This is stupid. Let me explain this: what they "discovered" was tiling a floor. The fact is that Penrose's stuff was only remarkable in its mathematical rigor. It's nothing innovative. The Greeks did similar stuff.
These are just crystallographers who, like many other practical scientists, think that when they run across some mathematics, that they were the first to invent it.
"This is stupid. Let me explain this: what they "discovered" was tiling a floor. The fact is that Penrose's stuff was only remarkable in its mathematical rigor. It's nothing innovative. The Greeks did similar stuff."
In fact, I remember reading Penrose's book "The Emperor's New Mind", where he also discussed "tilings" like these. I seem to recall reading in that book about some housewife from the Midwest (or something like that) who had come up with a whole bunch of these non-repeating tilings with various (typically fairly small) numbers of shapes. Very likely the guys who came up with these tilings were just very imaginative and good at what they did, but had no mathmatical background at all, beyond the relatively simple math required in their business.
It is an interesting subject, though.
Thank you. Referring to this sort of thing as a "math breakthrough" because it's an instance of whatever type of tiling Penrose identified and classified is like saying that whoever first drew a circle actually discovered the number pi. The headline's writer seems to understand neither math, nor breakthroughs.