  There are two big unsolved mathematical questions in artificial intelligence
(AI): (1) Why is deep learning so successful in classification problems and (2)
why are neural nets based on deep learning at the same time universally
unstable, where the instabilities make the networks vulnerable to adversarial
attacks. We present a solution to these questions that can be summed up in two
words; false structures. Indeed, deep learning does not learn the original
structures that humans use when recognising images (cats have whiskers, paws,
fur, pointy ears, etc), but rather different false structures that correlate
with the original structure and hence yield the success. However, the false
structure, unlike the original structure, is unstable. The false structure is
simpler than the original structure, hence easier to learn with less data and
the numerical algorithm used in the training will more easily converge to the
neural network that captures the false structure. We formally define the
concept of false structures and formulate the solution as a conjecture. Given
that trained neural networks always are computed with approximations, this
conjecture can only be established through a combination of theoretical and
computational results similar to how one establishes a postulate in theoretical
physics (e.g. the speed of light is constant). Establishing the conjecture
fully will require a vast research program characterising the false structures.
We provide the foundations for such a program establishing the existence of the
false structures in practice. Finally, we discuss the far reaching consequences
the existence of the false structures has on state-of-the-art AI and Smale's
18th problem.
