Medhavi is the person who has both great memory and intelligence.
The Supreme Lord is the most intelligent. He has very intelligently created this entire Universe and each of the beings in it. He has the most excellent memory as He knows the past, present and future of each if the beings here.
bījaṁ māṁ sarva-bhūtānāṁ viddhi pārtha sanātanam
buddhir buddhimatām asmi tejas tejasvinām aham (BG 7.10)
O son of Pṛthā, know that I am the original seed of all existences, the intelligence of the intelligent, and the prowess of all powerful men.
Kṛiṣhṇa is the source of everything and He is like the root of a tree that maintains the whole tree. Krishna is the original root of everything and maintains everything in this material world. This is confirmed even in vedic texts.
nityo nityānāṁ cetanaś cetanānāmeko bahūnāṁ yo vidadhāti kāmān (Katha Upanishad 2.2.13)
He is the prime eternal among all eternals. He is the supreme living entity of all living entities, and He alone is maintaining all life. One cannot do anything without intelligence, and Kṛiṣhṇa also says that He is the root of all intelligence. Unless a person is intelligent he cannot understand the Supreme Personality of Godhead, Kṛiṣhṇa.
na dveṣṭy akuśalaṁ karma kuśale nānuṣajjate
tyāgī sattva-samāviṣṭo medhāvī chinna-saṁśayaḥ (BG 18.10)
The intelligent renouncer situated in the mode of goodness, neither hateful of inauspicious work nor attached to auspicious work, has no doubts about work.
Lets chant the Holy Name of the most intelligent personality and try to use the intelligence given to us by Him to understand Him and serve Him always
Nama 78 – VishnuSahasranama