Mathematics is a science that studies quantitative relations and spatial forms in the real world. The "number" and "shape" here should be broadly understood. This can include structures, categories, models and other objects. The first is the Pythagorean paradox. The philosophical basis of Pythagoras school is "everything counts". "All numbers can be expressed as integers or the ratio of integers" is the mathematical belief of this school. However, the number such as the root number 2 cannot be expressed by the ratio of two integers, so the concept of "irrational number" appeared.

The second is Zeno's paradox. This paradox puts forward that if the jogger is in front of the runner, the runner will never catch up with the jogger, because the runner must first track the jogger's starting point. When he reaches the jogger's starting point, the jogger runs forward for a while, and a new starting point is waiting for him. There are countless such starting points. This paradox directly led to the appearance of calculus.

The third is Russell Paradox, also known as Barber Paradox. Barbers only cut people who don't cut their own hair. Does he cut his own hair? People can't make an accurate judgment on this, which contributed to the birth of set theory. Teacher Hua Yinglong talked about these three mathematical paradoxes to tell students that the kingdom of law has national boundaries, and taking a step forward may be a fallacy.