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The Diamond Sutra, Heart Sutra, the Perfection of Wisdom Sutra in 8000 lines and others are grouped together as Prajnaparamita (perfection of wisdom). Why is this?

Why are they seen as a coherent collection? Are they thematically similar or is the link because they were written at a particular geographic and historical period? Are they maybe linked because of they a reaction against other schools of Buddhist thought at that time? Should they be linked together at all?

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The first answer is only partly right. The main thing that links these texts is the reference to prajñāpāramitā. They do share the point of view that elements of experience (dharmas) are empty of any self-existence (svabhāvaśūnya). They also seem to be against the tendency to Realism that emerged in the later Abhidharma traditions.

Many of the texts are obvious expansions of the original prajñāpāramitā. So Ratnaguṇasamcayagāthā (Collection of Verses on the Precious Qualities) and Aṣṭasāhasrikā-prajñāpāramitā-sūtra (The Perfection of Wisdom Consisting of 8000) are early Sanskrit translations of the basic text which was composed in Gāndhārī ca. 100 BCE. The Aṣṭasāhasrikā was expanded into texts of 10, 18, 25, and 100 thousand lines. They are a distinct group and very closely related.

The Heart Sutra or Prajñāpāramitāhṛdaya was composed ca. 7th century in Chinese using quotes from a Chinese translation of the 25,000 line sūtra (Taishō 223) translated by Kumārajīva. It combined some themes from Chapter three of T223 with devotion to the Bodhisatva Avalokiteśvara and a dhāraṇī (magic spell) taken from the Chinese Mahāmegha Sūtra (T387). It was subsequently back translated into Sanskrit and then expanded and translated into both Chinese and Tibetan.

The Diamond Sūtra or Vajracchedikā-prajñāpāramitā is another early sūtra on the subject of prajñāpāramitā which shares many features with the Aṣṭasāhasrikā but was written in a different milieu.

Both Aṣṭasāhasrikā and Vajracchedikā have obvious links to certain early Buddhist texts such as the Suññatā Suttas (MN 121 & 122). They both seem to focus on describing the point of view of someone who is immersed in the śūnyatā-samādhi. It seems likely that both were composed before the Mahāyāna became well defined as a distinct movement within Mainstream Buddhism (and modern scholarship suggests that this too centuries and was not complete until the 4th or 5th century CE).

Most of the other Prajñāpāramitā texts are Tantric texts that are written very much later, but in the style of the earlier texts. They are really of a different type and emphasis, but are lumped in with the others mainly because they call themselves Prajñāpāramitā texts.

Two excellent articles by David Drewes sum up and critique recent scholarship on the Mahāyāna. See his academia.edu page. On the very early history of the Prajñāpāramitā see the recent article by Karashima: Was the Aṣṭasāhasrikā Prajñāpāramitā Compiled in Gandhāra in Gāndhārī?

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All of these sutras are on the subject of wisdom, or "voidness", "sunyata", or the "emptiness".

There are many good teachings on the concept; here's one: Advice for Studying Voidness (Emptiness)

Every school has its own teachings on the subject. Indeed, all of them (I think) advocate meditation on the concept at some point. One form of Mahamudara meditation advocates using it from the beginning: Mahamudra Meditation Manual.

Good stuff!

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    +1. The Diamond Cutter Sutra, The Heart of Prajna-Paramita Sutra, The Prajna-Paramita Sutra in 8000 lines -- are all essentially about the same topic, that all dharmas have the character of Emptiness and that Enlightenment is Self-Existent. And yes, in a way they are all reactions against Abhidharmists reifying dharmas and indeed the very Dharma itself. – Andrei Volkov Jul 31 '14 at 16:13

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