An Old Conjecture Falls, Making Spheres a Lot More Complicated | Quanta Magazine

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.

**Hasnain says:**

“There are different types of progress in math and science. One kind brings order to chaos. But another intensifies the chaos by dispelling hopeful assumptions that weren’t true. The disproof of the telescope conjecture is like that. It deepens the complexity of geometry and raises the odds that many generations of grandchildren will come and go before anyone fully understands maps between spheres.

“Every major advance in the subject seems to tell us the answer is a lot more complicated than we thought before,” Ravenel said.”