The einstein-wertheimer correspondence on geometric proofs and mathematical puzzles

Conclusions

The new letters fill gaps in what was known about the Einstein-Wertheimer correspondence. A previously published letter by Wertheimer, which was not presented here and which Miss Dukas believed was written in the winter of 1937, thanked Einstein for the beautiful example of the “ugly” and “beautiful” proofs concerning the theorem of Menelaus [11, p. 191]. Now it is dear that the reference was to the first new Einstein letter (Letter 1). The new letters also help to date the Wertheimer letter that was presented. Originally believed to have been written in 1934, it now seems dear that it was written in 1937, the same year as the new letters.

The letters also cast light on the relationship between the two friends and their mutual interests. Wertheimer’s letter followed up on their hours of conversation in Huntington about “the problem of axioms.” Einstein took the time to write a long letter rejecting Wertheimer’s example as irrelevant to the problem and giving the detailed proofs of an ancient geometric theorem that is not commonly taught today. Einstein contended that we could be completely satisfied with a proof only if we felt that each intermediate concept was intrinsically related to the proposition to be proved. This thesis reflected the influence of Wertheimer’s Gestalt psychology with its stress on intrinsic requirements. Einstein continued to think about the proofs, admitting that he felt uneasy even about the “better” proof, and adding the interesting belief that every proof leaves a certain residue of doubt. A long letter by Wertheimer, which was not presented here, further analyzed the two proofs and related them to the two friends’ mutual interest in thinking processes.

Perhaps it was this interest (or just fascination with “brain-teasers”) that motivated Wertheimer to send Einstein the two puzzles. We saw the human side of Einstein when he gleefully admitted that he and a friend were fooled by the first puzzle but only the friend by the second puzzle. His delight in the puzzles, and his comments that they show how stupid we are, further revealed his down-to-earth character. This characteristic was also apparent when Einstein called himself a stupid beast for having used the formal instead of the informal mode of address. Such informality was also found in Wertheimer’s drawing of a sailor hat, with his initials in it, as his signature. They obviously enjoyed seeing and writing to each other. To use Einstein’s words, the correspondence helped us to see each of them as “a real person.”