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Albert Einstein was a kind and gentle person, but there was one individual toward whom he did not feel the same warmth—his former geometry teacher, Hermann Minkowski, a brilliant mathematician. As a student, Einstein had a difficult relationship with Minkowski, who once called him a “lazy dog.” Years later, when Minkowski learned that this “lazy dog” had developed the theory of special relativity, he remarked that he would show how it could be expressed geometrically. When Einstein first encountered Minkowski’s mathematical formulation, he reportedly said, “A mathematician has managed to make my theory incomprehensible,” reflecting both surprise and perhaps lingering resentment toward his former teacher. Tragically, Minkowski’s life was cut short by appendicitis. Before his death, he is said to have expressed regret, saying, “What a pity to die at the dawn of relativity theory.” Today, the dawn of relativity has long passed, yet in science, there is always a new dawn on the horizon. And perhaps the real lesson is this: may each of us always have something new to discover—so that it is never a pity to leave the journey unfinished.

MRI scans have shown that this elegant and deeply meaningful equation affects the brains of mathematicians in the same way as a work of art!

The Feynman point is the 762nd decimal place of π, where the digit 9 appears six times in a row. The next occurrence of six identical consecutive digits in π appears much later, at the 193,034th decimal place.

In 1978, mathematician John McKay noticed something surprising: 196884 = 196883 + 1. At first, this looks like a simple and meaningless coincidence. But it turned out to be something much deeper. The number 196884 comes from a function in number theory called the j-invariant. The number 196883 comes from group theory, as part of the Monster group, a very large and complex mathematical object. At that time, these two areas of math were thought to be completely unrelated. This small observation led to a big idea: maybe the numbers from the j-invariant are connected to the Monster group. This unexpected link between two different fields became known as “Monstrous Moonshine.” After many years of work, this idea was finally proven in 1992 by Richard Borcherds.

A beautiful math coincidence

One of the most beautiful ideas in mathematics is: some infinities are bigger than others. Though it sounds strange, it is far from obvious. In the 1870s, Georg Cantor proved that the set of real numbers is larger than the set of natural numbers. No matter how you try to pair them, some real numbers are always left unmatched. Even more surprising, from any infinite set, we can construct a larger one. In other words: for every infinity, there exists a greater infinity. In 1900, David Hilbert praised this discovery, saying: “Nothing will remove us from the paradise that Cantor has created for us.”