While the Vedas are unanimously accepted by the scholars of all ages as the most ancient treatises of knowledge, there have been differences in assessment of the period of their origin. According to ancient Indian scriptures and sages, the Vedas are as old as Nature because they represent the divine voice, which emerged at the time of the Creation of Nature. Among the western scholars, Prof. F. Maxmuller (in the "History of Ancient Sanskrit Literature" pg. 244) recognizes the Vedas as written much before the articles of Egypt and Ninenvhe; he estimates their period to be somewhere in-between 1500 to 1200 years B.C. However, his views were not acceptable to many of his contemporary savants. In response to their criticism, Maxmuller has himself commented that - "We would not be able to lay down any terminus whether the Vedic hymns were composed in 1000 or 1500 or 3000 years B.C., no power on the earth could ever fix". According to Prof. Weber (c.f. "History of Indian Literature" pg. 4) -"Certainly, the most ancient literature (the Vedas) is available only in India".
McDonald and Keeth have approximated the period of Vedas as around 2000 to 1200 years B.C. In the views of Wolver it is 2000 to 1500 years B.C. Wilson (c.f. pg. 45 in the Introduction section of "Translation of Rig Veda" Vol.-1), Whitney, Hog, Griffith, Hillary, Schroeder, and Goldschar have argued that the period of the Vedas must have been before 2000 years B.C. Winternitz (pg. 6 of the Hindi translation of "Ancient Sanskrit Literature") has inferred the time of Vedas to be around 2500 to 2000 years B.C. whereas Jacobi (in "Indian Antiquary", Vol. 23, pg. 158) takes it back to 4000 to 3000 years B.C.
Thus, in all, the period of the Vedas is mostly approximated by the Western Scholars as 4000 to 1200 years B. C. It is anyway not possible for them to take the period of existence of anything before 4000 years B.C. because, as per the holy Bible, the age of present creation of the world is only around 6000 years; and the average time in which the above inferences were made by thinkers from Maxmuller to Jacobi was around 1950 AD. The observations of Justice Kashinath Trayambak Tailang Swami [c.f. the preface pp. 33-39 of his English translation and commentary of the holy Bhagvad Gita] are worth quoting in this context. He comments that -- The European scholars of Sanskrit construct some theories based on weak or approximate facts and principles and build their imaginative edifice on this raw (incomplete) foundation. Then they develop some logic to hide the shaky foundation (to justify their inferences)…. Apart from this, notable here is also the fact that irrespective of their numerical estimates of the likely period of the Vedas, the Western scholars have all recognized the Vedas as the most ancient scriptures of knowledge for the human race. Most remarkable are the views of Nobel Laureate Materlink as discussed below.