The root formula of the univariate cubic equation x 3+px+q = 0, (p, q∈R) is 1545, which was published by the Italian scholar Caldan in his book Algebraic Dafa, and people called it the Caldan formula (some mathematical data call it the "Catan formula"). But in fact, the person who discovered the formula was not Kadan himself, but Tattaglia N. (about 1499~ 1557). After discovering this formula, he had a problem-solving contest with many people. He was often the winner, so he became famous in Italy. When the doctor and mathematician Kadan learned that Tattaglia always won, he tried his best to ask Tattaglia his secret. At that time, scholars usually did not rush to reveal their secrets to the people around them, but used them as secret weapons to challenge others to compete, or waited for the reward to be solved to get bonuses. Although Kadan tried his best to find out Tattaglia's secret, Tattaglia kept silent for a long time. Later, however, due to Kadan's repeated earnest demands and his oath to keep a secret, Tattaglia told Kadan his discovery in an obscure poem of 1539, but did not give detailed proof. Kadan didn't keep his oath. 1545, he announced this solution to the world in the book "Important Art". He wrote in this book: "This solution comes from a most respectable friend-Tattaglia in Brescia. At my request, Tattaglia told me this method, but he didn't give any proof. I found several proofs. The law is hard to prove, I will describe it like this. " Since then, people have called the formula for finding the root of the univariate cubic equation Catan formula. Tattaglia flew into a rage when she learned that Kadan had made her secret public. According to people's ideas at that time, Kadan's practice was tantamount to betrayal, and the postscript about who discovered the law could only be regarded as an open insult. So Tattaglia and Cardin had an open debate in a church in Milan. Many materials have described the argument between Tattaglia and Kadan about the formula for finding the root of the cubic equation with one variable, but the solution of the cubic equation with one variable is called Kadan formula, which was really discovered by Tattaglia. Kadan failed to keep his oath and was accused by Tattaglia and many documents. Kadan's mistake is culpable of punishment, but when publishing this solution, Kadan did not attribute the credit for discovering this method to himself, but truthfully stated that it was Tattaglia's discovery, so it was not plagiarism. Moreover, the proof process was given by Kadan himself, which shows that Kadan also did his work. Kadan supplemented Tattaglia's secret with his own work, broke the oath and made it public, which accelerated the popularization of the root formula of the cubic equation of one yuan and the process of human exploration of the root solution of the cubic equation of one yuan. But the name of the formula should still be called fontana formula or Tattaglia formula; It is a historical misunderstanding to call it Catan formula. A univariate cubic equation should have three roots. Tattaglia formula only gives one real root. About 200 years later, with the deepening of people's understanding of imaginary numbers, it was not until 1732 that Euler, a Swiss mathematician, found the complete expressions of the three roots of the cubic equation with one variable.

Tartaglia is an Italian, born in 1500. /kloc-at the age of 0/2, the head and tongue were cut off by the invading French soldiers. He has been stuttering ever since. People nicknamed him "tartaglia" (in Italian, it means stuttering), but his real name was rarely called. He taught himself to be a mathematician and announced that he had found the solution of cubic equation. Someone is not convinced, come to him for a competition. Each person gave 30 questions, which were answered by the other party. Results All the solutions of tartaglia's 30 cubic equations were worked out, but none of the other problems were worked out. Tartaglia won by a landslide. At this time, the Italian mathematician Cardin appeared and asked Tarta Gerry to tell him how to solve the equation, but he was rejected. Later, Cardin pretended to recommend him to Tarta Gerry as a Spanish artillery consultant, and claimed that he had many inventions, but he was miserable because he could not solve cubic equations. He also vowed never to reveal the secret of tartaglia's solution to the cubic equation of one yuan. Tartaglia told Cardin the secret of solving a cubic equation with one variable. Six years later, although the original promise failed, Cardin published an improved solution of cubic equation in his book Algebraic Dafa. Later generations called this method Karting formula, but tartaglia's name was forgotten, just as his real name was buried after stuttering.

Tartaglia was very angry at Cardin's treachery and wrote letters to scold each other. Finally, on an unknown night, Kadan sent someone to secretly assassinate tartaglia.

As for the root formula of unary quartic equation AX 4+BX 3+CX 2+DX+E = 0, it was discovered by Cardan student Ferrari.

Regarding the formula for finding the roots of cubic and quartic equations, because it involves the concept of complex number, complex number refers to the number a+bi which can be written in the following form, where A and B are real numbers and I is imaginary unit (i.e.-1 open root). Cardin, an Italian scholar in Milan, was first introduced in16th century. Through the work of D'Alembert, De Moivre, Euler and Gauss, this concept was gradually accepted by mathematicians. There are many ways to express complex numbers, such as vector representation, triangle representation, exponential representation and so on. It satisfies the properties of four operations. It is the most basic object and tool in complex variable function theory, analytic number theory, Fourier analysis, fractal, fluid mechanics, relativity, quantum mechanics and other disciplines.

After finding the root formulas of univariate cubic and quartic equations, people are trying to find the root formulas of univariate quintic equations. Three hundred years have passed, but no one has succeeded. There are many great mathematicians among those who have tried but failed to get results.

Later, Abel, a young Norwegian mathematician, proved in 1824 that the equation of degree n (n≥5) has no formula solution. However, the research on this problem is not over, because it has been found that some N-degree equations (n≥5) can have formulas for finding roots. So what kind of unary n-degree equation has no root formula?

Soon, in the first half of the19th century, this problem was proved by a brand-new mathematical method created by French genius mathematician Galois, and a new branch of mathematics, group theory, was born.