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Sarvepalli Radhakrishnan, the second President of India, is known to have written a commentary on the Brahma-Sutras. Radhakrishnan's Vedanta philosophy was Advaita. Now my question is that is there any difference between Radhakrishan's understanding of Brahma-Sutras and Adi Shankara's understanding of Brahma Sutras?

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Sarvepalli Radhakrishnan was an Advaitin and follower of Adi Shankaracharya. In his book on the Brahma Sutras, he generally explains each Sutra according to how Adi Shankaracharya interprets it, although he sometimes points out areas where different commentators disagree. Here is what he says in the preface:

In this book I have followed principally Shankara's commentary which is accepted generally by others except where doctrinal differences are indicated.

But he rarely actually disagrees with Adi Shankaracharya's interpretation of a Sutra. One place where he does disagree with Adi Shankaracharya, though, is in Adhyaya 1 Pada 3, when Adi Shankaracharya says that low-caste people aren't eligible for Jnana. As a member of what is often called the neo-Vedanta movement, Radhakrishnan was against the caste system. So after presenting the relevant Sutras and what Adi Shankaracharya says about them, Radhakrishnan says this:

The different methods of gaining salvation, meditation, devotion which lead to Brahma-knowledge are open to all. The restrictions with regard to Vedic study cannot be defended. If we take our stand the potential divinity of all human beings, whatever be their caste or class, race or religion, sex or occupation the methods of gaining release should be open for all.

But I'm not sure if he disagrees with Adi Shankaracharya's interpretation of these Sutras or if he disagrees with the Sutras themselves.

On a side note, if you want a book that does a more detailed comparison of what different commentators say about each verse of the Brahma Sutras, see Roma Bose's translation of Nimbarka's commentary on the Brahma Sutras. I've uploaded it here.

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