[drieddust]

Isha Upnishad[0] was written in 1st half of 1st millennium BCE as per the conservative estimates. Its Shanti Mantra(wishing peace to all living beings) of says:

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते ।

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥

ॐ शान्तिः शान्तिः शान्तिः ॥

Om Puurnnam-Adah Puurnnam-Idam Puurnnaat-Puurnnam-Udacyate | Puurnnasya Puurnnam-Aadaaya Puurnnam-Eva-Avashissyate || Om Shaantih Shaantih Shaantih ||

Rough Translation:

That (god) is complete(puurnnam), this living being is complete. From completeness emerges completeness. When this completeness (living beings) emerges from that completeness (god), only completeness remains.

This verse describes God. But it can also be describing concept of zero and infinity. Buddhist philosophy emerging in 500 BCE is based in shoonyata[1] (nothingness) so concept of zero was definitely known for a long time.

As far as mathematical applications are concerned, we can't say for sure as a lot of knowledge was lost to invasions which specifically targeted universities like Nalanda[2].

Hindus imagined time scales of microseconds to trillions of years which in IMHO difficult to imagine without zero based mathematics[3].

Having said that there are a large number of manuscripts in the hands of small groups and families are yet to be discovered so these dates.

[0] https://en.wikipedia.org/wiki/Isha_Upanishad [1] https://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81 [2] https://www.myindiamyglory.com/2017/09/11/nalanda-9-million-... [3] https://en.wikipedia.org/wiki/Hindu_units_of_time

[KingOfCoders]

The idea of zero is that it's used in a positional numeric system, not just as a symbol for nothingness, like in

    1305
  + 0935
    ----
    2240

or in calculations

   ((5-5)+2)*0 = (0+2)*0 = 2*0 = 0

[drieddust]

Thanks, but that's such a narrow definition of the concept.

Shukla Yajurveda[0] conservatively estimated to be written in 1200- 800 BCE period in 17.2.20 constructs powers of 10 upto a billion by names by adding shunya successively to 10.

[0] https://en.m.wikipedia.org/wiki/Yajurveda

[braindead_in]

As Swami Sarvapriyananda is fond of saying, this verse encapsulates the essence of Advaita Vedanta. This verse is in fact his favourite. He has given hours and hours of talks on it. There is a lot packed into it.