The Concept This is the arithmetic that determines how many possibilities exist. How many 3-scoop combinations can you make with six distinct ice cream flavours? This branch of maths allows us to predict outcomes.
The Story While European mathematicians like Fermat were just beginning to play with the math of “choice” in the 1600s, ancient Indian surgeons and philosophers were already calculating the infinite. In the Sushruta Samhita, doctors realized there were exactly 63 ways to combine the six primary tastes—sweet, sour, salty, and so on—to create complex medicines. Later, the Jain mathematicians took this further, using factorials to calculate the combinations of the senses and atoms. Even the Gods weren’t exempt: the mathematician Bhaskara calculated that a 10-handed Shiva could be sculpted in over 3.6 million different ways. India didn’t just count the world; they calculated every way the world could possibly exist.
The Timeline
| Milestone | Details |
| Western Ref. |
1600s CE (Pascal & Fermat)
|
| Indian Source |
Prior to 5,000 BCE (Sushruta Samhita); 850 CE (Mahavira)
|
| Chron. Gap |
Over 6,000 Years
|
The Original Text
Sanskrit Shloka: षट् पञ्चचतुस्त्रिद्विकसंयोगे षड् रसाः पृथक् । एकैकशः षड् व्याख्याताः संयोगास्त्वेकषष्टिधा ॥ Transliteration: Ṣaṭ pañcacatustridvikasaṃyoge ṣaḍ rasāḥ pṛthak | Ekaikaśaḥ ṣaḍ vyākhyātāḥ saṃyogāstvekaṣaṣṭidhā || (Sushruta Samhita – 63.3)Meaning: “By combining six, five, four, three, or two tastes, or taking them separately (one by one), the combinations are explained. Taken separately they are six; the total combinations are sixty-three.”
Related Innovations Hundreds of years before Europe, Jain mathematicians discovered how to count permutations using factorials ($n!$). The Sangita Ratnakara employed similar approaches to catalogue thousands of musical scales (Ragas).
Fun Fact Bhaskara was correct when he stated that there were 3,628,800 ways to create Shiva sculptures with ten hands, each holding a different weapon.
The Modern Legacy This math is behind cryptography, password security, and genetic research
