Hilbert's tenth problem, posed in 1900 by David Hilbert, asks for a general algorithm to determine the solvability of any given Diophantine equation. In 1970, Yuri Matiyasevich proved the DPRM theorem which implies such an algorithm cannot exist. This paper will outline our attempt to formally state the DPRM theorem and verify Matiyasevich's proof using the proof assistant Isabelle/HOL.

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How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert's tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as demonstrated by our example, proof assistants are feasible for beginners to formalize mathematics. With the aim to make the field more accessible, we also survey hurdles that arise when learning an interactive theorem prover. Broadly, we advocate for an increased adoption of interactive theorem provers in mathematical research and curricula.

We will present a novel elementary and self-contained proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on algebra. In particular, we will not make use of results from local class field theory or Galois cohomology."There are several ways to prove the Kronecker-Weber theorem, even if class field theory [...] seems inevitable." -P. Guillot (Preface, [3])