History of Maths in India – a good book

In recent years, this has been one of the best books on the history of mathematics in India. The late Prof. Divakaran was a theoretical physicist and a scholar.

This book is also an excellent example of how a scientist can present historical facts and analyse them with rigour and nuance. Particularly, it puts the Indian contribution in the global context and shows how ideas are exchanged across the geography. The writing is jargon-free and can be understood by anyone interested in mathematics.

Unfortunately, the cost of the book ranges from Rs 8800 to Rs 14,000 (depending on the version), which is a shame. Part of the reason why scholarly books, particularly in India, don’t get the traction is because of such high cost. This needs to change for the betterment and penetration of knowledge in a vast society such as India.

There is a nice video by numberphile on Prof. Divakaran and his book:

Random Walks in Polarization

I have been teaching polarization of light in my optics class. In there, I introduced them to matrix representation of polarization states. One of the standard references that I use for explanation is a 1954 paper in American J. Physics, by McMaster titled: “Polarization and the Stokes Parameters.”

While skimming through the pdf of the journal paper, I found an excerpt from a 1954 book, which quotes Fresnel writing to Thomas Young:

Further, I knew from the past that S. Chandrasekhar (astrophysicist) had a role in rejuvenating Stokes vector formalism in radiative transfer. Below is his description from AIP oral history archives (May 1977):

” I started the sequence of papers, and almost at the time I started it, I read the paper by Wick in which he had used the method of discrete coordinates,* and I realized at once that that method can be used in a large scale way for solving all problems. So that went on. I have always said and felt that the five years in which I worked on radiative transfer [1944 – 49] is the happiest period of my scientific life. I started on it with no idea that one paper would lead to another, which would lead to another, which would lead to another and soon for some 24 papers — and the whole subject moved with its own momentum.” (emphasis added)

He further states how he rediscovered Stokes polarization vector formalism:

“All this had a momentum of it own. Then suddenly I realized one had to put polarization in; the problems of characterizing polarized light — my rediscovery of Stokes original paper, writing on Stokes parameters and calling them Stokes parameters for the first time“

Chandra further adds that the Stokes formalism was almost forgotten for 50 years, and he had a role in resurrecting it.

Next, there was some noise on social media where some one questioned the utility of matrix multiplication. For them, below is a wonderful review article by McMaster (again), to explore from polarization viewpoint, and realize the power of non-commutative matrix algebra:

Finally, the original paper by Stokes on his formalism, which is hard to find (thanks to paywall). But, classic papers are hard to suppress, and I found the full paper on internet archives.

Below is a snapshot:

Enjoy your random walk !

Conversation with Jyotishman Dasgupta

Welcome to the podcast, Pratidhavani – Humanizing Science

Jyotishman Dasgupta is a professor at TIFR, Mumbai, in the Department of Chemical Sciences. His research focuses on probing dynamical structural events leading to charge generation in molecular materials, particularly for bio-inspired photocatalysis and solar electricity generation. He uses ultrafast spectroscopy, including Stimulated Raman spectroscopy, to study reaction mechanisms in these systems.

Jyotishman effectively combines his love and passion for research and teaching with compassion and mentoring researchers. In this free-wheeling conversation, we discuss his intellectual journey so far.

References:

TIFR – Department of Chemical Sciences. ‘TIFR – Department of Chemical Sciences’. Accessed 3 November 2025. https://www.tifr.res.in/dcs/faculty-detail/91.

‘‪Jyotishman Dasgupta‬ – ‪Google Scholar‬’. Accessed 3 November 2025. https://scholar.google.com/citations?hl=en&user=DS8RvTcAAAAJ&view_op=list_works&sortby=pubdate.

‘Jyotishman Dasgupta | LinkedIn’. Accessed 3 November 2025. https://www.linkedin.com/in/jyotishman-dasgupta-312578a/.

X (Formerly Twitter). ‘Jyotishman Dasgupta (@jd1278) / X’. 27 October 2025. https://x.com/jd1278.

3 Questions for the AI age

3 Questions to Ponder in the Age of Artificial Intelligence (AI).

  1. What will you do with the time you gain from the utility of AI?
  2. How will you utilize your individual short-term and long-term memory?
  3. What is your definition of intelligence in humans?

I think it is worth thinking about.

‘We’gnana !

Recently, I saw the following tweet from the well-known historian William Dalrymple.

Congrats to the listed authors, who deserve rewards (and the money) for their effort.

I have 3 adjacent points to make:

1) India badly needs to read (and write) more on science and technology. Here, I am not referring to textbooks, but some popular-level science books (at least). Generally, educated Indians are exposed to science only through their textbooks, which are mostly dull, or, in this era, YouTube videos, which have a low signal-to-noise ratio. Good quality science & tech books at a popular level can add intellectual value, excitement, and expand scientific thinking via reading, not just in students, but also in adults.

2) In India, most of the non-fiction literature is dominated by the social sciences, particularly history (as seen in the best-seller list). I have no problem with that, but non-fiction as a genre is a broad tree. Indian readers (and publishers) can and should broaden this scope and explore other branches of the tree. Modern science books (authentic ones), especially written in the Indian context, are badly in need. I hope trade publishers are reading this!

3) Most of the public and social media discourse in India does not emphasize (or underplays) the scientific viewpoint. Scientific literature and scientific discourse should become a central part of our culture. Good books have a major role to play. Remember what Sagan’s Cosmos did to American scientific outlook, and indirectly to its economic progress. The recent Nobel in economics, especially through the work of Joel Mokyr, further reinforces the connection between science, economics and human progress. This realization should be bottom-up, down to individual families and public places.

One of the great scientists, James Maxwell, is attributed to have said: “Happy is the man who can recognise in the work of today a connected portion of the work of life and an embodiment of the work of Eternity.…“

Science, with its rich, global history and philosophy, in the form of good books, can connect India (and the world) to the ‘work of eternity’, and make us look forward.

Embedding science within culture, in a humane way, can lead to progress. Science books have a central role to play in this.

विज्ञान (Vignana) should transform to ‘We’gnana !

Conversation with Vijay Chikkadi

Welcome to the podcast, Pratidhavani – Humanizing Science
Vijay is an Associate Professor of Physics at IISER Pune, and works on various aspects of Soft Matter Physics, including deformation and flow of soft matter, and active matter.

In this episode, we discuss various facets of soft matter physics and Vijay’s research on these fascinating materials.

‘Vijayakumar Chikkadi – IISER Pune’. Accessed 1 November 2025. https://www.iiserpune.ac.in/research/department/physics/people/faculty/regular-faculty/vijayakumar-chikkadi/252.

‘Soft & Active Matter Lab’. Accessed 1 November 2025. https://sites.google.com/site/vchikkadi/home.

‘Soft & Active Matter Lab – PEOPLE’. Accessed 1 November 2025. https://sites.google.com/site/vchikkadi/people.

‘‪Vijayakumar Chikkadi‬ – ‪Google Scholar‬’. Accessed 1 November 2025. https://scholar.google.co.il/citations?hl=en&user=Xex6qvIAAAAJ&view_op=list_works&sortby=pubdate.

Sahu, Ratimanasee, Mohit Sharma, Peter Schall, Sarika Maitra Bhattacharyya, and Vijayakumar Chikkadi. ‘Structural Origin of Relaxation in Dense Colloidal Suspensions’. Proceedings of the National Academy of Sciences 121, no. 42 (2024): e2405515121. https://doi.org/10.1073/pnas.2405515121.

Have You Seen the Bird Flying? by D. R. Bendre

ಕನ್ನಡ ರಾಜ್ಯೋತ್ಸವದ ಶುಭಾಶಯಗಳು

Reproducing one of Da. Ra. Bendre’s Kannada poems titled “ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?” which translates to Have You Seen the Bird Flying?

A comment on the poem: In my reading, this poem is a metaphor for the exploration of the universe through the exploration of a bird. The poet periodically asks: “Have you seen the bird flying?”, thereby motivating the reader to observe what the bird may be seeing and doing. It is a poem read by school children, but there is a deeper philosophical meaning in asking humans to look up at the sky and realize the flight of a bird in themselves. YouTube also has the original audio of Bendre reciting the first few lines of the poem, and it is worth listening to.

Below is the poem, followed by a decent translation.

“ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?”

ಇರುಳಿರುಳಳಿದು ದಿನದಿನ ಬೆಳಗೆ
ಸುತ್ತಮುತ್ತಲೂ ಮೇಲಕೆ ಕೆಳಗೆ
ಗಾವುದ ಗಾವುದ ಗಾವುದ ಮುಂದಕೆ
ಎವೆ ತೆರೆದಿಕ್ಕುವ ಹೊತ್ತಿನ ಒಳಗೆ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?

ಕರಿನೆರೆ ಬಣ್ಣದ ಪುಚ್ಚಗಳುಂಟು
ಬಿಳಿ-ಹೊಳೆ ಬಣ್ಣದ ಗರಿ-ಗರಿಯುಂಟು
ಕೆನ್ನನ ಹೊನ್ನನ ಬಣ್ಣಬಣ್ಣಗಳ ರೆಕ್ಕೆಗಳೆರಡೂ ಪಕ್ಕದಲುಂಟು
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?

ತಿಂಗಳಿನೂರಿನ ನೀರನು ಹೀರಿ
ಆಡಲು ಹಾಡಲು ತಾ ಹಾರಾಡಲು
ಮಂಗಳಲೋಕದ ಅಂಗಳ ಕೇರಿ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?

ಮುಟ್ಟಿದೆ ದಿಙ್ಮಂಡಲಗಳ ಅಂಚ
ಆಚೆಗೆ ಚಾಚಿದೆ ತನ್ನಯ ಚುಂಚ
ಬ್ರಹ್ಮಾಂಡಗಳನು ಒಡೆಯಲು ಎಂದೋ
ಬಲ್ಲರು ಯಾರಾ ಹಾಕಿದ ಹೊಂಚ
ಹಕ್ಕಿ ಹಾರುತಿದೆ ನೋಡಿದಿರಾ?

Translation (ChatGPT):

Have You Seen the Bird Flying?
(by D. R. Bendre — English rendering)

Night after night melts into day,
All around, above and below —
the world moves on and on,
as the moment of awakening opens —
Have you seen the bird flying?

It has a tail dark as rainclouds,
and feathers white, shining bright;
its wings on either side
are tinted with colors of gold and light —
Have you seen the bird flying?

It drinks the silvery water of the moon,
to play, to sing, to soar;
it enters the courtyard of the blessed world —
Have you seen the bird flying?

It’s touched the edge of the horizon,
stretched its beak to the farthest reach;
who knows — since when it has tried
to break open the universe itself —
Have you seen the bird flying?

π and population

‘There is a story about two friends, who were classmates in high school,
talking about their jobs. One of them became a statistician and was working
on population trends. He showed a reprint to his former classmate, The
reprint started, as usual, with the Gaussian distribution and the statistician
explained to his former classmate the meaning of the symbols for the actual
population, for the average population, and so on. His classmate was a
bit incredulous and was not quite sure whether the statistician was pulling
his leg. “How can you know that?” was his query. “And what is this
symbol here?” “Oh,” said the statistician, “this is π.” “What is that?”
“The ratio of the circumference of the circle to its diameter.” “Well, now
you are pushing your joke too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle.”’

These are the opening lines of Wigner’s famous essay titled: The Unreasonable Effectiveness of Mathematics in the Natural Sciences