It involves approximating numbers with fractions:

The duo’s solution came as a surprise to many in the field. “The general feeling was that this was not close to being solved,” says Aistleitner. “The technique of using [graphs] is something that maybe in the future will be regarded as just as important [as]—maybe more important than—the actual Duffin-Schaeffer conjecture,” says Jeffrey Vaaler, a retired professor at the University of Texas, Austin, who proved a special case of the conjecture in 1978.

It may take other experts several months to understand the full details. “The proof now is a long and complicated proof,” says Aistleitner. “It’s not sufficient just to have one striking, brilliant idea. There are many, many parts that have to be controlled.” At 44 pages of dense, technical mathematics, even leading mathematical minds need time to wrap their heads around the paper. The community, however, seems optimistic. Says Vaaler: “It’s a beautiful paper. I think it’s correct.”

Leila Sloman, “New Proof Solves 80-Year-Old Irrational Number Problem” atScientific American

So math isn’t as cut and dried as some students fear.

*See also:* Some philosophical questions to keep you awake, if the prospect of partying doesn’t:

Does the size of the universe sweep us toward atheism?

Philosopher: If there is something rather than nothing, questions around God cannot be ignored Waghorn: “Firstly, that on the most plausible demarcation criterion for science, science is constitutionally unable to show theism to be a redundant hypothesis; the debate must take place at the level of metaphysics. ”

Is zero even?

Absolute zero proven mathematically impossible?

Is celeb number pi a “normal” number? Not normal. And things get worse. Surely this oddity is related in some way to the unreasonable effectiveness of mathematics.

Durston and Craig on an infinite temporal past . . .

Physicist David Snoke thinks that Christians should not use the kalaam argument for God’s existence

and

Must we understand “nothing” to understand physics?

Why is space three dimensions anyway? Why not six? A new theory is offered. They want to test their theory? What a great idea! In an age of wars on falsifiability, that’s a refreshingly new/old idea. Anyway, our universe seems pretty smart and can keep us awake.

Follow UD News at Twitter!

Of related note, irrational numbers and/or fractions also played a large part in Cantor’s work in trying to ‘tame infinity’ in mathematics. His effort to ‘tame infinity’ in mathematics, and the questions that his effort raised for the foundations of mathematics itself, played a large part in Godel’s subsequent work formulating the Incompleteness theorem for mathematics.

Here is a documentary that tells that story

I like the way Perry Marshall’s lays out the implications of Godel’s incompleteness theorem

Of related note, Gödel’s Incompleteness Theorem is not just some interesting abstract mathematical proof, but has now been extended to physics and is also now turning out, (since Darwinism itself is based on the presupposition of reductive materialism), to be relevant in biology as well:

The following article entitled ‘Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics’, which studied the derivation of macroscopic properties from a complete microscopic description, the researchers remark that “even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour”,,, The researchers further commented that their findings “challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”

And on the following episode of ID the Future, Dr. Richard Sternberg, research fellow at the Biologic Institute, speaks on his mathematical/logical work showing the difficulty of identifying genes purely with material phenomena, and that DNA doesn’t have all that’s needed to direct the development of organisms. The math, he says, is even showing gaps in the computability of what happens in the cell, which could help shed light on how machine-like organisms are or are not, how evolvable they are, and whether artificial life is possible.

Supplemental notes:

De proof: https://arxiv.org/abs/1907.04593