eureka (I have found it)," which became one of the most classic scenes in the history of science. Using only the volume of displaced water, he precisely measured the density of the crown and easily solved an age-old puzzle.
But Archimedes' brilliance goes far beyond a few small stories from textbooks — he was truly a genius who alone was worth an army.
When the Roman legions attacked Syracuse, the city was weak and the forces were vastly outnumbered; everyone thought defeat was certain. At the critical moment, the aged Archimedes upheld the entire city with science.
He designed giant catapults that precisely hurled boulders to smash Roman warships; invented a mechanical arm for grabbing ships that lifted enemy vessels straight out of the sea and dashed them to pieces; and legend has it that he used mirrors to focus sunlight and set enemy sails on fire.
Through one man's inventions and creations, the weak Syracuse held off the Roman army for years. Roman soldiers at one point suffered from "Archimedes phobia," trembling with fear at the sight of any strange device.
In scholarship, Archimedes utterly crushed his era.
He precisely calculated the range of pi, leading the world by eight hundred years; he exhaustively studied the geometry of curved surfaces and spheres, deriving the formulas for the volume and surface area of a sphere; and he was the earliest to pioneer the idea of limits, nearly 2,000 years before the birth of calculus.
It is no exaggeration to say that more than half the foundations of modern mathematics, physics, and engineering stem from Archimedes' research.
Yet the end of this peerless genius was incomparably tragic.
In 212 BC, the Roman army breached the city, and the whole city fell into chaos. At that moment Archimedes, completely ignoring the flames of war, was crouching on the ground intently working out geometric figures.
A Roman soldier burst into the courtyard and ordered him to get up and leave at once. Archimedes, immersed in his scholarship, did not even raise his head, and merely said calmly: "Do not disturb my circles."
This sentence infuriated the soldier, who drew his sword and struck him down. A peerless genius of the age thus fell, at the age of 75.
Afterward the Roman commander was filled with deep regret — he had long since ordered that Archimedes not be harmed — but this sage who transcended his era ultimately did not die of old age, but of barbarism and ignorance.
Archimedes' life had no high office or generous salary, no striving for fame and profit; he loved only truth and science all his life.
In an era ruled by force and theology, he alone explored the truths of the universe with reason, formulas, and logic, single-handedly pushing human civilization forward by a thousand years.
Newton, Galileo, and Einstein all regarded him as the patriarch of science. He was not a god, yet with mortal wisdom he touched the very limits of science.
On his deathbed, Archimedes was thinking of his circles; and what I think about is whether I can help more people avoid the detours I took when I learned linear algebra back then. This is also the original intention behind my website "Matrix Intuition."
Related Reading The Birth Story of Matrix Intuition Website — Why I built this website, and why I dared to write Learn Linear Algebra in Three Days
New book Learn Linear Algebra in Three Days: Use vectors as the fulcrum to leverage the whole of linear algebra
