Some background insights are given to us by Professor T.R.V. Murti. Excerpts follow:

The Madhyamika philosophy claims our attention as the system which created a revolution in Buddhism and, through that, in the whole range of Indian philosophy. The entire Buddhist thought turned on the Sunyata doctrine of the Madhyamika.... The Madhyamika, however, has no doctrine of existence, ontology.... Not only affirmative predicates but also negative predicates are denied of the real…. It is not opposed to commonsense or science, where our aim is to know and handle things presented to sense in the phenomenal sphere. The categories of thought, causality, substance, identity and difference, good and bad etc., are certainly not applicable to the ultimately real, being relative: but the Madhyamika does not deny their utility as patterns of explanation in the empirical region.... As for some texts which speak of the sole reality of consciousness, they have been taught by Buddha as a preparatory step leading to the Sunyata doctrine, without unduly frightening the feeble minded. Therefore it is declared in the texts that, through wisdom, the ‘real things’ are not made unreal; things themselves are unreal.

In particular:

A further vital consideration with regard to Sunyata is that it is truly universal, the whole reality…. Sunyata does not need to be declared as Sunyata; the Real, or the Truth, is not constituted by our knowing or not knowing it as such…. Only a being which enjoys a sort of dual existence, having one foot in phenomena and the other in the Absolute, can possibly know the Absolute and reveal it to others.

Was there a cross-current of influence between Vedanta and Madhyamika?

For its dialectical technique, the Vedanta is clearly indebted to the Madhyamika…

In it’s a radical form, as in the Advaita Vedanta, it denies the reality of the apparent, the impermanent and the many; and equated that with the false....

In the Madhyamika, however, Nirvana is not identified with consciousness or bliss. For the Vedanta, mukti is not merely absolute existence, free from suffering, but consciousness and bliss as well. Buddha nowhere acknowledges his indebtedness to the Upanishads or to any other teacher for his characteristic philosophical standpoint. Although Brahma, the deity, is referred to several times, Brahman (the Absolute) is never mentioned. Buddha always considers himself as initiating a new tradition, as opening up a path never trod before… Origination, decay etc. are imagined by the uninformed; they are speculations indulged in by the ignorant…. But the texts which speak of them as illusory and fit to be rejected cannot be understood in any other manner except as the ultimate teaching….

All things are unreal; they are deceptions…-Buddha

This is a significant admission that the real heart of Buddha’s teaching is the doctrine of Sunyata as the Madhyamikas claim....  The Madhyamikas have but systematically formulated his suggestions and drawn out their implications fully. 

Regarding development:

All this finds the fullest expression in the works of Nagarjuna and his followers... It is common ground between the Madhyamika and absolutist systems such as Vijnanavada and Vedanta that they all begin with negation or consciousness of illusion... Gaudapada appears to us as the Brahmanical thinker boldly reformulating the Upanishadic ideal in the light of the Madhyamika and Vijnanavada dialectic... We have undeniable evidence of Madhyamika and Yogacara influence in the Mandukya Karikas… The conclusion is irresistible that in the Mandukya Karikas, Gaudapada, a Vedanta philosopher, is attempting an advaitic interpretation of Vedanta in the light of Madhyamika and Yogacara doctrines. He even freely quotes and appeals to them… Ajativada is established again, but this time as the true import of the Buddha's teachings… It is possible, even probable, the such a school existed and exerted its influence on the Madhyamika and that it became the dominant Vedantic school owing to the efforts of Gaudapada and Shankara…

Madhyamika and Yogacara also had a theory of illusion to account for the emergence of appearance. Knowledge of this turn in Buddhism must have sent the Vedantin back to his own texts and enabled him to perceive the truer meaning of the Upanishads, in advaitism.

The view:

The Madhyamika method is in deconceptualise the mind and to disburden it of all notions, empirical as well as a priori…

Of all theories, Kasyapa, Sunyata is the antidote. Him I call the incurable who mistakes Sunyata itself as a theory. – Buddha

Madhyamika, in being aware of the illusoriness of views, is aware of the illusoriness of the world which is characterized by these views. For instance, in rejecting the different theories of causation, the Madhyamika has rejected causation as a constitutive feature of the real… A view is false, because it falsifies the real, makes the thing appear other than what it is in itself… Universality is obtained not by a combination of particular viewpoints, but by abolishing viewpoints. Certitude is gained, not by dogmatic assertion, but by critical reflection.

The outcome:

In one sense, the Madhyamika may seem one of the most intolerant of systems, as it negates all possible views without exception… Sunyata guards against the error of regarding nirvana as a separate reality… But the Madhyamika view is that nirvana is identical with the world of phenomena, as its transcendent ground; the difference between them exists merely in thought… It is pointed out that whether the Buddhas are born or they are not, the nature of the Ultimate Reality remains utterly unaffected… It is the contention of the Madhyamika that freedom cannot be attained without the realization of the unreality (sunyata) of things.

A sutra:

    This I call neither coming nor going nor standing,

        neither origination nor annihilation.

    Without support, without beginning,

        without foundation is this.

    The same is the end of suffering.

Nagarjuna claims:

All is concord indeed for him who to Sunyata conforms….