At a recent conference, mathematicians announced that they had proven the telescope conjecture false, making it the only one of Ravenel’s original conjectures to not be true. This discovery has far-reaching implications, showing that the universe of different shapes in high dimensions is more complicated than previously thought. To classify shapes, mathematicians use homotopy theory, which considers two topological spaces to be fundamentally the same if one can be deformed into the other without tearing. Homotopy theory is also important for understanding maps between spaces. Mathematicians are interested in determining the number of maps between spaces of different dimensions, and they have been able to compute this for dimensions up to 100.
https://www.quantamagazine.org/an-old-conjecture-falls-making-spheres-a-lot-more-complicated-20230822/