In an interview (I link the Google translation), Voevodsky talks about how, in the late 2000s, he worked on the problem of "restoring the history of populations according to their modern genetic composition". Some of his unpublished papers on this topic are now available online. For example, a paper titled "Singletons" is available on the IAS website. Why did Voevodsky abandon the subject of this rather fleshed-out paper so suddenly?
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Dan Grayson features this paper in his talk at the Voevodsky memorial conference. He points to an interview by Mikhailov, where VV says (Google translate):
As a result, I chose, as I understand correctly now, the problem of restoring the history of populations according to their modern genetic composition. I was busy with this task for a total of about two years and in the end, already in 2009, I realized that what I had invented was useless. In my life, for now, this was probably the biggest scientific failure. A lot of work was invested in the project, which completely failed. Some benefit, of course, nevertheless, was - I learned a lot from probability theory, which I did not know well, and I also learned a lot about demography and demographic history.
answered Nov 22, 2018 at 6:07
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7$\begingroup$ Indeed, this is where I first heard of the linked paper. But it doesn't quite answer the question of in what way the paper(s) failed to meet Voevodsky's goals. What exactly makes his singletons work useless for this purpose? $\endgroup$ Nov 22, 2018 at 7:46
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3$\begingroup$ Hmm, unfortunately we may never know... $\endgroup$– David Roberts ♦Nov 22, 2018 at 19:49