It's a 22-page review, but I attach the first five pages, which should suffice with regard to Beckwith's Buddha-was-a-Scythian thesis, and hopefully won't exceed "fair use".
And another, much shorter, review by Patrick Lambelet of the University of California, Santa Barbara:
Beckwith sets out to challenge traditional claims about the origins and development of Buddhism and to show that there was far more fluidity and cross-influence in relations between Indic, Greek, Central Asian, and Chinese cultures than scholars have generally assumed. The project is ambitious, and Beckwith makes a number of intriguing claims, but in taking on so much material across such a wide array of fields, the book comes across as overly confident in its assertions, and sometimes superficial in its treatment.
Among the more provocative claims are that Pyrrho’s philosophy was largely derived from early Buddhist thought; that the Upaniṣadic teachings (and Jainism) did not exist prior to the advent of Buddhism; that the Buddha was of Scythian, and not Indian, origin (his name being Śākamuni, “Sage of the Scythians,” rather than Śākyamuni, the “Sage of the Śākyas”); and that Buddhism may have been directly influenced by Chinese and Central Asian thought. We even have an appendix that asks if Buddhism and Pyrrhonism are both Greek in origin. Perhaps the most compelling argument is the demonstration of similarities between Pyrrho’s philosophical teachings—which had little in common with other contemporaneous Greek schools—and early Buddhist notions of the trilakṣaṇa, or three characteristics (impermanence, unsatisfactoriness, and no-self). However, arguments based on etymological speculations, such as the claim that the name Gautama may have been a derivation of the name Lao Tzu, are less convincing. The sheer scope of the project—encompassing philosophy, philology, history, and archaeology across a broad cultural range—is often disorienting, and ends up overreaching, even if many of the questions are well worth exploring in more depth. For scholars interested in the cultural intersections of philosophy and religion, the book suggests fascinating possibilities, but leaves the reader wishing for more focus and clarity.