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AUM (ॐ) is the vibrational blueprint of existence. It maps the totality of an individual’s being. It encapsulates the four states of consciousness & three bodies. It guides awareness from the transient to the eternal, from the seen to the seer, from the finite to the infinite 2/N
The correct pronunciation of AUM (ॐ) is not just a phonetic act - it is a vibrational key that aligns individual consciousness with its fundamental reality

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In the seventh mantra of the Mandukya Upanishad, Consciousness (Turiya - तुरीय) is described as अव्यपदेश्यम् (Avyapadeshyam), meaning it cannot be designated or named. 2/N
This mantra describes Consciousness as beyond the three states of experience: waking (Jāgrat - जाग्रत्), dreaming (Svapna - स्वप्न), and deep sleep (Suṣupti - सुषुप्ति).

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This is a thread about how two related yet subtly different concepts of Vimarsha (विमर्श) in Kashmiri Shavisim (त्रिक) and Swaprakasha (स्वप्रकाश) in Advaita Vedanta (अद्वैत वेदान्त) shape the two frameworks of self-realization. 2/N
Kashmiri Shaivism and Advaita Vedanta are two profound streams of Indian philosophy. They both focus on the journey of self-realization, where the ultimate truth lies in the recognition of one's innate, undivided consciousness

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The story of Ganesha’s birth is a profound allegory and a masterpiece of iconography that encapsulates the journey of self-realization. This thread attempts to shed some light on that. 2/N
The story of Ganesha's birth is primarily found in several important Puranas including Shiva Purana, Skanda Purana, Padma Purana & Brahmanda Purana.

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This is a thread on how ancient Indians pioneered the field of large numbers & fast-growing functions - what is today known as Googology. 2/N
For our journey into ancient India’s discovery of large numbers, we will look into multiple schools of thoughts including Vedic, Jaina & Buddhist.

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This is a thread on two geometry problems: circling the square & squaring the circle. These problems were first proposed & analyzed by ancient Indian Hindus before 2000 BCE. They also designed multiple methods & provided approximate solutions before 800 BCE 2/N
Circling the square is an important problem in geometry which refers to the problem of constructing a circle with the same area as that of a given square.

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In my discussion & debates with Momins, I have often found a pattern of logical fallacies they routinely use. I typically don't expect any coherent argument from them. But I thought it would be interesting to document some of the patterns for future reference. 2/N
A hot favorite among eager Muslims in a debate is to use circular arguments. A circular argument is one that uses the same statement as both the premise and the conclusion. No new information or justification is introduced

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Ancient Indians were the first to invent numerical methods to find cube roots. In this thread I am going to trace the development of these methods & show how it it spread to Europe via works of Arabic & Persian mathematicians 2/N
The first mention of a numerical method to compute cube root of a number is found in the mathematical treatise Āryabhatīyam (आर्यभटीयम्) of Āryabhata (आर्यभट)

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This is a thread on how ancient Hindu & Jain Indian mathematicians approached the study of mensurations of quadrilaterals & cyclic quadrilaterals. 2/N
Specifically we are going to trace the events surrounding quadrilateral, cyclic quadrilateral & its diagonals analyzed by Indian mathematicians as recorded in texts such as Śulbasūtras, Brāhmasphuṭasiddhānta, Gaṇitasārasaṅgraha, Līlāvatī etc.

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This is a thread on finding positive integer (x, y) pairs of solutions for second order indeterminate equations of the form Nx^2 + k = y^2 where N is a non-square positive number. 2/N
Solution to this category of equations was invented by ancient Indian mathematicians by at least 628 CE, approximately 1000 years before the mathematicians in Europe started thinking about it.

1/N: Applications of the right-angled triangle theorem, or what is popularly known as the Pythagorean theorem are ubiquitous today. It is implicitly present in many engineering computations including mathematical physics, continuum mechanics, machine learning etc. 2/N: Many supervised and unsupervised algorithms in machine learning & deep learning use distance measures today - one of which is the Euclidean distance, which is nothing but an application of the right-angled theorem to compute the difference between two n-dimensional vectors.

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It is not an exaggeration to state that the monumental computational achievement of the human race which fuels innovations such as digital networking & 3D reconstruction of MRI images - all can be traced back to a single invention - the invention of zero Nothingness - 2/N
Ancient Indians pioneered the concept of zero and used it to advance applications in fields such as beejganit (algebra), jyamiti (geometry), trikonomiti (trigonometry), yuktibhasha (calculus), goladhyaya (spherical geometry)