Negative numbers and sign rules
Números negativos y regla de signos
- Date
- c. 100 BCE · confidence medium
- Place
- Chang'an (Xi'an), China
- Credited to
- Authors of The Nine Chapters on the Mathematical Art (Jiuzhang suanshu); commented on by Liu Hui (263 CE)
- Field
- Knowledge & symbols
What it is
Use of red and black counting rods to represent positive and negative quantities in solving systems of linear equations, with explicit rules of addition and subtraction. The first systematic treatment of negatives.
Diophantus (3rd century CE) rejected negative solutions as absurd; Europe did not fully accept them until the 17th century.
What it led to
- Solving of linear systems by elimination (the Gaussian method) 1,800 years before Europe
- Accounting of debts and credits as mathematical quantities
- Indian algebra (Brahmagupta) with rules for multiplying signs
- An expansion of the concept of number
Built on
- Early counting board / abacusc. 2400 BCE
- Counting rods (decimal place-value numerals)c. 400 BCE
- Chinese counting rods
- Chinese decimal numeration
Made possible
- Li Ye's tian yuan algebra1248
- Double-entry bookkeeping1340
- Brahmagupta's algebra
- Gaussian elimination method