It turned out that most differential equations of the useful kind—the apple-falling-in-the-real-world kind, not the apple-falling-down-a-chalkboard kind—presented just the same impassable problem. These were not equations that could be solved by formulas or shortcuts, only by trial and error, or intuition, or luck. To solve them reliably—to bring the force of calculus to bear on the industrial problems of power transmission or telephone networks, or on the advanced physics problems of cosmic rays and subatomic particles—demanded an intelligence of another order.
