Here is an incomplete proof that varieties are fiber bundles of formal disks over their deRham Stacks. The fact makes intuitive sense, the deRham stack is the variety without infinitesimal data, and then by adding the infinitesimal data (formal disks) back in, you recover the result. However, the fact that you can build anything non infinitesimal out of formal disks fills me with confusion and awe.
Acknowledgements: This is the result of a working group with Dan Fletcher, Adam Holeman, and me as part of the Northwestern Homotopy Working Seminar (started by Matthew Weatherly, Grigory Kondyrev, and me). The working session in which Adam and I figured out the proof, Dan was not there, which is why his name is not mentioned, but he was very helpful in understanding the claim. This proof is the result of Yaroslav Khromenkov coming up with the idea of it, and Adam and I understanding and correcting his solution during a working session.