A difficult mathematical problem baffles two mathematicians

（ This article is reproduced from today's headlines , Author linyuke ）

1799 year , German mathematical genius Gauss , In his doctoral thesis, he proposed that the general quintic equation has no algebraic solution , But it is hard to prove . However , A year later , Italian mathematician rufini was born , Continuous fire 4 Papers , Gives a perfect proof , But they were ignored because they were not famous enough , Almost gave up this achievement .

In Mathematics , Euler and Gauss are two names that can never be separated , These two geniuses seem to be able to solve all the problems .

However , There is a problem , But neither of them can figure it out .

The problem is , Whether a general quintic equation has an algebraic solution ？

Euler has studied this problem for a long time , Even paid a lot of effort for it , But he was forced back twice in a row , There is no proof at all , Only the expression of an auxiliary equation is left .

later , On this basis, Lagrange , Conducted in-depth research , But still can not give a definite answer .

Until the Italian mathematical genius rufini was born ……

He followed the idea of Lagrange ——

Lagrange has proved that , In order to obtain the algebraic solution of the general quintic equation , We need to find a cubic or quartic resolvent equation .

However, rufini carefully observed the possible values of the polynomial of the transformation unknown quantity , For the general quintic equation , We can't get a cubic or quartic resolvent equation .

Obviously , This is a clear contradiction ！

And this contradiction , The ultimate answer to this question .

Rufini was ecstatic , From this point of view, it is proved that the general quintic equation has no algebraic solution .

This is a year 1798 year , Before the great Gauss 1 year —— Gauss is in 1799 The same point of view was recorded in the doctoral thesis in , But there is no proof .

It's just , Rufini's first proof is a little flawed , And he knows this very well .

therefore , He went back to 1803 year 、1808 Years and 1813 year , The second one was published like a hat trick 、 The third and fourth proofs .

this 4 A proof , No matter what, there is no defect , Even perfect .

But I never thought of that. , Maybe it's because rufini is not famous enough , His great testimonials were ignored .

Rufini had no choice , These proofs can only be sent to the most senior mathematician of that era , Including Lagrange , But he was rejected by the other party with an arrogant attitude .

When there is no way out , Rufini submitted the certificate to various academic groups , But the ending is the same —— No takers .

until 1822 Before his death in , Poor rufini just got one person's approval , He is the great mathematician corcy .

Thanks to Cauchy , Rufini's name just appeared in “ Abel - Rufini theorem ” In —— Abel is recognized as the man who solved this problem ——

Anyway? , Rufini barely made his mark in the history of mathematics .

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