I reviewed at
four nearly identical unpublished papers by Dynin on the Clay millennium problem. The most recent paper claims at the beginning of Section 1:
``A mathematically rigorous solution is given for both parts of the
7th Millennium problem of Clay Mathematics Institute''
As I discuss in my review, his claim is wrong. Neither are the explicit requirements of the problem definition satisfied (no discussion of Poincare invariance and causality), nor is the paper mathematically rigorous in a crucial part of the construction (it is not proved that there is an operator with the anti-normal symbol specified in the construction).
The main criticism also applies to the published paper
Quantum Yang-Mills-Weyl Dynamics in Schroedinger paradigm,
Russian Journal of Mathematical Physics 21 (2014),No.2,169-188.
which wrongly claims to give a construction of massless QED.
Note that there are other attempts in the literature to settle this millennium problem or variants of it.
Simone Farinelli, Four Dimensional Quantum Yang-Mills Theory and Mass Gap I: Quantization of the Solution of the Classical Equation, claimed to prove a mass gap given existence of a quantum Yang-Mills theory. This claim was reviewed at http://www.physicsoverflow.org/21788 and also found wanting.
Agostino Prastaro, Quantum Extended Crystal Super Pde's, claimed to have quantized a super-Yang-Mills theory with mass gap; see Theorem 3.28. An invitiation to review the claim is at http://www.physicsoverflow.org/21787 .