b. 476 CE
Āryabhaṭa
Place value, sine tables, and a cosmos that computes.
Bharatiya foundations
Āryabhaṭa, Bhāskara, Brahmagupta
Three minds, one number line with origin at zero — the inheritance Podometic returns to the K–8 classroom.
b. 598 CE
Brahmagupta
The Brāhmasphuṭasiddhānta states laws for positives, negatives and zero.
12th century
Bhāskara
Līlāvatī turns the same logic into a classroom a child can love.
शून्य
Zero is the floor of the universe
Negative quantities are no longer less than zero. The least quantity of universal matter and energy you can have is zero. A hole is real — debt, opposite force — but it is not a pile that went through the floor of existence.
Eighteen sūtras of symmetry
Brahmagupta, made visible
Positive + positive
Two gold blocks together are a larger pile of the same kind.
Negative + negative
Two holes together are a larger hole — never “less than zero”.
Positive + negative
A block dropped into a hole cancels. What remains is whichever kind was greater.
Anything + zero
Zero is origin. Adding origin changes nothing.
Take a positive
Removing blocks from a pile. If you remove more than you have, a hole appears.
Take a negative
Filling holes. Taking a hole away is the same as placing a block.
Take zero
You cannot take origin away. Zero is the floor of matter and energy.
Unlike kinds
Minus a minus is not a chant — it is filling.
Positive × positive
Scaling a pile of blocks. More of the same kind.
Negative × negative
Scaling holes by a hole-count reverses the hole. Symmetry, not a rule.
Unlike signs
Scaling a pile into holes yields holes.
Anything × zero
Scale by origin and you have origin.
Like signs
How many piles fit in a pile is a count of the same kind.
Unlike signs
How many holes fit in a pile is a hole-count.
Zero ÷ non-zero
Origin contains no piles and no holes.
Division by zero
Origin is not a measuring stick. Undefined.