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The History of Hindu Mathematics (Bibhutibhushan Datta and Avadesh Narayan Singh) vol.1 p.1:

The earliest works available, the Vedas (c. 3,000 B.C. or probably much earlier), although consisting mainly of hymns of praise and poems of worship, show a high state of civilization. (...) It is here that we find the beginnings of the science of mathematics (arithmetics, geometry, algebra, etc.).

Wikipedia, History of mathematics, Indian mathematics:

The earliest civilization on the Indian subcontinent is the Indus Valley Civilization that flourished between 2600 and 1900 BC in the Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.

Question: Did the science of mathematics begin with the Vedas? If yes, why?
Was the concept of numbers transmitted by rishis? When?

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    I am not sure how much of mathematics is found in the 4 Vedas. But the Vedic people had advanced in mathematics. You could see this lecture on Evolution of Indian Mathematics: youtube.com/watch?v=aDy0axJfzrY – Bharat Aug 11 '14 at 23:10
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Yes, vedic mathematics is one subject, deep subject. It gives short cuts for big number calculations. Some people also wanted to implement that logic in making ALUs- Arithmatic and Logical Unit of computer but did not succeed yet.

Rishes gave lots of techniques to solve maths problems in the form of sutras.

Read them here Vedic Mathematics Tricks

What is Vedic Mathematics?

Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras or word-formulae.

Source : What is Vedic Mathematics? <- this link contains many sutras explanation with examples...

In hanuman chalisa, sage Tulsidas mentioned

Yug sastra yojan par bhanu, lilyo tahi madhur fal janu

means in childhood hanumanji jumped to eat sun considering sun is fruit, the distance between sun to earth they mentioned is exactly proven by NASA.

1 Yug = 12000 years
1 Sahastra = 1000
1 Yojan = 8 Miles
Yug x Sahastra x Yojan = -> 12000 x 1000 x 8 miles = 96000000 miles

Convert miles to km

1 mile = 1.6kms
96000000 miles = 96000000 x 1.6kms = 1536000000 kms
to Sun NASA has said that, it is the exact distance between Earth and Sun(Bhanu).

In vedas also numbers are used to mention hymns, also in Mahabharata count of people died in armies is mentioned.

Geometry is also given as maps of rivers etc.

Kings used to make a move during battles by creating vyuha on dummy maps based on their area's geometry only. They also try to increase the area of their territory.

I have no idea about algebra during vedic period.

In ramayana pushpak Plane is also mentioned. This mean aeronautical ideas were also there at that times.

And bridge over sea is also mentioned , so civil engineering concepts can also be understood which has also proofs about Golder Dwarka City in Gujarat.

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    Is there any verse from the 4 Vedas which have mathematical sutras(formulas)? I am skeptical about a Pushpak Vimana actually existing. It might have just been a concept. – Bharat Aug 13 '14 at 19:17
  • Then how a person can travel through sea and reach to svaymvar in janak's palace in just hours, also how a person can meet jatayu in hours after kidnapping sita? There must be some fast transport vehicle available... It may be a concept only.. because no body was there at that time.. :) – Mr. P Aug 13 '14 at 19:23
  • Bharati Krishna Tirthaji's "Vedic Mathematics" is not actually Vedic. Tirthaji claimed that his 16 Sutras were from the Parishishta of the Atharvana Veda, but they're not actually found there. For the real mathematics of the Vedic period, see here: en.wikipedia.org/wiki/Indian_mathematics#Vedic_period – Keshav Srinivasan♦ Feb 18 '15 at 9:26
  • Here is a good paper discussing the provenance of Tirthaji's Vedic Mathematics: tifr.res.in/~vahia/dani-vmsm.pdf – Keshav Srinivasan♦ Feb 18 '15 at 9:40
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    No. Vedic maths is just a hype, it is common mathematics technique just given the name "Vedic" so that people may find it interesting. – user12826 Feb 13 '18 at 5:44
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Based on the available mathematical evidence and the level and depth of mathematics, we can say that only simple concepts of mathematics such as addition, subtraction, multiplication and division was known in the Vedic ages. Using these four simple mathematical operation, basic geometry such as area of triangles and rectangles and approximate areas of circles were known. But anything more complicated than that was unknown in the Vedic ages.

  • The earliest available reference to something like Pythagoras theorem and Pi etc. in any Indian religious or mythological or astrological text or hymn dates back only to Budhiyana who lived around 5th century BC
  • Similarly, the earliest available reference to the mathematical concept of zero as we know it today dates only to Aryabhatta who lived around the 6th century AD

Both these dates are much younger than the Vedic ages so unless you consider elementary things like addition, subtraction, multiplication and division as good enough mathematical concepts, you cannot say with certainty that the Vedas contains anything more mathematically.

Sources:

  • Baudhāyana Shrautasūtra - Sulba Sūtra no. 58
  • Aryabhatiya (Arya-shatas-aShTa) - Ganitapada
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