If you didn't know anything about stabilization phenomena in algebraic topology and were trying to discover/prove theorems about the homotopy theory of spaces, what clues would point you toward results such as Freudenthal suspension or the existence of stable homotopy groups of spheres?

References suggest that Freudenthal originally stated his result in this 1938 Paper, although I'm unable to find an English translation. This was published only a few short years after the discovery of the Hopf fibration, so I find it pretty surprising that not only would there have been clear notions of $\pi_{\geq 2}$ at the time, but also enough evidence to suggest looking for things like the suspension map or stable homotopy groups.

Analogous stabilization phenomena do seem to occur elsewhere in mathematics: for instance, vector bundles that become isomorphic after taking Whitney sums with trivial bundles. From there, it may not be *that* much of a leap to suppose that something similar might work for fibrations.

However, it also seems that Freudenthal's paper predated results like this, and so historically, perhaps the flow of ideas was the other way around. What other results might have motivated his suspension theorem? Or in retrospect, what are some signs that such a thing might have worked and been useful?

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