I read all the comments in the times post and no one mentions that this is due to the motion of the Artemis II. On the moon there is no "earthrise" or "earthset", only a yearly wobble. On the earth the moon rises and sets because of the earth's rotation. I guess the editors of the NYT knew this so that they put the "earthset" in quotes.
It looks like they chose to use the "universal gravitational constant" "k" instead of Newton^s constant, "G": p.23, "k^2 = universal gravitational constant, 1.32452139x10^20, m^3/(sec^2)(sun mass units)"
But the value and unit of "k" given in the Wikipedia page is different. Do you know what NASA document means by "universal gravitational constant" in modern sense?
"What's irrefutably proven is that if you take this particular set of axioms, then these conclusions hold."
This is what I tried to say in my comment. It's the author who talks about the truth of the axioms. I'm objecting to his claim that we end up with "something we can know for sure". No. Your truth depends on your assumptions.
"If the axioms are true, and the subsequent reasoning is sound, then the conclusion is irrefutable. What we now have is a proof: something we can know for sure."
... if the axioms are true. We still don't know for sure absolutely.
"The idea of self-evident truths goes all the way back to Euclid’s “Elements” (ca. 300 B.C.), which depends on a handful of axioms—things that must be granted true at the outset, such as that one can draw a straight line between any two points on a plane."
Strictly speaking, Euclid does not state axioms. He starts with 23 Definitions, 5 Postulates and 5 Common Notions. Drawing a straight line from any point to any point is stated as Postulate 1.
“the greatest scientist of all time is undoubtedly Sir Isaac Newton”
Newton routinely explained natural phenomena with supernatural causes, like God. In fact he overruled his mathematics with his supernatural explanations. A well-known example is his rationalization of chaotic behavior in his calculations of orbital motions with “the hand of God.” For this reason alone I would downgrade Newton’s scientific status and say that he was a prominent researcher in the 17th century but definitely not “undoubtably the greatest scientist of all time”. Today, we would not call someone who explains natural phenomena with supernatural causes a scientist.
"It concerns the size of the largest sum-free set [0]. Take a (finite) set of integers, A. What is the largest subset of A such that no two entries sum to a third."
Yes, it seems to me we are focusing mainly about sets, not addition. Addition is secondary. Mainly I'm debating the title. The word "set" ought to be in the title too. I guess not a big deal.