The true purport of immortality is detailed in Hinduism scriptures. Immortality in Hinduism always belonged to the spirit, Prana existing in all living beings in their heart as the soul atman.
Immortality was never meant for physical body as the life of physical body ordained by god is average 100 years. After that and sometimes even before that individual body parts start failing.
Immortality does not relate to medical science. No matter how much medical science progresses, the physical human form could never become immortal.
As per Hinduism scriptures the spirit, soul atman existing in heart is indestructible, could neither be created or destroyed and was immortal from the beginning of life when it started its cosmic journey.
After death of mortal body, the released soul atman again manifests a new body to start a new journey of life. This cycle of birth and death continues until human beings decide to indulge in spirituality and reach state of enlightenment, moksha salvation in their lifetime.
Mahavira, Gautama Buddha even Jesus Christ and Prophet Mohammed wanted to curtail this endless cycle of birth and death and hence embarked on spiritual journey. They successfully reached the end becoming an enlightened one at the end of spiritual journey.
Not in physical form but Mahavira, Gautama Buddha even Jesus Christ and Prophet Mohammed became immortal through their teachings forever. And so did Adi Shankaracharya, Sri Ramakrishna Paramhansa and Maharshi Ramana.
In human form immortality is never gained bodily but through teachings left behind after death of mortal body.