yam hi na vyathayanty ete
purusham purusharsabha
sama-duhkha-sukham dhiram
so ’mrtatvaya kalpate

 Translation of Bhagavad Gita 2.15

O best among men [Arjuna], the person who is not disturbed by happiness and distress and is steady in both is certainly eligible for liberation.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

Anyone who is steady in his determination for the advanced stage of spiritual realization and can equally tolerate the onslaughts of distress and happiness is certainly a person eligible for liberation. In the varnashrama institution, the fourth stage of life, namely the renounced order (sannyasa), is a painstaking situation. But one who is serious about making his life perfect surely adopts the sannyasa order of life in spite of all difficulties. The difficulties usually arise from having to sever family relationships, to give up the connection of wife and children. But if anyone is able to tolerate such difficulties, surely his path to spiritual realization is complete. Similarly, in Arjuna’s discharge of duties as a kshatriya, he is advised to persevere, even if it is difficult to fight with his family members or similarly beloved persons. Lord Caitanya took sannyasa at the age of twenty-four, and His dependents, young wife as well as old mother, had no one else to look after them. Yet for a higher cause He took sannyasa and was steady in the discharge of higher duties. That is the way of achieving liberation from material bondage.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

Practicing tolerance with this discernment, the experience of the sense objects will, with passage of time, not give distress at all. When one reaches this state where there is no distress from the objects of the senses, he is qualified for liberation (amrtatvaya).Commentary by Sri Ramanuja of Sri Sampradaya:

2.15 That person endowed with courage, who considers pain as inevitable as pleasure, and who performs war and such other acts suited to his station in life without attachment to the results and only as a means of attaining immortality — one whom the impact of weapons in war etc., which involve soft or harsh contacts, do not trouble, that person only attains immortality, not a person like you, who cannnot bear grief. As the selves are immortal, what is to be done here, is this much only. This is the meaning. Because of the immortality of the selves and the natural destructibility of the bodies, there is no cause for grief. It was told (previously): ‘The wise grieve neither for the dead nor for the living’ (2. 11). Now the Lord elucidates the same view.
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

Rather than attempting to adopt a technique or remedy to try to purify the contacts of the senses with the sense objects; one should simply tolerate them as this leads to prodigious results. The Supreme Lord is declaring that whomever the sense objects are unable to overpower, subdue or afflict and who is equipoised in pleasure and pain not being attached to either due to spiritual knowledge becomes a fit candidate for immortality. which is liberation from the material bondage of birth and death due to the acquisition of spiritual knowledge.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

Here the results of the action are being described by this prescription. In this way one without attachment to the senses does not grieve. Inside one is equipoised and peaceful. Contrarily by being attached to the physical body everything is influenced by sorrow. The adjective purusa is used when one is not subject to sorrow. Why is there no grief? Because of being equipoised in both pleasure and pain. How is this possible? It is possible by being determined.

Now begins the summation.

The results gained is described by this prescription. Not by the merely being equipoised and dispelling all sorrow does one become self realised; but this indicates the correct process. When one has relinquished all conceptions of being the physical body one becomes naturally filled with the spiritual attributes that are inherent of the soul. Fixed in this awareness one is known as a purusa, thus this has been written in Pravritta scripture. The word pura in purusa signifies full, so full in noble attributes and full in wisdom the meaning of the word purusa is illuminated.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

If one were to question what would be the result if one ignores the connection between the senses and the sense objects Lord Krishna answers this by explaining that one who is performing their natural duty in life which is prescribed in the Vedic scriptures according to their own individual qualifications, without desiring any gratification for their actions; what then can deter this living entity and cause them to deviate irresponsibly. The spiritually intelligent, living entity, possessing patience, whom remains equal in happiness and unhappiness becomes eligible for immortality, by which lifes highest goal is acquired of ones individual spiritual nature devoid of the imperfections connected with the physical body such as of old age, disease and death.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.15 What will happen to one who bears cold and heat? Listen: Verily, the person…,’etc. (O Arjuna) hi, verily; yam purusam, the person whom; ete, these, cold and heat mentioned above; na, do not; vyathayanti, torment, do not perturb; dhiram, the wise man; sama-duhkha-sukham, to whom sorrow and happiness are the same, who is free from happiness and sorrow when subjected to pleasure and pain, because of his realization of the enternal Self; sah, he, who is established in the realization of the enternal Self, who forbears the opposites; kalpate, becomes fit; amrtattvaya, for Immortality, for the state of Immortality, i.e. for Liberation.
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.15 But, because all these different situations are of the nature of coming and going, on that account itself are they not to be lamented on ? It is not so. As for instance : What is this which is termed ‘coming’ ? If it is ‘birth’, what is that ‘birth’ itself ? It is wrong to say that is the same as gaining the self by what is non-existent. For, to be of the nature of non-existence, is indeed to be devoid of every inherent nature and to be devoid of the very self. If a thing is devoid of the self and devoid of every nature, how is it possible to convert it into what has an intrinsic nature ? Surely, it is impossible to convert the non-blue into blue. For, it is faulty and undesirable to covert the non-blue into blue. For, it is faulty and undesirable to conclude that a thing with certain in nature changes to be of a different nature. Hence the scritpure goes – ‘The intrinsic nature of beings would not cease to exist, e.g., the heat of the sun’. On the other hand, if the ‘birth’ signifies the gaining of self just by what [really] exists, even then, why the lamentability on its coming ? For, what has gained a self, could never be non-existent and consequently it would be eternal. Likewise, is the act of ‘going’ also meant for the existent or the non-existent ? What is non-existent is just non-existent [for ever.] How can there be a non-existence-nature even in the case of that which is of the existence-nature ? If it is said that it is of the non-existence-nature in the second moment; [since its birth], then it should be so even in the first moment; and so nothing would be existent. For, the intrinsic nature [ever] remains unabandoned. But is it not that the destruction of it (i.e., of a given thing, like a pot) is brought about by the stroke of a hammer etc.? Yet, if that destruction is altogether different [from the existent one i.e. the pot], then what does it matter for what is existent ? But, it is not be seen [at that time] ? Yet, what is actually existent (pot) may not be seen just as when it is covered with a cloth; but it has not turned to be altogether different. In fact, it has been said [in the scriptures] that this is not different [from the existent]. Summarising all these, [the Lord] says –Sanskrit Shloka Without Transliteration Marks:

yam hi na vyathayanty ete
purusam purusarsabha
sama-duhkha-sukham dhiram
so ‘mrtatvaya kalpate

Sanskrit to English Word for Word Meanings:

yam — one to whom; hi — certainly; na — never; vyathayanti — are distressing; ete — all these; puruṣam — to a person; puruṣa-ṛṣabha — O best among men; sama — unaltered; duḥkha — in distress; sukham — and happiness; dhīram — patient; saḥ — he; amṛtatvāya — for liberation; kalpate — is considered eligible.