We see all the time conjectures and proofs that specific (real) numbers are (more often than not) irrational. I'm wondering that apart from the mathematical curiosity motivating such proof attempts, are there technical reasons to consider the rationality or irrationality of certain real numbers. That is, are there real numbers whose rationality or irrationality if proven will have important consequences to mathematics (apart from the fact in itself that the numbers are rational or irrational)?
2026-03-29 23:29:15.1774826955
Are there numbers that if proven rational (or irrational) will have important consequences to mathematics?
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