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Bruno's Chess Problem: 20/10/2021

M.Caillaud, Europe-Echecs, 1987

Mat en 2(***)

Les blancs jouent

Astuce :

La solution du problème de mat du jour est disponible à partir du lendemain.

1. d6! ... 2. Qd5#   1... Rd3 2. Qxf4#   1... Rc3+ 2. Qxc3#   1... Re4 2. Qa5#   1... Rf3 2. Qd4#   1... Re2 2. Bd4#

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2021-10-21 01:28:49, by slowbut2

thank you for the info, problemist

2021-10-20 18:56:13, by slowbut2

i see now, again, that it was demonstrated by computer\s. Suddenly it appears that a demonstartion by independent computers and independent teams are or could be made to feel more reliable than a lengthy and combersome traditional non-computer demonstartion.

2021-10-20 16:15:04, by problemist

Of course there are many incorrect proofs around (just think about those of the P-NP problem). Here is a more interesting example from Sir Alfred Kempe (see Wikipedia) which shows that also an incorrect proof may be of later use:
"In 1879 Kempe wrote his famous "proof" of the four colour theorem, shown incorrect by Percy Heawood in 1890. Much later, his work led to fundamental concepts such as the Kempe chain and unavoidable sets."

2021-10-20 13:45:01, by slowbut2

"Incorrect proofs are another topic.... For examples of perfect proofs please refer to the cited publication. " -- thank you.
And more about incorrect proofs?

2021-10-20 12:55:48, by problemist

There are imperfect but correct proofs, this is meant by ugly mathematics. E.g. the four color theorem relies on computer assistance, so no perfect proof has been found yet. But anyone who has proved something by oneself has plenty of examples of ugly proofs :) These are often the first proofs one comes up with. For a perfect proof much more work is needed. Incorrect proofs are another topic. For examples of perfect proofs please refer to the cited publication.

2021-10-20 12:25:51, by slowbut2

re "The Book, in which God maintains the perfect proofs for mathematical theorems" one may wonder what is the mathematical definition of an imperfect proof, because
the thought of possibly relying on mathematical theorems based on too imperfect proofs [i.e. invalidating erroneous proofs] - accepted after cumbersome original submissions containing errors and after the reviewers missed them [a phenomenon known to exist] - is pretty demoralizing and frightening

2021-10-20 06:59:48, by problemist

"Paul Erdős [1913-1996] liked to talk about The Book, in which God maintains the perfect proofs for mathematical theorems, following the dictum of G. H. Hardy that there is no permanent place for ugly mathematics. Erdős also said that you need not believe in God but, as a mathematician, you should believe in The Book." Martin Aigner (* 1942), Günter M. Ziegler (* 1963) "Proofs from THE BOOK" (1998), Preface.

FIDE Album, 10 points. 3rd HM. Meredith. Shown is an "exquisite quintuple avoidance" (David Shire) after the unblocking 1. d6 (2. Qd5#) "now multiple mates are are separated following defences by a BR" (DS) 1.. Re2, Rf3, Rd3, Rc3+, Re4 2. Bd4#, Qd4#, Qxf4#, Qxc3#, Qa5#. Reprinted in "2345 Chess Problems" (1997), "The Problemist," Nov 2008, p. 513.

Michel Caillaud (* 10.4.1957) French composer and Grandmaster, see wikipedia de, en, fr, it, lv. "Michel Caillaud is a phenomenon: Grandmaster in solving and in composing, he was crowned twice world chess solving champion in 1987 and 2000 and has scored more than 250 points in the FIDE Album. He composes in all genres (twomovers, retro problems, helpmates, fairy problems, you name it). He is also International Judge, the French delegate at the WFCC and he organizes every year the Champagne tourney and a composing tourney at the Messigny meeting. The quality of his problems never disappoints: out of his 2100 problems registered in a database, 29% were awarded a prize (this is an exceptionally high rate). In spite of all this, Michel is still very modest and good natured."

2021-10-20 02:16:01, by slowbut2

before my seeing others’ chess comments: My solution [arrived to through the 32-pixel, B&W, restartable-moving-pieces setting and “(?)”]: in view of the following possibility\s::::::
queen mate [or white south-bishop mate] aafter pawn moves away \\ ,,,,,,,,,,,,,,,,,,,,, it seems [ re-verification is intended later on and before seeing others’ comments] that white's dsix starts

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