In the timeperiod after the vedic area master Adi Shankara introduced the Advaity Vedanta sampradaya. He divided india into four areas (maths) - each with a Shankaracharya.
A visit to the Shankaracharya (TM-EX-Letter of Robert Kropinski from the internet) :
At least since the 80s the Shankara-Order does not official accept Maharishi and rejects him, who brazen relies on the holy tradition of Guru dev Brahmanada Saraswati..
Maharishi Mahesh Yogi was only the secretary of Guru Dev and a sadhu and not an initiated disciple. Guru Dev, who evtl. died from poison, had wanted two other persons as successor, and there is no proof that Guru Dev was a fully enlightened master (Unity).
Advaita is not the highest teaching - It sees Shiva as a servant of Vishnu - though some ashrams added later the Sadashiva and Sri Vidya to the teachings. But the practice of methods of Shaiva Siddhanta and Kashmir Shaivism can be difficult in daily life, and such high states need the individual dharma - and not only a blue eyed aspiration.
Maharishis teachings inclusive the Transcendental Meditation and the siddhis are very different from the traditional Advaita-Vedanta -Teachings of the Shankara-Order, and he does not represent the "Holy tradition" (and i am fully convinced that he is a black tantric master or Rudra-master !).
The (alleged) siddhis are in clear contradiction to the teachings of the order, and even Pantanjali warns before them.
* Wiki : TM-History
At the beginning of the nineties Maharishi moved the Guru Dev somewhat into the background and turned to Veda, which Shankara had once superseeded with 'Advaita' because of the many errors which had crept into the understanding of traditional Veda, and to Ayurveda and Siddhis like doubtful yogic "flying"(Superfoam hopping), 'peace'- palaces and ' invincibility'(-towers)...