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For instance, Riemann mapping theorem is more than just incredible: merely using the word 'incredible' to describe it is not enough. So, what is more incredible than incredible?

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    Why is incredible not enough? It has an absolute meaning, i.e. not-believable, so I find it hard to see how you could go beyond that. If you want to describe why it is not-believable, you could try absurd, but a bit of context and an explanation of why incredible is insufficient would greatly improve your question. – 568ml May 27 '14 at 7:43
  • Ingenious. Evolution is the ingenious mechanism of nature to produce its own persistent eternal companion. – Blessed Geek May 27 '14 at 8:37
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    Either something is credible or it is not. – Preston May 27 '14 at 10:25
  • @PrestonFitzgerald There are degrees of credibility. – Mitch May 27 '14 at 17:31
  • incrediburgable! – Oldcat May 27 '14 at 18:18
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Paradoxical (seemingly impossible)?

Counter-intuitive - not as string but certainly apt for your example.

And unbelievable - is means exactly the same as incredible, but it may have some stronger connotations because the link to stronger forms of beliefs is more obvious.

You could use an actual hyperbole: impossible!

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inconceivable

Inconceivable unbelievable; incredible.

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    You keep using that word. – Mitch May 27 '14 at 17:18
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I suppose uncountenanceable means 'not even admitting of consideration that [it] might be possible'. It's rare enough to be self-emphasising. But it doesn't fit as a descriptor for a theory, of course.

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Riemann mapping theorem is extraordinary.

Alternately, consider such colloquialisms as mind-boggling and unreal.

mind-boggling: having a powerful or overwhelming effect on the mind

unreal: so remarkable as to elicit disbelief; fantastic; unbelievable

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You can use the expression "beyond human knowledge" to give the idea of something really difficult to conceive.

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For these cases I normally use "mind-blowing" E.g. "The multiverse theory is just mind-blowing"

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I think phenomenal is more than incredible. You might be an incredible basketball player but only a few are phenoms.

adjective: exceedingly or unbelievably great

If you just can't believe something because it is so incredible then it is incredulous.

adjective: not disposed or willing to believe; unbelieving

And in the very rare cases, the word we might reserve for the other-worldly, is preposterous.

extremely unreasonable or silly

  • [adjective: not disposed or willing to believe; unbelieving] "If you just can't believe something because it is so incredible then it is incredulous." Oh, hell no!! According to the definition you supplied: If you just can't believe something because it is so incredible then YOU ARE incredulous. – Senex Ægypti Parvi Jun 20 '16 at 23:38
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Try superlatively incredible.​​​​​​​​​​​​​​​​​​​​

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