Tag: education

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:

‘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 !

Light pressure – Lebedev coin

Today, in my optics class, I discussed optical forces due to momentum in electromagnetic waves. Towards the late 1800s, it was realized that light can impart momentum. This manifested as radiation pressure in the electromagnetic theory proposed by James Maxwell.

Pyotr Nikolaevich Lebedev (24 February 1866 – 1 March 1912) was one of the earliest to experimentally measure (~1899) the radiation pressure on a surface (link to his 1900 paper in German). In 1991, the Soviet Union released a 1 ruble coin (pictured above) to commemorate Lebedev’s scientific achievement.

The formula expresses the total momentum transferred per unit time ( radiation pressure, P) by a beam of N photons, each of energy hν, that is incident on a surface with a coefficient of reflectivity ρ. The constant, c, is the speed of light.

The discussion in the class was mainly related to Ashkin’s work. I have written about this in the past.

Shared below is a delightful lecture given by Ashkin at the age of ~96, after he received his Nobel prize.

Some writing advice (mainly physics) for UG students

Some writing advice (mainly physics) I shared with my undergraduate class. This may be useful to others.

  1. Equations, data and figures make meaning when you include a context. This context is expressed using words. Symbols and data by themselves cannot complete the meaning of an argument, unless one knows the context. A common mistake undergraduates make in an exam is to answer questions using only symbols and figures and assume the reader can understand the context.
  2. One way to treat writing in physics (in this case, an exam paper or an assignment) is to imagine you are talking to a fellow physics student who is not part of the course you are writing about. This means you can assume some knowledge, but not the context. Anticipate their questions and address them in the text you are writing. This model also works while writing research papers with some caveats.
  3. While you refer to equations, data and figures in your assignment, make sure you cite the reference at the location of the content you are discussing. Merely listing the references at the end of the document does not make the connection. Remember, while talking, you never do this kind of referencing.
  4. It is useful to structure your arguments with headings, sub-headings and a numbered list. This gives a visual representation of your arguments. You may not find this kind of structured writing in novels, other forms of fictional writing and also in some literature related to social sciences, but in natural sciences with dense information, this will be very useful. Always remember, while writing science (or any form of nonfiction writing), clarity comes before aesthetics.

Also, below is another blog related to written assignments.

Basic advice to undergrads: written assignments

Blog highlighted by SciRio

A nice article by @RutujaUgale in @Sci_Rio that discusses public engagement by scientists as influencers of scientific thought.

Thanks, Rutuja, for profiling my blog, ‘Vismaya’.

Here is my quote from the article:

“For me, there are two implications of doing science. One is that science is extremely useful to society, and the second is that it is a good, thoughtful way of living one’s life. Communicating the second implication is important to me, and I do this by researching, writing, and podcasting about the history and philosophy of science (physics in particular). This path helps people understand the human element of doing science and reveals a context. Some of my blogs (filtered here) discuss why I do science and how I do it. More than ‘influencing’ the audience, I am interested in inviting them to explore science by themselves via their own curiosity. That is one reason why my blog is called VISMAYA.”

Link to the full article.

Conversation with Aparna Deshpande

Welcome to the podcast, Pratidhavani – Humanizing Science

Aparna Deshpande is an Associate Professor of Physics at IISER Pune, specializing in atomic-scale exploration of two-dimensional materials and their interfaces using scanning tunneling microscopy. She is deeply engaged in research on nanomaterials and is active in physics education (as part of the department of science education at IISER Pune), communication, and outreach at IISER Pune.

Aparna is also the faculty in charge of the Smt. Indrani Balan Science Activity Centre at IISER Pune, where she leads diverse science outreach and STEM education initiatives, promoting hands-on multi-lingual learning and innovative workshops for students and teachers across India.

In this conversation, we explore her research in physics and science education.

You can also watch or listen on spotify

References:

[1] “Dr. Aparna Deshpande.” Accessed: Sept. 25, 2025. [Online]. Available: https://draparnadeshpande.github.io/portfolio/

[2] “Dr. Aparna Deshpande (@DrAparnaIISERP) / X.” X (formerly Twitter). Accessed: Sept. 25, 2025. [Online]. Available: https://x.com/draparnaiiserp

[3] “Aparna Deshpande | LinkedIn.” Accessed: Sept. 25, 2025. [Online]. Available: https://www.linkedin.com/in/aparna-deshpande-01927015/?originalSubdomain=in

[4] “Aparna Ramchandra Deshpande – Google Scholar.” Accessed: Sept. 25, 2025. [Online]. Available: https://scholar.google.com/citations?user=f5FnqMIAAAAJ&hl=en

[5] “Aparna Deshpande – IISER Pune.” Accessed: Sept. 25, 2025. [Online]. Available: https://www.iiserpune.ac.in/research/department/physics/people/faculty/regular-faculty/aparna-deshpande/259

[6] J. Poskett, Horizons. London, UK: Penguin Books, 2023. Accessed: Sept. 25, 2025. [Online]. Available: https://www.penguin.co.uk/books/313423/horizons-by-poskett-james/9780241986264

[7] P. Lockhart and K. Devlin, A Mathematician’s Lament. Illustrated ed. New York, NY: Bellevue Literary Press, 2009. https://www.blpress.org/books/a-mathematicians-lament/

Satish Dhawan – truly a man for all seasons

Image credit: Current Science 119, no. 9 (2020): 1427–32

Today is the birth anniversary of Satish Dhawan (25 September 1920 – 3 January 2002). He was probably India’s best scientist-administrator who headed institutions such as the Indian Institute of Science and the Indian Space Research Organization. With a PhD from Caltech, he came back to India and set up a marvellous research enterprise on fluid mechanics, including aerospace science and engineering. He mentored some of the outstanding scientists of India and led scientific institutions with vision, openness and informality, which is still a great benchmark to emulate1.

Below are a couple of historical documents related to Dhawan:

The first one is a lecture note from 1979, on making a case for a national satellite system and how it influences science and scientific activity (a copy of this note has been reproduced in a wonderful tribute to Satish Dhawan written by P. Balaram on his birth centenary2).

The next one is a beautiful perspective article written by Dhawan on ‘Bird Flight’ from an aerodynamics perspective3. It is a detailed overview of the dynamics of bird flight and shows Dhawan’s interest and ability to bridge two facets of science. It is a prototypical example of interdisciplinary research.

Finally, let me end the blog with a quote from P. Balaram on Satish Dhawan4:

“Dhawan mentored some remarkable students and built the discipline of aeronautical engineering at the Institute. He influenced aeronautical research and industry in India in a major way. He shepherded the Indian space programme following Vikram Sarabhai’s untimely death. He served the Indian scientific community in many ways. His stewardship transformed IISc. How then do we describe such a man? Dhawan studied English literature obtaining a Master’s degree in his youth. It may therefore be appropriate for me to borrow a 16th century description of Sir Thomas More:


‘[Sir Thomas] More is a man of an angel’s wit and
singular learning. I know not his fellow. For where is
the man of that gentleness, lowliness and affability?
And, as time requireth, a man of marvelous mirth and
pastimes, and sometime of as sad gravity. A man for
all seasons.’

Satish Dhawan was truly a man for all seasons.”

Happy Birthday to Prof. Satish Dhawan!

References:

  1. Current Science, in 2020, had a section of a volume dedicated to the birth centenary of Satish Dhawan, and has a foreword by his daughter and articles by many of his students and co-workers. https://www.jstor.org/stable/e27139029 ↩︎
  2. P. Balaram, “Satish Dhawan: The Transformation of the Indian Institute of Science, Bangalore,” Current Science 119, no. 9 (2020): 1427–32. This reference has many interesting references, including a handwritten obituary of CV Raman written by Dhawan https://www.jstor.org/stable/27139041. ↩︎
  3. S. Dhawan, “Bird Flight,” Sadhana 16, no. 4 (1991): 275–352, https://doi.org/10.1007/BF02745345. ↩︎
  4. P. Balaram, Current Science 119, no. 9 (2020), page 1432. https://www.jstor.org/stable/27139041. ↩︎

Sir MV on Education

In India, “National Engineers’ Day is celebrated every year on September 15 to honor the birth anniversary of Sir Mokshagundam Visvesvaraya, one of India’s greatest engineers”. Sir MV, as he was known, is one of the 20th-century Indians I admire. He was a forward-looking statesman who contributed immensely to building India (literally and figuratively). MV was a well-read and well-travelled person for his era, and wrote a few books and memos that are still pertinent to the current developments in India and the world.

Reconstructing India (1920)

One of his books, Reconstructing India (1920), reveals his thoughts on how and why India needs to reconstruct itself based on knowledge in science, technology and humanities. The title page is shown below, and the book is free to read online, thanks to the Internet Archive.

The book, as mentioned by MV in the preface, was written just after the First World War, and contemplates problems faced by India in light of geopolitical developments. In the 17 chapters of the book, divided into 4 parts, MV discusses specific issues faced by India, and proposes that political and administrative reforms can help India become a progressive society.

The largest part of the book is on economic reconstruction, in which he proposes contemporary methods (for the 1920s) to improve various sectors of manufacturing, including agricultural technology and communication media.

The third part of the book is on social reforms, and in there, he has a dedicated chapter on Education, which caught my attention, and I found it relevant even for today’s India.

Education, Humanities, and STEM

It is important that students of science and technology have a good exposure to some aspects of the humanities, including economics, history and philosophy. The pursuit and ability to choose good problems in science and technology critically depend on the social and economic structure in which they are practiced in universities and research institutions. MV anticipated this and highlights it as:

“Secondary and university education, though producing many able recruits for subordinate positions in the Civil Service, does not provide the men needed to carry on the work of agriculture, engineering, commerce and technology. The provision for training in economics and history is inadequate, and the study of those subjects is even discouraged. An attempt is actually made to teach economics in such a way as to render India’s emergence from a state of dependency difficult.”

Even in 2025, I would suggest that STEM students pay attention to economics, as it anchors them to understand the need and functions of a society, and therefore, their work can be calibrated accordingly. This is not to discourage open-ended research, but to understand how natural sciences are connected to the societal thoughts and needs. It gives us a broader understanding of the context, which is so important while understanding the evolution of ideas.

Comparative Education Systems

There is always a lot to learn from various societies and cultures. In order to do so, one needs comparative analysis. This helps one to choose some good elements from a society that can be emulated elsewhere. MV compares and comments on the 1900s British educational system in contrast to the German and Japanese counterparts. Note that India in the 1920s was still a British colony, and in a way, MV is critical of the system in which he himself was educated and trained. As he notes:

“Britain herself has had to pay a heavy price for her hand-to-mouth policy in regard to education. The educational chaos still existing there compares unfavourably with the great yet orderly progress made by Germany and Japan, both of which countries, after weighing and testing the educational systems of the world, absorbed the best of all.”

These were words written long before the Second World War, and give us a glimpse of how German and Japanese systems were functioning in the 1920s and had a lot to offer to the world. Of course, history took its own path, and German and Japanese society had other ideas.

Incidentally, I am writing this piece sitting in Leipzig (eastern Germany), and I am amazed by its architectural marvels that date back centuries. Indeed, German society had (and has) a lot to offer to the world. As MV indicates above, we need to absorb the best that is on offer. In doing so, we also need to reject that which is not good for any society.

Liberal Education and Financial Support

He further adds how liberal education adds value to a society, and calls not only the government but also the people to recognize the importance of financial support for education.

“Both the Government and the people must recognize that only by pursuing a liberal educational policy, and making generous financial provision for schools and colleges can they lift India out of her present low condition and ensure rapid progress.”

These words still hold good, and as a society, India has to re-emphasize modern education that helps us become not only better doctors and engineers, but also better human characters that can add value to the “modern” world.

Call to Action

In the final part of the book, MV makes a passionate appeal to the people of India, calling them to take action and move towards becoming a progressive nation:

“Do the people of India propose to profit by the lessons which world experience has to teach them, or will they be content to allow matters to drift and themselves grow weaker and poorer year by year?
This is the problem of the hour. They have to choose whether they will be educated or remain ignorant; whether they will come into closer touch with the outer world and become responsive to its influences, or remain secluded and indifferent; whether they will be organized or disunited, bold or timid, enterprising or passive ; an industrial or an agricultural nation ; rich or poor ; strong and respected, or weak and dominated by forward nations. The future is in their own hands.”

Indeed, the future is in our hands, and these words written more than 100 years ago still resonate loudly. We need more engineers like Sir MV. The reason he was so effective was that he combined thinking and doing. Importantly, the lesson we can learn from MV’s life and by reading this book, is that an open mind can grasp good ideas at any time and anywhere. Implementing those ideas is an equally important challenge, and MV was up to this in his own way. Are we, as Indians, open to this prospect and engineer our future?

Gardner’s Synthesis

Once in a while, during my research, I come across writing by scholars from other disciplines that gives me a perspective that not only helps me to grasp the complexity of learning across disciplines, but also resonates with some thoughts on education.

Howard Gardner is one such academic who works on developmental psychology and has researched extensively on cognition and education. He has written ~30 books and ~1000 articles, and blogs regularly, even at the age of 82 or so. His recent book is titled A Synthesizing Mind.

Howard Gardner is a renowned Harvard academic and, as his book describes him as follows:

“Throughout his career, Gardner has focused on human minds in general, or on the minds of particular creators and leaders. Reflecting now on his own mind, he concludes that his is a ‘synthesizing mind’—with the ability to survey experiences and data across a wide range of disciplines and perspectives. The thinkers he most admires—including historian Richard Hofstadter, biologist Charles Darwin, and literary critic Edmund Wilson—are exemplary synthesizers. Gardner contends that the synthesizing mind is particularly valuable at this time and proposes ways to cultivate a possibly unique human capacity.”

While exploring the book and the related material, I came across an interview with Howard Gardner. In there, he is conversing about the theme of the book and discusses the synthesis of thought across disciplines. One of the pertinent aspects of learning is to know how innovation can be fostered by cross-disciplinary exploration without diluting disciplinary rigour. As Gardner says:

“I am not opposed to disciplinary learning—indeed I am an enthusiastic advocate. Any person would be a fool to try to create physics or psychology or political science from the start. But if we want to have scholars or professionals who are innovative, creative—and innovation is not something that we can afford to marginalize—then they cannot and should not be slaves of any single discipline or methodology.”

As a physicist, I can relate to this thinking within my discipline, and how innovative ideas, over the ages, have emerged by bringing ideas from mathematics, engineering and biology into physics. Particularly, the combination of biology, physics and mathematics is one of the most exciting frontiers of human exploration today, and Gardner’s words apply well in this scenario.

Going beyond science, I am always intrigued and amazed by artists (especially musicians) who can create art that simultaneously draws the attention of specialists and generalists. This is not a trivial achievement, and as a scientist, I am always trying to understand how artists resonate so well with the public. Gardner, in the abovementioned interview, frames this problem by looking at the goals of science and arts, and draws a contrast that is worth noting:

“Most scholars and observers like to emphasize the similarities between the arts and the sciences, and that is fine. But the goals of the two enterprises are different. Science seeks an accurate and well supported description of the world. The arts seek to capture and convey various aspects of experience; and they have no obligation other than to capture the interest and attention of those who participate in them.

Of course, there are some individuals who excel in both science and art (Leonardo is everyone’s favorite example). But most artists—great or not—would not know their way around a scientific laboratory. And most scientists—even if they like to play the violin or to draw caricatures or to dance the tango—would not make works of art or performances that would interest others.”

I partially agree with this assessment, as I know a few scientists who are deeply involved in various forms of art (including music) and do it very well, even at the professional level. In a way, Gardner is re-emphasizing the “two cultures” debate of C.P. Snow. My own thoughts on this viewpoint are ambivalent, as I see science, arts and sports as important pursuits that cater to different facets of the human mind. Of course, when it comes to expertise, the division may matter. There is a lot more to learn about the interface of art and science, at least for me.

Anyway, Gardner is a fabulous writer, and his blogs and books are worth reading (and studying) if one is seriously interested in understanding how to synthesize thought across disciplines.

Since we are discussing synthesis of thought, which is a kind of harmony, and coming together, let me end the blog with a line from Mankuthimmana Kagga by the Kannada poet-philosopher D.V. Gundappa:

“ಎಲ್ಲರೊಳಗೊಂದಾಗು ಮಂಕುತಿಮ್ಮ” (Eladaralongodhagu manku thimma)

which loosely translates to: oh fool…be one among all (blend into world, living in harmony).

Harmony of disciplines and minds – how badly the world needs it today?

A bit of advice…to students

To paraphrase something I tell my students, especially when they are starting a research project –

There are certainly many people in the world who think better than us. But the competition reduces when it comes to the people who take their thoughts and ‘do’ something with them. Novelty of ideas is in the novelty of connections of ideas. There is always more scope for new connections of old ideas.

Generally, the game is won not in out-thinking, but in out-doing. This does not mean that doing excludes thinking. In fact, many times, doing fosters thinking.