David Hilbert was a German mathematician who died in 1943. He discovered and developed many fundamental ideas, including Hilbert spaces in functional analysis. He claimed that if one were to bring 10 of the wisest men in the world together and ask them what the most stupid thing was in existence, they would not be able to discover anything as stupid as ... what?

It does not require a particularly wise man to realize that to defeat a four-spade contract, the defenders must take at least four tricks. How would that thought have helped West in this deal? He leads the diamond ace: five, two, four. What should he do next?

South opened three spades to show a respectable seven-card suit and 5-10 high-card points. West made a borderline takeout double. North raised, hoping his partner was short in diamonds. (Yes, three no-trump works here but is probably against the odds.)

What does East's diamond two say?

That he does not have a doubleton, when he would have started an echo (high-low). If South has two diamonds, can the second card disappear?

Only in layouts where the contract cannot be defeated. Which four tricks must the defenders get?

One heart, one diamond and two clubs, or one heart, two diamonds and one club.

This means that it must be best to shift to the club eight, high denying an honor.

As you can see, this defeats the contract. But if West cashes the diamond king at trick two, South's second club evaporates on the diamond queen.

Hilbert was talking about astrology. Do you agree?

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