Well, Sir Roger is the “other Penrose” to the chess community. Mildly amusing.
http://www.telegraph.co.uk/science/2017/03/14/can-solve-chess-problem-holds-key-human-consciousness/
What is the famous study (a century or so old) in which White achieves a fortress draw with 1.B(Q)a4+ Kxa4, 2.b3+, 3.c4+ 4.d5+, 5.e6 locking the pawn chain?
Found it by searching the pawn chain 
Rudolph, The Chess Amateur #0181, 1911
White to play and draw
(Give this position to your engine and see what happens. But an advanced beginner can understand the cute point.)
Hmm, nice. I’ll have to inflict it on a few people in future tournaments. (Or perhaps you’d prefer to do that yourself?)
Bill Smythe
I’m already inflicting it on a few humans here. But they will certainly get the point. Inflict it on the machines instead! Penrose’s point (and I submit that Rudolph’s study makes the same point as Roger Penrose’s, and far more artisticially) is that such positions are beyond a chess-playing program’s comprehension. I tested with Stockfish 8: he’s right.
But one need not be a grandmaster (like Roger’s brother, the #1 player in the UK in the 1960s) to get the point of either position.
If there’s a young person in your life (age 16-20) passionate about math & science, Penrose’s The Road to Reality is a wonderful gift.
I am not as big a fan of his “quantum nature of consciousness” work. Hey, QM makes semiconductors possible, too.
I’m very surprised to hear that. It seems like just the sort of thing a program would solve easily. It’s five moves deep, but only one move wide.
Tell me, what does Stockfish do with my two-rooks-vs-one problem?
Bill Smythe
The Smythe study in question is here: http://www.uschess.org/forums/viewtopic.php?p=314059#p314059
Stockfish jumps from +6 to +13 in a second or two, and shows mate in 33 by three or four seconds.
That seems way too high. White can get away from the checks in 13 moves, and I doubt whether it should take 20 more moves after that, with black already locked into the back rank (or a-file).
Bill Smythe
I was crestfallen when I fed the famous Korol’kov study into Fritz some years ago. Both Fritz and Stockfish solve the position in less than a second. In Stockfish’s eyes, heading for the lost KBN vs. K ending is maximum resistance
Korol’kov 1951
White to play and win
Minimax destroyed most of our aesthetic conceits about chess. (The twentieth anniversary of Kasparov’s loss to Deep Blue is coming up…)
But Penrose is right to note that we still spectacularly outperform the algorithms in certain rare positions.
Tablebases give you the “real” answer instantly: mate in 27. The first forced mate that Stockfish finds isn’t necessarily the fastest.
Ha: Frederic Friedel used the same study to make the same aesthetic point. And he first challenged a computer to solve the Rudolph study in 1992!
Well, it probably is the most famous blockade study. Or I may be a plagiarist 
http://en.chessbase.com/post/a-chess-problem-holds-the-key-to-human-consciousness