Littlewood's cylinder problem asks for the largest number of congruent infinite right circular cylinders in Euclidean
space 
whose interiors are disjoint and which touch pairwise. After scaling their common
radius to 
, their axes are lines at
pairwise distance 1. Matić et al. (2026)
proved that eight such lines cannot exist. Together with
the known construction of seven mutually touching cylinders,
this gives the exact maximum 7.
The condition is different from Kuperberg's six-cylinder conjecture, which concerns congruent infinite cylinders tangent to a common ball, rather than pairwise contact. Matić et al. (2026) used a computer-assisted exclusion of finite sign patterns.
