|A math professor and his beloved girlfriend try to imagine how they could win the approval of her father for their marriage. She laments that he could only do so by being helpful in her father's profession, which is the manufacture of shoes. At first, the professor does not see how his area of expertise, topology, could be useful in producing shoes. But, he eventually proposes the idea of a factory that produces only shoes for the right foot and then using a 3-dimensional analogue of the Möbius strip that he has proved exists in the Amazon rain forest to switch half of them to left shoes via inversion. (Apparently, we are supposed to believe that the cost of shipping shoes to the Amazon and back would be cheaper than the cost of operating separate equipment for producing left and right shoes.) Then, there is a shocking and humorous plot twist (which isn't much of a surprise if you think about the title)...
In the 1960s, Gamow was best known for his popular science writings (see One, Two, Three,...,Infinity), although he was also a professional physicist and cosmologist. This story was originally written as a gift for Niels Bohr's 70th birthday in 1955, but was published in 1962 as part of the collection The Expert Dreamers edited by Fredrik Pohl.
This story is reminiscent of some others in this database. Technical Error by Arthur C. Clarke, The Plattner Story by HG Wells, and Left or Right by Martin Gardner are also all about left/right reversal through topological means. (Like the first of those, this one also makes reference to the biological difficulties that an inverted person would have to endure due to the chirality in molecular biology.) The Tachypomp and The Geometrics of Johnny Day are also about a mathematician attempting to impress a father to win his daughter's hand in marriage, with the latter involving an application of the Möbius strip.
Thanks to Vijay Fafat who first mentioned this story to me and to Allan Goldberg who urged me to add it to the database and let me read his copy.