Blogs

1. The Fundamental Theorem of Algebra

   It once fell to my lot to teach Mathematics to first-year students at an Australian university. It is often said that you truly learn only when you start to teach. And so it was in my case.

   This blog is written for high school and first year students of mathematics whose primary interest is in the application of what they learn. The Fundamental Theorem of Algebra is usually glossed over with a passing reference, and without even a plausibility argument. Because of the theorem’s importance, I strike a balance here between being too rigorous and too lax, so that there is sufficient tension to sustain student interest, and sufficient detail to ensure that the proof is persuasive.

2. Biocontrol of Tropical Fire Ants

   The tropical fire ant, Solenopsis geminata, has been a destructive marauder in my garden for more than a decade. In the search for an organic biocontrol, I enlisted the help of AI. It suggested the remedy of drenching the soil near ant mounds with the solution of a fungus called Beauveria bassiana that would selectively kill the topical fire ants, but leave other insects, fish, and humans unscathed. This resulted in a temporary decrease in ant numbers at the place of drenching. But the ant colony was not eradicated. It merely relocated to where the treatment was not applied. The measure was palliative rather than curative. A truly long-term, reliable, and repeatable organic solution to this problem awaits future research.

3. My Brief Experience with AI

   My initial foray into AI was in 2025. I wanted it to suggest suitable software to plot the curves I needed for my blogs. That was when I first became aware of the strengths and weaknesses both of AI in general and of different AIs in particular.

   In this blog, I chronicle my adventures in AI-land. I recount in detail five specific examples in the use of AI, and the experiences that unfolded. Later, I distil the generic lessons that I have learned so that other users might benefit. I conclude by quoting a paper that points out the dangers of emotional entanglement with an AI, especially by the young.

4. The Dearness Code

   What causes an object or person to be dear? This question is discussed to finality in this blog that portrays the famous dialogue between the Vedic Ṛṣi Yājñavalkya and his wife Maitreyī, with some ideas thrown in from physics as we know it today.

5. YouTube and the Trust Deficit

   YouTube is awash with slick videos that offer seemingly authoritative advice on health, wealth, current affairs, and many other aspects of life. But if you were to look behind the curtain, all you would see is smoke and mirrors—not human experts. There is an uncanny resemblance to the revelatory scene in the movie, The Wizard of Oz. This is especially annoying and alarming, and is typical of the devaluation of truth that we are currently experiencing. And I think that AI, in collusion with human frailty and fallibility, has facilitated this trust deficit.

6. Food as Medicine: Purple and Orange Sweet Potatoes

   The sweet potato, Ipomoea batatas (L.) Lam., is a humble and shy vegetable—a root tuber that hides itself by growing underground.

   Although its name has the adjective sweet in it, the Glycemic Index (GI) of sweet potatoes is lower than that of the normal potato, when cooked the same way. A lower glycemic index means blood sugar rises more slowly after eating, which is important for diabetics and for weight watchers. The resistant starch and fibre in sweet potatoes also feed gut-friendly bacteria and promote gut health.

   The anthocyanins in purple sweet potatoes act as antioxidants and boost overall health by neutralizing free radicals and preventing oxidative stress. It helps in preventing degenerative conditions like diabetes, heart disease, cancer, dementia, etc.

   The orange pigment in orange sweet potatoes, beta-carotene, is a precursor from which the body makes the fat-soluble Vitamin A, which promotes night vision, eye moisture, and overall immune function.

   Through this blog, I wish to disseminate the benefits of purple and orange sweet potatoes so that local farmers feel sufficiently motivated to cultivate and sell them at produce markets. If the buying public see the new cultivars and are inspired to try them out, we would be on the cusp of a revolution to improve overall public health through health-promoting food.

7. On Binet’s Formula

   The formula of Binet for the Fibonacci sequence for the n^th Fibonacci number presents an excellent example to showcase the same mathematical result, arrived at from quite different approaches and perspectives, demonstrating the self-consistency of mathematics.

8. Demystifying Fractional Powers

   It is incredible how a simple question about the square root symbol and an exploration of fractional exponentials can lead us through a spellbinding journey of discovery, and ultimately open the vistas of advanced mathematics. Who would have guessed that the cube root of \(-8\) would have one real and two complex roots? Or that \(z^6 - 1\) would have roots that are multiples of \(\omega\) and \(\omega^5\)? Mathematics can be engrossing and endlessly fascinating as long as we are bold and patient enough to engage with it. The rewards are enormous and often totally unexpected.

9. Gnuplot for the Plotless

   In the recent past, however painful it was, I had adopted a solution using TikZ-PDF, or Matplotlib, or Typst, without giving gnuplot any thought. Now I would venture first with gnuplot. Its syntax is uncluttered and unentangled. It may be easily tested interactively. Changes may be made and checked rapidly, to allow for a faster solution, without compromising on the quality of the output. Yes, gnuplot has come a long way. It is still recognizable. Just as powerful as before, if not more. But it has far more sheen than when I last met it. Power and Beauty have met at last!

10. A Tetrad of Captivating Problems

    This blog is the sandwich filling between two blog-slices: The Exponential and Logarithmic Functions and e Unleashed. It consists of a tetrad of captivating problems that are related to exponents, which assumed centre stage after Euler showcased the number e and explored its facets in the eighteenth century.