A "conjecture on" or a "conjecture about"?
As a non-English scientist, the question bothers me. Maybe the answer depends on the context? Allow me to give a few examples. These are titles of a short text:
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Is it better to say "A conjecture on the inner mechanisms of cells" or "A conjecture about the inner mechanisms of cells"?
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Is it better to say "A conjecture on the working of enzyme XYZ" or "A conjecture about the working of enzyme XYZ"?
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Is it better to say "A conjecture on the structure of DNA" or "A conjecture about the structure of DNA"?
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Is it better to say "A conjecture on deducing the molecular structure" or "A conjecture about deducing the molecular structure"?
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Is it better to say "A conjecture on the origin of chirality" or "A conjecture about the origin of chirality"?
For those who do not believe it: Google gives only a few pages of hits when searching for the two expressions ("A conjecture about": 13 pages; "A conjecture on": 7 pages). The number is so small that no conclusion can be drawn. Also there seems to be no discussion of the issue anywhere on the web.
Update: For usage statistics, look at https://books.google.com/ngrams/graph?content=a+conjecture+concerning%2Ca+conjecture+respecting%2Ca+conjecture+regarding%2Ca+conjecture+on%2Ca+conjecture+about&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Ca%20conjecture%20concerning%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20respecting%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20regarding%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20on%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20about%3B%2Cc0#t1%3B%2Ca%20conjecture%20concerning%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20respecting%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20regarding%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20on%3B%2Cc0%3B.t1%3B%2Ca%20conjecture%20about%3B%2Cc0
Neither seems natural English to me. If one wishes to write elegant scientific English (and “conjecture” suggests the poster might) I suggest:
“A conjecture regarding…”
A matter of taste, but I think my answer tastes better than the accepted one.