Ernst Eduard Kummer, one of the great algebraists of the nineteenth century, had a strange weakness that made his students both amused and bewildered — he was terrible at arithmetic. In the classroom, where one would expect flawless calculations, Kummer often found himself pausing mid-problem, turning to his students for help with even the simplest numbers. One day, while teaching, he arrived at what seemed like an easy step. “Seven times nine,” he began confidently. Then his voice faltered. “Seven times nine is… er… ah… ah… seven times nine is…” The room grew quiet. Students exchanged glances. Finally, a voice from the front row broke the silence. “Sixty-one,” the student said. Relieved, Kummer nodded and wrote 61 on the blackboard. But before the chalk could settle, another student quickly stood up. “Sir, it should be sixty-nine.” Kummer turned, slightly puzzled but entirely serious. “Come, come, gentlemen,” he said, raising his hand. “It can’t be both. It must be one or the other.” He tried to reason it out logically. “The product cannot be 61,” he said, “because 61 is a prime number. It cannot be 65, because 65 is divisible by 5. It cannot be 67, for it too is prime. And 69 is clearly too large…” He paused, thinking carefully, then concluded with quiet satisfaction: “Only 63 is left.” And just like that, through pure reasoning rather than calculation, Kummer arrived at the correct answer — reminding everyone in the room that while arithmetic may fail you, deep mathematical thinking rarely does.