Why did Max Planck initially consider his radiation formula a lucky intuition?

Max Planck initially considered his radiation formula a "lucky intuition" because it was a mathematical guess rather than a derivation from established physical principles.1

In October 1900, Planck learned from experimental colleagues that Wien’s law failed to accurately describe blackbody radiation at low frequencies, even though it worked well at high frequencies. Knowing the required mathematical dependencies for both the high- and low-frequency regions, Planck guessed that he could combine these two expressions into a single, simple formula relating energy to frequency.1

While this resulting formula—Planck’s radiation law—perfectly matched experimental data, it lacked a theoretical foundation at the time of its discovery. To Planck, who sought to understand the absolute laws of nature, a mere guess was insufficient. He immediately directed his efforts toward deriving the formula from first principles, a process that ultimately forced him to abandon his belief in the absolute nature of the second law of thermodynamics and introduce the concept of energy quanta.1