Difficulty of proving the Generalized Poincaré Conjecture as a function of dimension:

n=1: Trivial

n=2: Easy (19th century)

n=3: Perelman (2003), declined Fields Medal

n=4: Freedman (1982), won Fields Medal

n≥5: Smale (1961), won Fields Medal

The difficulty of the generalized Poincaré conjecture is non-monotonic in dimension!

#Poincaré #PoincaréConjecture #Perelman #FieldsMedal #Geometry #MillenniumPrize #GrigoriPerelman #HenriPoincaré #Freedman #Smale #Conjecture

Great news today! Wendy #Freedman has received the #NationalMedalOfScience at the White House. Cordial congratulations and I very much appreciate the work she has done to advance our understanding of late-universe #cosmology & #astrophysics.

https://news.uchicago.edu/story/wendy-freedman-awarded-national-medal-science

#science #astronomy #astrophysics #LocalUniverse