Gauss Reading

Quote: "Early in this period-perhaps at the age of 14 or 15- he discovered the prime number theorem, which was finally proved in 1896 after great efforts by many mathematicians."

Question: How can someone so young figure out a theorem that many mathematicians couldn't figure out?

Comment: This quote interested me because Gauss figured out a theorem that mathematicians had a hard time figuring out and they were about half (or more) his age, and they probably had more experience than he did. But yet he figured that out before them and they finally had proved his theorem many years after he had.

Euler Reading QQC

Quote: "The French physicist Arago, in speaking of Euler's incomparable mathematical facility remarked that 'He calculated without apparent effort, as men breath, or as eagles sustain themselves in the wind.' "

Question: What does it mean when it says that Arago was speaking of Euler's incomparable mathematical facility? Was he stating that Euler was that good at math that no man could compare to how good he was.

Comment: I picked this quote because I really like the analogy that Arago gave for Euler's mathematical genius. He compared how Euler was so good at math and he did it without any effort just like a eagle keeps themselves flying in the wind. The part where it says "speaking of Euler's incomparable mathematical facility," kind of confused me because I was wondering, was there anyone who really compared or was on the same level as Euler was on the terms of mathematical genius.

Leibniz Reading QQC 1/4/10

"Leibniz lived in a period when it was still possible - as his own astounding career demonstrated - for a very highly intelligent and hard-working scholar to absorb all the knowledge of his time."

Are they saying that it is still not possible in any other period that a intelligent and hard-working scholar can absorb all the knowledge of his time? or was it only possible during Leibniz' time?

This quote confused me because I didn't understand if they were saying that no other intelligent and hard-working scholar can absorb all of the knowledge of their time, unless they lived during Leibniz' time period. Because there are some people in our time that could absorb all of that knowledge, if they really wanted to.