On Hinduism

First, Soul is not Atman.

Think of Atma (or Soul as in this question) as the life energy within you that moves from one body to another body in the cycle of life and death that we call Samsara. This life energy is a part of the infinite,  unbounded energy that prevails the entire cosmos (Parmatama). When one talks about life energy, it is unbounded and not in terms of numbers. 

People ask when more births are happening than death, does that mean souls are coming from other life forms (animals, plans, etc.) and the total aggregate number of souls is constant on Earth?

Please know that numbers are only for the physical world, the life force (atma) knows no such physical limit and its arithmetic as the fundamental life force is unbounded and permeates the entire existence. 

I have one lit candle. Five people come by and light their candles from my one light. Where have the new flames come from? The rules of physical mathematics do not apply to the spiritual realm.

Can we reach infinite by counting 1, 2, 3 to 100, to 1000, to millions and so on? We will keep counting endlessly but will never reach the Infinite. So the question of the finite number of souls on earth would not be a valid one as soul is an infinitesimal part of this unbounded infinite energy and we can not count in terms of numbers. 

Source: Sadhguru Satsang

Other reading material:

Relevant videos: Swami Nikhil Anand Is the soul of an ant bigger than the soul of a whale?,

Contributor: Vikas Gupta

Location of this post (16a): https://www.hinduspeakers.org/ufaqs/if-a-soul-goes-to-a-new-body-where-does-a-new-soul-come-for-increased-world-population/

According to Hindu scriptures, there is no death for the Atman (soul is a wrong term). The human Atman (jīvātma) is considered to be of the same essence as the Divine Supreme Atman (paramātma), also termed as Consciousness. Hence the Atman, in the Hindu context, is eternal, imperishable, changeless, and that which illumines everything. 

The Atman can be thought of as a source of light. While the furniture in a room might keep changing, the reason one can see and experience these items is due to the presence of the light. Similarly, we are able to perceive, feel and think in the world because of our soul.

Lord Krishna declares in the Bhagavad Gita, Chapter 2, Verse 20:

na jāyate mriyate vā kadāchin nāyaṁ bhūtvā bhavitā vā na bhūyaḥ

ajo nityaḥ śhāśhvato ’yaṁ purāṇo na hanyate hanyamāne śharīre

The Atman is neither born, nor does it ever die; nor having once existed, does it ever cease to be. It is without birth, eternal, immortal, and ageless. The Atman is not destroyed when the body is destroyed.

Thus, Hindu theologians conclude that the Atman does not die. When a person passes on, their body decays, mind stops thinking, but the Atman, however, continues to exist. It leaves the body and moves onto a different realm of experience, based on what that particular Atman needs for evolution. This is valid for all living beings, and not just humans. It is due to this belief system that Hindus propound the theory of karma and reincarnation. The Atman evolves by taking on different births, until it reaches spiritual maturity and finally merges with the Divine Consciousness. This, liberation (moksha), is the goal of life on earth.

Other reading material: Reincarnation: WHO is it that Travels? Atma? Jiva? Subtle body?

Relevant videos: Swami Nikhil Anand Hinduism Q & A: What happens when we die?, Hinduism Q & A: Can the soul die?, Hinduism Q & A: What is Reincarnation?, 

Contributor: Lakshmi Subramanian

Location of this post (16b): https://www.hinduspeakers.org/ufaqs/can-the-soul-die/