Was kann eine Maschine lernen und ein Mensch nicht?

                A young researcher thinks he has made a great discovery. A prestigious journal even published his research. Here are the links to the two articles:

https://www.researchgate.net/publication/334837030_Lecture_Notes_on_Machine_Learning_Maximum_Product_of_Numbers_of_Constant_Sum 

https://www.researchgate.net/publication/334848381_Lecture_Notes_on_Machine_Learning_Minimum_Sum_of_Numbers_of_Constant_Product

Unfortunately, neither the mentor of this young researcher nor the Referent of these articles noticed that the two theorems have been known for a long time. Some would say that they are consequences of the inequality of the arithmetic and geometric means. But I say that the inequality precedes the notion of a radical of order $n$.

            For these the inequality

$$\left ( \frac{a_1+a_2+\cdots +a_n}{n} \right )^n \geqslant a_1\cdot a_2 \cdots a_n$$

is sufficient, which I think, at least in the case of $n=2$, was known since the time of Euclid.

          Therefore, man still needs to learn, so that the machine does not overtake him !!