Galileo once proved that DE is the center line of △ABC, DE= 12BC. If you draw any straight line through A, then P' on DE and P on BC must be in one-to-one correspondence. So DE contains as many points as BC, and it is concluded that DE=BC, 1=2. This is a mathematical paradox.

Because the study of infinity often leads to some logical but absurd results (called "paradox"), many great mathematicians are afraid of falling into it and adopt an evasive attitude. 1874- 1876, a young German mathematician Cantor (1845- 19 18) declared war on the mysterious infinity. With hard sweat, he successfully proved that points on a straight line can correspond to points on a plane one by one, and can also correspond to points in space one by one. In this way, it seems that there are "as many" points on the 1 cm long line segment as there are points in the Pacific Ocean and the whole earth! In the following years, Cantor published a series of articles about this kind of "infinite set" and drew many amazing conclusions through strict proof.

Cantor's creative work has formed a sharp conflict with the traditional mathematical concept, which has been opposed, attacked and even abused by some people. Some people say that Cantor's set theory is a kind of "disease", Cantor's concept is "fog in fog", and even Cantor is a "madman". Great mental pressure from the authority of mathematics finally destroyed Cantor, making him exhausted, suffering from schizophrenia and being sent to a mental hospital.

True gold is not afraid of fire, and Cantor's thought finally shines. His achievements were recognized at the first international congress of mathematicians held in 1897. Russell, a great philosopher and mathematician, praised Cantor's work as "probably the greatest work that can be boasted in this era". But at this time, Cantor was still in a trance, unable to get comfort and joy from people's reverence. 1918 65438+1October 6th, Cantor died in a mental hospital.

Cantor was born in a wealthy Danish Jewish family in Petersburg, Russia. /kloc-moved to Germany with his family at the age of 0/0, and was interested in mathematics since childhood. He received his doctorate at the age of 23 and has been engaged in mathematics teaching and research ever since. The set theory he founded has been recognized as the basis of all mathematics.