Binary search with lies
Stanisław Ulam was one of the great mathematicians of the last century. We talked about him in a recent post on his prime spiral and other strange mathematical facts. He is associated with several famous problems, including the 3n+1 problem and the Graph Reconstruction conjecture.
Today we want to talk about one of his oldest conjectures.
The conjecture was first stated in 1945. It is simple to state, seems plausible that it is true, but so far has resisted all attempts at resolution. René Descartes could have stated in the 1600s—well almost.
You can skip this and the next section on Ulam and get right to his conjecture. But its been open almost sixty years, so it can wait a minute or two.
Ulam did amazing work that impacted a vast part of mathematics and physics. He also wrote popular articles that were wonderful to read. The areas
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