Transcendental numbers are irrational numbers, and all transcendental numbers are irrational numbers. However, some irrational numbers are not transcendental numbers. The proof of transcendental number has brought great changes to mathematics. It is proved that the three difficult problems in mathematics for thousands of years, namely, the cubic problem, the problem of bisecting any angle and the problem of turning a circle into a square, are all problems that a ruler cannot prove.

The nature of transcendental numbers can help us understand complex mathematical problems. For example, the Liouville theorem shows that all Liouville numbers are transcendental numbers. The proof of this theorem is actually not complicated. Then, Joseph Liouville constructed the first transcendental number with conclusive evidence: c = ∑ n =1∩√ (2n+1) (1-/(2n+1)).