Why can we guess Demosthenes' age from his epitaph?

This article introduces the academic influence of the book "Arithmetica" written by the ancient Greek mathematician Diophantus, and explains that since Diophantus's epitaph records the proportion of the length of each stage of his life and the specific number of years in the form of mathematical riddles, his age can be guessed by calculation to be 84 years old.

Why can we guess Demosthenes' age from his epitaph?

The work "Arithmetic" by the ancient Greek mathematician Diophantus (who lived in the 3rd century AD) represents the highest achievements of ancient Greece in the fields of algebra and number theory, and its influence has lasted to this day. There are two important disciplines in modern mathematics: "Diophantine equations" (polynomial indeterminate equations) and "Diophantine approximation" (rational approximation of real numbers), which originate from "Arithmetic". The famous Fermat's Last Theorem is actually an assertion about a simple Diophantine equation. People usually call the self-multiplication of a number a "square" (the area of a square), and its self-multiplication a "cube" (the volume of a cube), which also originates from "Arithmetic".

There is little historical record about Diophantus's life. However, it is said that there is a poem engraved on Diophantus's tombstone, which describes his life in the form of a mathematical riddle, the gist of which is as follows: Diophantus lies in the tomb, and the tombstone tells his age in a wonderful way; God gave him a childhood of one-sixth; After another one-twelfth, he became a young man with a beard on his cheeks; After another one-seventh, he was able to get married; Five years later, he was blessed with a son; Poor son of the sage, he only lived half as long as his father; He studied number theory to cope with his fate, and ended his life four years later. If x represents Diophantus's lifespan, the following equation can be derived: x=84. That is to say, Diophantus spent 14 years in childhood, 21 years in adulthood, 33 years in marriage, 38 years in having a son, 80 years in losing his son, and 84 years in passing away.