Mathematics is more than the dry textbook exercises students at various levels in India, beginning from school, are made to solve. What is missing in high school and college curricula is the excitement of mathematical research. Students, and the public, interested in mathematics, who wish to read something other than jargon-filled academic material, have nowhere to turn to. Whereas other countries have long had mathematics publications that serve the curious, the interested, and the cognoscenti, Bhāvanā is the first such initiative in India.

Bhāvanā is a Sanskrit word that was used by ancient Indian algebraists to name a principle of “composition” introduced by Brahmagupta (born in 598 CE) in the seventh century.

In verses 64 and 65 of chapter 18 titled Kuṭṭakādhyāyaḥ of his magnum opus Brāhma-Sphuṭa-Siddhānta (628 CE), Brahmagupta discusses the problem of finding positive integer solutions to the equation $Nx^2+1=y^2$ for any arbitrary $N$. Brahmagupta’s composition law shows how to combine two solutions of this equation to produce a third solution. In particular, it combines two expressions of the form $y_1^2-Nx_1^2$ and $y_2^2-Nx_2^2$ to get a third expression $y_3^2-Nx_3^2$. The precise identity that one gets

$$(y_1^2-Nx_1^2)(y_2^2-Nx_2^2)=(y_1y_2+Nx_1x_2)^2-N(y_1x_2+y_2x_1)^2$$

is now called “Brahmagupta’s identity”.

The equation $Nx^2+1=y^2$ for a fixed positive integer $N$ was later called “Pell’s equation” in modern Europe. Since Brahmagupta is arguably the first mathematician to investigate this important equation in a general framework, the equation is nowadays called the Brahmagupta–Pell equation. For more, see the article “The bhāvanā in Mathematics”.

Besides this mathematical usage, the word bhāvanā has profound nuances easily relatable in the larger Indian context, transcending linguistic barriers. In Sanskrit, its meanings include “creating”, “producing”, “generating”, “effecting”, “composing”, “accomplishing”, and “manifesting”. The word bhāva refers to a high spiritual state.

chief editorC.S. Aravinda
aravinda@math.tifrbng.res.in
contributing editors
Nithyanand Rao
nithyanand.nrao@gmail.com
Sudhir Rao
sudhi00@gmail.com
Ashutosh Simhaashutosh.iisc@gmail.com
Anupam Ghoshanupam.ghoshh@gmail.com
multimedia editor
Mohan Raj
rmohan689@gmail.com
corresponding editors
P. AjithICTS-TIFR, Bengaluru
Matthias BeckSFSU, San Francisco
Anil BeraUIUC, Urbana-Champaign
Sourav ChakrabortyCMI, Chennai
Rohini GodboleIISc, Bengaluru
Mahan MjTIFR, Mumbai
A.K. NandakumaranIISc, Bengaluru
P. RajendranFormer Senior Editor, India Abroad
Joseph SamuelRRI, Bengaluru
Riddhi ShahJNU, New Delhi
B.R. ShankarNIT Surathkal
K.R. Yogendra SimhaIISc, Bengaluru
M.A. SofiKashmir University, Srinagar
Kaushal VermaIISc, Bengaluru
Phillip WilsonUniversity of Canterbury

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