Twitter called my attention to this (hastily written and error-prone, according to the comments) post in SciAm. The picture looks beautiful (though the link to a larger version doesn't work) and it seems like it might be really important. Anybody math savvy enough to weigh in?
The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved. --
When arranging the natural numbers in a spiral and emphasizing the prime numbers, an intriguing and not fully explained pattern is observed, called the Ulam spiral. (This is the caption to the image that fails to enlarge)
Diary enhanced at Palantir's request over the croissant.
The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved.
This is what the original piece in
Nature says.
The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant. “The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem,” says Dorian Goldfeld, a mathematician at Columbia University in New York. “If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century.”
More significant than Fermat's Last Theorem? Books have been written about that!
A couple more quotes:
Like Fermat’s theorem, the abc conjecture refers to equations of the form a+b=c. It involves the concept of a square-free number: one that cannot be divided by the square of any number. Fifteen and 17 are square free-numbers, but 16 and 18 — being divisible by 42 and 32, respectively — are not.
“The exciting aspect is not just that the conjecture may have now been solved, but that the techniques and insights he must have had to introduce should be very powerful tools for solving future problems in number theory.”
When I first posted this I was intrigued by the picture and the hype. I realize that I am asking for a bit much to be enlightened on something this esoteric but I am pleased to share and if anyone can post some pretty graphics to help all of understand what we are confronting here, it would be great.