Let us go through each one of the above in detail:
1. The Aryan invasion theory
The colonial scholars came up with the theory of the Aryans invading India around 1000 BCE. Since the events and genealogy mentioned in the Puranas pre date 1000 BCE, the Puranas were summarily dumped as mythical.
In the last 20 years enormous research has gone into the validity of the Aryan invasion theory. Based on the modern scientific reasoning the whole Aryan invasion theory seems to be untrue.
Max Muller in his own lifetime had repudiated the Aryan invasion theory.
Europe and England have now totally abandoned this theory.
The Saraswathi river civilization, which was primarily an Arya civilization now, has been scientifically proved to predate the Aryan invasion dates.
With all this the Aryan invasion or migration theory into India is not only questioned but is also being disproved.
2. Alexander's visit
Alexander invaded the Sindh region of India and engaged Porus in battle.
The British Colonial historians gave enormous importance to this invasion of Alexander and made it the sheet anchor of Indian history. They wrote that no incident of India before 327 BCE can be considered historical and hence this Purana and Itihasa were dubbed as mythical. They said the advancement of Indian arts and sciences were outcome of Alexander's invasion due to knowledge flow from Greece.
Modern historical evidences and circumstantial evidences suggest that Porus defeated Alexander.
3. Genealogy incoherent
The chronologies of Purana have been summarily dismissed as imaginative fabrications. It is true the genealogy list in the Purana has flaws. The chronologies of other ancient civilizations like Egypt, Sumeria which go back to about 2500 BCE, are also not flawless. The Indian chronology in the Purana goes back to well over 5000 BCE and beyond. In this incredibly long period of history, flaws are bound to creep in.
In fact the Purana and Ithihasa records are far more complete than any other record in the rest of the world.
Our ancient writers of the Purana well realized the impossibility of recording all the names of the Kings and their achievements. Because of the enormous time spans of well over 7000 years they concentrated more on inculcating the social values than on the exactness of the genealogy. This realization determined the histography method of ancient India, namely importance to social values over chronological records
4. Creation Date
As most Purana records predate the Christian Creation date of 23rd October 4004 BC the Purana were summarily rejected as mythical.
This date of 23rd October 4004 BC was decreed only in the year 1664 CE and has no Biblical sanction. Modern science has disproved this date.
Such being the case we need to relook at the historicity of our Purana and Itihasa
On the above four counts the colonial historians had branded our Purana as mythical. Now modern science has proved these four to be incorrect. Hence we need to revisit our Purana and Itihasa and do a honest re-evaluation of them to bring to light a correct picture of our antiquity.
Our Puranas is just not chronology of victories and defeats of the past kings but also carry stories of interesting legends in which the science and achievements of the bygone civilization are mentioned in detail.