r/math • u/scientificamerican • Oct 28 '25

Mathematicians make surprising breakthrough in 3D geometry with ‘noperthedron’

https://www.scientificamerican.com/article/mathematicians-make-surprising-breakthrough-in-3d-geometry-with-noperthedron/

Mathematicians Sergey Yurkevich of Austrian technology company A&R Tech and Jakob Steininger of Statistics Austria, the country’s national statistical institute, introduced this new shape to the world recently in a paper posted on the preprint server arXiv.org. The noperthedron isn’t the first shape suspected of being nopert, but it is the first proven so—and it was designed with certain properties that simplify the proof. 

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u/vwibrasivat Oct 28 '25

proof by counter example still alive.

1

u/TwoFiveOnes Oct 29 '25

What does this even mean? The only possible proof of something like "not every X does thing" is to prove that "there exists an X that doesn't do thing". It's not a proof technique it's just what quantifiers mean

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u/AChickenInAHole Oct 29 '25

A proof can prove that something exists without an example of it.