Yes it's "likely" to be transcendental, maybe there are some evidences that support this, but this is not a proof (keep in mind that it isn't even proven to be irrational yet). Similarly, most mathematicians/computer scientist bet that P ≠ NP, but it doesn't make it proven and no one should claim that P ≠ NP in some article just because "it's most likely to be true" (even though some empirical real life evidence supports this hypothesis). In mathematics, some things may turn out to be contrary to our intuition and experience.

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auggierose 13 hours ago | parent [-]

It comes with the explicit comment "Not proven to be transcendental, but generally believed to be by mathematicians."

That's really all you can do, given that 3 and 4 are really famous. At this point it is therefore just not possible to write a list of the "Fifteen Most Famous Transcendental Numbers", because this is quite possibly a different list than "Fifteen Most Famous Numbers that are known to be transcendental".

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senfiaj 12 hours ago | parent [-]

So "Fifteen Most Famous Transcendental Numbers" isn't the same as "Fifteen Most Famous Numbers that are known to be transcendental"?

I might be OK with title "Fifteen Most Famous Numbers that are believed to be transcendental" (however, some of them have been proven to be transcendental) but "Fifteen Most Famous Transcendental Numbers" is implying that all the listed numbers are transcendental. Math assumes that a claim is proven. Math is much stricter compared to most natural (especially empirical) sciences where everything is based on evidence and some small level of uncertainty might be OK (evidence is always probabilistic).

Yes, in math mistakes happen too (can happen in complex proofs, human minds are not perfect), but in this case the transcendence is obviously not proven. If you say "A list of 15 transcendental numbers" a mathematician will assume all 15 are proven to be transcendental. Will you be OK with claim "P ≠ NP" just because most professors think it's likely to be true without proof? There are tons of mathematical conjectures (such as Goldbach's) that intuitively seem to be true, yet it doesn't make them proven.

Sorry for being picky here, I just have never seen such low standards in real math.

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auggierose 12 hours ago | parent [-]

You are not picky, you just don't understand my point.

"Fifteen Most Famous Transcendental Numbers" is indeed not the same as "Fifteen Most Famous Numbers that are known to be transcendental". It is also not the same as "Fifteen Most Famous Numbers that have been proven to be transcendental". Instead, it is the same as "Fifteen Most Famous Numbers that are transcendental".

That's math for you.

	▲	senfiaj 11 hours ago \| parent [-]
		Again, it seems we are arguing because of our subjective differences in the title correctness and rigor. Personally, I would not expect such title even from a pop-math type article. At least it should be more obvious from the title. "Transcendental" or even "irrational" isn't a vibesy category like "mysterious" or "beautiful", it's a hard mathematical property. So a headline that flatly labels a number "transcendental" while simultaneously admitting "not even proven" inside the article, looks more like a clickbait.