Mahat-tattva, Pradhana and Prakriti

What are they?
What is the difference between Mahat-tattva, Pradhana and Prakriti?

Pradhana and Prakriti

We find an answer in Srimad-Bhagavatam 3.26.10.

sri-bhagavan uvaca
yat tat tri-gunam avyaktam
 nityam sad-asad-atmakam
pradhanam prakrtim prahur
 avisesam visesavat

Synonyms:
sri-bhagavan uvaca — the Supreme Personality of Godhead said; yat — now further; tat — that; tri-gunam — combination of the three modes; avyaktam — unmanifested; nityam — eternal; sat-asat-atmakam — consisting of cause and effect; pradhanam — the pradhana; prakrtim — prakrti; prahuh — they call; avisesam — undifferentiated; visesa-vat — possessing differentiation.

Translation:
The Supreme Personality of Godhead said: The unmanifested eternal combination of the three modes is the cause of the manifest state and is called pradhana. It is called prakrti when in the manifested stage of existence.

Purport:
The Lord points out material nature in its subtle stage, which is called pradhana, and He analyzes this pradhana. The explanation of pradhana and prakrti is that pradhana is the subtle, undifferentiated sum total of all material elements. Although they are undifferentiated, one can understand that the total material elements are contained therein.
When the total material elements are manifested by the interaction of the three modes of material nature, the manifestation is called prakrti.
Impersonalists say that Brahman is without variegatedness and without differentiation. One may say that pradhana is the Brahman stage, but actually the Brahman stage is not pradhana. Pradhana is distinct from Brahman because in Brahman there is no existence of the material modes of nature. One may argue that the mahat-tattva is also different from pradhana because in the mahat-tattva there are manifestations. The actual explanation of pradhana, however, is given here: when the cause and effect are not clearly manifested (avyakta), the reaction of the total elements does not take place, and that stage of material nature is called pradhana. Pradhana is not the time element because in the time element there are actions and reactions, creation and annihilation. Nor is it the jiva, or marginal potency of living entities, or designated, conditioned living entities, because the designations of the living entities are not eternal. One adjective used in this connection is nitya, which indicates eternality. Therefore the condition of material nature immediately previous to its manifestation is called pradhana.

Mahat-tattva

Srimad-Bhagavatam 3.5.27
Purports by Srila Prabhupada

tato ’bhavan mahat-tattvam
avyaktāt kāla-coditāt
vijñānātmātma-deha-sthaṁ
viśvaṁ vyañjaṁs tamo-nudaḥ

Synonyms
tataḥ — thereafter; abhavat — came into existence; mahat — supreme; tattvam — sum total; avyaktāt — from the unmanifested; kāla-coditāt — by the interaction of time; vijñāna-ātmā — unalloyed goodness; ātma-deha-stham — situated on the bodily self; viśvam — complete universes; vyañjan — manifesting; tamaḥ-nudaḥ — the supreme light.

Translation
Thereafter, influenced by the interactions of eternal time, the supreme sum total of matter, called the mahat-tattva, became manifested, and in this mahat-tattva the unalloyed goodness, the Supreme Lord, sowed the seeds of universal manifestation out of His own body.

Purport
In due course of time, the impregnated material energy was manifested first as the total material ingredients. Everything takes its own time to fructify, and therefore the word kāla-coditāt, “influenced by time,” is used herein. The mahat-tattva is the total consciousness because a portion of it is represented in everyone as the intellect. The mahat-tattva is directly connected with the supreme consciousness of the Supreme Being, but still it appears as matter. The mahat-tattva, or shadow of pure consciousness, is the germinating place of all creation. It is pure goodness with the slight addition of the material mode of passion, and therefore activity is generated from this point.

Our short explanation
Therefore for those who wants a short simple answer we’ll say that:
Pradhana is matter in its unmanifested and indifferentiated state;
Prakriti is matter its manifested and indifferentiated state;
Mahat-tattva is matter in its manifested and differentiated state, ready for creation.

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