Mathematical sutras and subsutras

Here are the Sanskrit sutras and subsutras revealed by His Holiness Bharati Krishna Tirthaji Maharaja as encoding deeper mathematical knowledge. The Maharaja, who later became the Shankaracarya of Puri, wrote 16 volumes on the detailed application of these sutras in mathematics, one volume for each sutra. He was firmly convinced of their wide scope of application and wrote: "The sutras apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry - plane and solid, trignometry - plane and spherical, conics - geometrical and analytical, astronomy, calculus - differential and integral, etc). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction."

THE 16 SANSKRIT SŪTRAS ON MATHEMATICS
1	Ekādhikena Pūrveṇa	By one more than the previous one
2	Nikhilam Navataścaramam Daśataḥ	All from nine and the last from ten
3	Ūrdhva-tiryagbhyām	Vertically and crosswise
4	Parāvartya Yojayet	Transpose and apply
5	Śūnyam Sāmyasamuccaye	If the sum is the same, it is zero
6	(Ānurūpye) Śūnyamanyat	If one is in ratio, the other is zero
7	Saṇkalana-vyavakalanābhyām	By addition and by subtraction
8	Pūraṇāpūraṇābhyām	By the completion or the non-completion
9	Calana-kalanābhyām	Differential calculus
10	Yāvadūnam	By whatever the extent of its deficiency
11	Vyaṣṭisamaṣṭiḥ	Specific and general
12	Śeṣāṇyaṅkena Carameṇa	The remainders by the last digit
13	Sopāntyadvayamantyam	The ultimate and twice the penultimate
14	Ekānyūnena Pūrveṇa	By one less than the previous one
15	Guṇitasamuccayaḥ	The product of the sum is equal to the sum of the product
16	Guṇakasamuccayaḥ	The factors of the sum is equal to the sum of the factors

THE RELATED SUBSŪTRAS (COROLLARIES)
1	Ānurūpyeṇa	Proportionately
2	Śiṣyate Śeṣasaṁjñaḥ	The remainder remains constant
3	Ādyamādyenāntyamantyena	The first by the first, the last by the last
4	Kevalaiḥ Saptakam Guṇyāt	For seven, the multiplicand is 143
5	Veṣṭanam	By osculation
6	Yāvadūnam Tāvadūnam	Whatever the deficiency, lessen by that amount
7	Yāvadūnam Tāvadūnīkṛtya Vargañca Yojayet	Whatever the deficiency, lessen by that amount and set up the square of the deficiency
8	Antyayordaśake 'pi	Last totalling ten
9	Antyayoreva	Only the last terms
10	Samuccayaguṇitaḥ	The sum of the products
11	Lopanasthāpanābhyām	By alternative elimination and retention
12	Vilokanam	By mere observation
13	Guṇitasamuccayaḥ Samuccayaguṇitaḥ	The product of the sum is the sum of the products
14	Dhvajāṅka	On top of the flag

However the original manuscripts of the 16 volumes, given by the Shankaracarya to one of his disciples for safe-keeping prior to being published, were lost without trace. During his last few years, the Shankaracarya embarked on re-writing his lost works from memory. After completing the manuscript of one introductory volume, the Shankaracarya attained samaddhi in 1960. His sole volume on Vedic mathematics summarises the application of some of the above sutras. That's all the world is left with, until another genius of similar calibre as the late Shankaracarya of Puri emerges to research and decipher further scientific knowledge from these sutras and other portions of the Vedic texts.