Sthiramathi - What it means to me.

Sthiramathi is a Samskrit term. I will only attempt an English equivalent, since I believe that the real sense of the term cannot be conveyed completely in another language, or even outside the context of the Bhagavadgita.
The closest English equivalent would probably mean - "Of unshaken mind/intellect."
I encountered the term in the 12th Chapter of the Bhagavad Gita (Bhakti Yoga) where Shri Krishna describes to Arjuna the qualities of an ideal disciple.
Sthiramathi and Sthithapragna were two words which struck me, and I sort of, never recovered.
Objectivism is the closest closest school of philosophy I have encountered to resemble the Sthiramathi or Sthithapragna.

Please note that at the time I encountered the BhagavadGita, and hence these two words, I was religious, so to say.
There was'nt too much of a choice there I guess, since the typical Indian is brought up that way. Ethics and moral values often take the help of religious values, and children are brought up quite often as believers.

Atheism and agnosticism came across as options only around the time I was mature enough to think beyond the concepts of God and Religion.

So, the Sthiramathi, as it were should not need a religious identity.
Though the idea of the Sthiramathi is explained completely only in the context of the BhagavadGita, a deeply religious (Hindu) work of literature, I would want to look at it from a philosophical perspective.

Having said this, I confess lack of sufficient "philosophical" knowledge of any religion, including Hinduism.