Bhagwan Mahaweer: the Mathematical Genius 

Mathematics in Jainism dates back to Rishabhdew, the first Tirthankar of this awasarpini kalarddha (half-cycle, downward serpantine aeon). He taught mathematics to His daughter Sundari. Author of Ganita Sangrah, Acharya Mahaweer (814-877 CE) wrote: “लेहइयाओ गणियप्पहणओ।” It means, script full of mathematics. The reference to 12 agama, 14 purwa, 72/64 arts for men/women is the simplest example of number system then used.

Jains were the first to conceive transfinite numbers (7th century BC), a concept which was much later developed in Europe by German mathematician Georg Canter (1845-1918) through his ‘Set Theory’. Jain thinkers also introduced the notion of infinity as a quantity whose denominator was zero. This means that zero was known to Jain mathematicians before Pingala who used zero to develop decimal number system.

Although Jain Mathematics predates Bhagwan Mahaweer, most of the mathematical texts were composed after 600 BC. This is an important link between the wedic period (80000-1500 BC) and classical period (800 BC-600 AD). Acharya Mahaweer described Bhagwan Mahaweer as: “संख्यान ज्ञानप्रदीपेन जिनेन्द्र।” It means, Jinendra, the illuminator of knowledge of mathematics. Bhagwan Mahaweer had used many mathematical topics in His discourses. The diameter-periphery relationship constant, pi was used with value 3.18, which is square root of 10. He also used 84×10 raised to 5, purwang as a number, signifying use of indices. He had stated that there can be maximum 4 eclipses in a year and the synodic lunar month is 29 and 16/31 days long, which is very close to the value determined by modern science. His apostles, ganadharas, delivered countless lectures on His teachings and later acharyas composed texts to carry His teachings forward.

The scripture Surya Pragyapti composed 400-300 BC, contained theory of numbers, theory of limits, theory of sets. The scripture Wyakhya Pragyapti (300-200 BC) contains combinatorial analysis, simple algebraic equations, binomial expansion, so-called Pascal’s triangle, cubic equations, seven-fold predications of pluralism (anekant) and relativism (syadwad). The scripture Sthanang Sutra (300-200 BC) contains ten mathematical operations called parikarma.

Bhagwan Mahaweer had developed mathematics to suit his times and needs, independent of other systems. He stated that zero is only a symbol, not a number as there is nothing that can be called as nothing. So, zero as a number does not exist. It does not obey the laws of mathematics: 0 + 0 = 0, that is adding zero to zero remains zero; 0 – 0 = 0, 0 * 0 = 0; 0/0 is indeterminate. In the same manner He defined number 1 in a distinctly different manner.

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