1, hippasus (Mitte Penden, about 470 BC) found that the hypotenuse of an isosceles right triangle with a waist of 1 (that is, the square root of 2) can never be expressed by the simplest integer ratio (incommensurability ratio).
Thus, the first irrational number was discovered and Pythagoras' famous theory was overthrown. It is said that Pythagoras was at sea at that time, but because of this discovery, Herb was thrown into the sea.
2. The rationality of calculus is seriously questioned, which almost subverts the whole calculus theory.
3. Russell Paradox: S is composed of all elements that do not belong to itself. Does s belong to s? In layman's terms, one day Xiaoming said, "I'm lying!" "Ask xiao Ming is lying or telling the truth. The terrible thing about Russell's paradox is that it doesn't involve the profound knowledge of sets like the maximum ordinal paradox or the maximum cardinal paradox. It is simple, but it can easily destroy set theory.
Controversy in Mathematics: Zeno Paradox
This is also a controversy in the field of physics. Achilles and Zhi Nuo the tortoise ran together. Before Achilles started running, the tortoise was 65,438+000 meters ahead of Alisky.
Achilles runs 100 meter, the tortoise runs one meter more, Achilles runs one meter, and the tortoise runs one centimeter more. It can be inferred that Achilles will never outrun the tortoise. Although it runs very fast in reality, it seems that it will never catch up with it in mathematics.