Professor Boldyrev is known for his pioneering works on superhalogens, superalkalis, tetracoordinated planar carbon, inorganic double helix, boron and aluminum clusters, and chemical bonding theory, especially aromaticity/antiaromaticity in all-metal structures, and development of the Adaptive Natural Density Partitioning (AdNDP) method.

degree, Alexander Boldyrev was doing his research at the Institute of Catalysis, USSR Academy of Sciences under Dr. Vasily Avdeev supervision.

After graduation from the university, he moved to another academic city, Chernogolovka, and joined Dr. Oleg Charkin's group when he worked on Non-rigid molecules and polytopic bonds.

His works together with Paul von Ragué Schleyer were among the prediction of new way to achieve planar tetracoordinated carbon and participated in the first experimental conformation of such species in molecular beams with Prof. Lai-Sheng Wang.

In analogy to superhalogens, Boldyrev and Gutsev introduced superalkalis,[6] species with extremely low Ionization potential, lower than that of a Caesium atom.

Alexander Boldyrev together with Lai-Sheng Wang made a large contribution to the theory of chemical bonding, especially in the topic of Aromaticity and Antiaromaticity.

In 2013, a Solid State Adaptive Natural Density Partitioning (SSAdNDP), an extension of AdNDP, was introduced by Timur Galeev and Alexander Boldyrev in collaboration with Benjamin D. Dunnington and J. R.