Context:
In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras.
Hypothesis: It was pointed out by Yuri Manin that quantum algebras play an important role in the theory of quantum groups.
No
Context:
Derwael Ice Rise is 40 km long, 35 km wide and about 400 m tall ice rise in ice shelf off Princess Ragnhild Coast, Antarctica. Situated 70 km east of Breid Bay in northern part of Roi Baudouin Ice Shelf, directly in front of Western Ragnhild Glacier. Named for geodesist of Belgian Antarctic expedition Jean-Jacques Derwael.
Hypothesis: Derwael Ice Rise is 35 km long, 40 km wide and about 400 m tall.
No
Context:
If one were honest, one would ask why did she have four children at such a young age? If one were honest, one would ask why did she keep having babies with a man who has “problems of his own”? As far as I can tell, this person created her own mess and is responsible for her own situation.
Hypothesis: The woman in the text was four years old.

No