A consortium of 64 mathematicians built SOOHAK, a new AI benchmark with 439 handwritten tasks, including 99 that are deliberately unsolvable. Google's Gemini 3 Pro leads on research-level problems at 30 percent. But no model cracks 50 percent on spotting broken tasks. More compute makes models better at solving. It doesn't improve them at admitting a problem has no answer. SOOHAK tries to pin down the gap between a few flashy results and the broad research skills AI systems still lack.