Recently, I had the pleasure of attending a family dinner hosted by Vishal Arora, a young CEO and a friend of my son Amol. His wife’s parents were also present. Although they all come from New Delhi, they seemed to carry with them something of the city’s older culture—refinement in living, warmth in social relationships and a deep appreciation of food. We spent nearly four hours together, but the evening passed like a mild breeze.

As we were leaving, Vishal, who is also an accomplished chef by passion, presented me with a small glass jar of pickle. He invited me to choose from a remarkably wide variety that he had prepared and curated himself. I selected a dried raw-mango pickle seasoned prominently with black mustard seeds—rai in Hindi. It contained only a minimal quantity of mustard oil, used less as a heavy covering than as a medium for carrying the flavour and aroma of the spices.

Pickles are almost inseparable from Indian food. A small portion may accompany an otherwise simple meal of dal, rice, roti, curd or khichdi and transform its entire sensory character. Vishal’spassionately curated collection made me reflect upon the considerable science concealed within this ordinary-looking food. A pickle is not merely a fruit or vegetable immersed in salt, oil and spices. It is a deliberately constructed biochemical environment in which water, acidity, oxygen, microbial life, plant enzymes and aromatic molecules are brought into a controlled relationship.

The first principle of pickling is the management of water. Fresh mango, lemon, chilli, carrot, radish, amla, garlic and most other vegetables contain enough available water to support the growth of bacteria, yeast and mould. Salt begins the preservation process through osmosis. When salt surrounds the plant tissue, water moves out of the cells towards the region of higher solute concentration. This produces the familiar brine that appears even when no water has been added. The removal and binding of water reduce its availability to microorganisms. At the same time, salt penetrates the plant tissue, changing its texture and creating conditions in which some organisms are inhibited while more salt-tolerant species may survive. Studies of vegetable fermentation show that salt concentration influences not only preservation but also the composition of the microbial community, the speed of fermentation and the final flavour. Excessive salt may inhibit even desirable fermentative organisms, while insufficient salt can permit spoilage microbes to dominate.

Drying, as in the mango pickle Vishal gave me, adds another layer of protection. Sun-drying or controlled dehydration removes a substantial part of the fruit’s moisture before it enters the jar. The biochemical reactions that require available water consequently slow down. Enzymes become less active, microbial multiplication becomes difficult, and the mango acquires a concentrated sourness and a resilient, chewy texture. Drying does not sterilise the fruit, but it makes the internal environment much less favourable to rapid decomposition.

Acidity is the second great principle. Raw mangoes and lemons naturally contain organic acids, while many recipes add vinegar or lemon juice. In genuinely fermented pickles, naturally occurring lactic acid bacteria metabolise sugars present in the fruit or vegetable and convert them largely into lactic acid. As acidity increases and the pH falls, many undesirable organisms are progressively excluded. Fermentation also creates new flavour molecules, which is why a fermented pickle tastes more complex than a vegetable merely dipped in vinegar. Traditional Indian pickles have yielded diverse lactic acid bacteria, yeasts and other microorganisms, demonstrating that the pickle jar can become a small, evolving ecosystem.

It is important, however, not to call every pickle ‘fermented’. Many Indian achaar preparations are preserved primarily through a combination of drying, salt, natural or added acid, spices and oil. Their purpose is to prevent microbial activity rather than encourage a controlled fermentation. Similarly, not every homemade pickle should automatically be described as probiotic. Researchers have isolated organisms with potentially beneficial properties from certain traditionally fermented mango pickles, but such findings relate to particular strains studied under defined conditions. Whether those organisms survive storage, remain present in sufficient numbers and withstand digestion must be demonstrated before a specific pickle can legitimately be regarded as probiotic.

Mustard seeds bring a small chemical drama to the pickle jar. Black and brown mustard contain sinigrin and an enzyme called myrosinase, which are stored separately within the seed. Crushing and moistening the seed brings them together, producing allyl isothiocyanate—the volatile compound that gives mustard its sharp, nose-clearing bite. It can also inhibit some bacteria and fungi, allowing rai to contribute both flavour and modest chemical protection. Yet it is only one part of the preservation system.

Mustard oil spreads spice aromas, coats the fruit or vegetable, and helps limit contact with air and moisture. The oil layer at the top of a jar also discourages surface contamination. But oil alone cannot preserve a wet, poorly salted or insufficiently acidic pickle. Safety and stability arise from several barriers working together: salt, acidity, reduced moisture, antimicrobial spices, limited oxygen and clean handling.

The glowing colours of Indian pickles are also products of chemistry. Turmeric owes its golden hue mainly to curcumin, a pigment that can also slow some oxidation reactions. In experimental studies on pickled cucumbers, turmeric reduced the formation of volatile aldehydes associated with oxidative deterioration. Chillies add red carotenoid pigments and capsaicinoids, the compounds responsible for their heat. Fenugreek, fennel, cumin, ajwain, ginger, garlic and asafoetida contribute their own essential oils, sulphur compounds, phenolics, bitters and aromatic molecules. Together, they create a rich flavour system: acids provide sourness, sodium ions saltiness, plant compounds bitterness, mustard and chilli pungency, and numerous volatile molecules the characteristic aroma.

Time then works quietly within the jar. Salt and acid move deeper into the mango, while spice compounds pass into the oil and plant tissue. Sharp individual flavours gradually blend and soften. Some aromas fade, new ones emerge, and the texture changes as cell membranes and cell-wall materials are altered. A freshly prepared pickle and a matured one may contain exactly the same ingredients, yet taste remarkably different. Maturation is therefore not merely waiting; it is a continuing series of physical and biochemical exchanges.

India also has a smaller but notable tradition of non-vegetarian pickles, particularly those made from fish and prawns in coastal and southern regions. The basic principles remain the same—thorough cooking, moisture reduction, salt, acid, spices and oil—but the chemistry is more demanding. Protein-rich foods can support microbial growth, while animal fats are vulnerable to oxidation and may develop rancid flavours. Careful cooking, scrupulous hygiene, minimal residual moisture and proper storage are therefore essential to the pickle’s safety, quality and shelf life.

Pickles are best enjoyed in modest quantities. Their concentrated salt, acidity, oil and pungency allow even a small spoonful to stimulate the appetite, sharpen flavours and provide a lively contrast to the rest of the meal. Larger quantities, however, may add excessive salt and oil while overpowering the food they are meant to complement.

The science of pickles offers a useful lesson about tradition. Traditional practice should neither be romanticised as infallible nor dismissed as primitive simply because its practitioners did not speak in the language of pH, water activity, osmotic pressure, glucosinolates or microbial ecology. Through generations of observation, households learned that mango must be dried, jars must remain clean, moisture must be controlled, salt must be sufficient, spices must be properly prepared, and the contents must be protected from air and contamination.

Science does not diminish this inheritance. It reveals its architecture. The jar that Vishal placed in my hands contained mango, mustard, salt, oil and spices—but it also contained osmotic gradients, organic acids, enzyme reactions, volatile antimicrobials, antioxidant molecules and the memory of countless domestic experiments. What appears at the table as a modest spoonful of achaar is, in reality, a beautifully balanced exercise in biochemistry.

A recent knowledge-sharing session titled CSR Meets the Social Stock Exchange: A Journey Ahead, organised by Equippp Social Impact Technologies Limited (EQUIPPP) and held at Yashoda Hospitals, Hyderabad, recently introduced me to Dr. Bhaskar Chatterjee, a veteran IAS officer, who played a pioneering role in shaping India’s Corporate Social Responsibility framework. The gathering represented a broad cross-section of the social development ecosystem.

Hosted by Dr. Chinnababu Sunkavalli, a robotic cancer surgeon and Founder of the GRACE Cancer Foundation, the programme marked the Foundation’s listing on the Social Stock Exchange. Dr. Chinnababu is also a valued friend, and I have long admired his sustained commitment to making cancer care and early detection accessible to underserved communities. What appeared to be a specialised financial event was, in fact, an important attempt to bring the discipline, transparency and accountability of capital markets into the service of social good.

The Social Stock Exchange addresses a familiar yet persistent problem. Compassion is abundant, but often fragmented. Individuals are willing to contribute, companies have CSR commitments, and social organisations possess valuable field experience. Yet these strengths do not always converge within a credible, transparent and scalable system. Whether donated funds are ultimately deployed for genuine, measurable social good often remains uncertain—an enigma at best and a serious concern at worst.

The term ‘Social Stock Exchange’, or SSE, can initially be confusing. A conventional stock exchange enables companies to raise capital and investors to seek financial returns by buying and selling shares. Are we now proposing to buy and sell charities? “No, no—a thousand times no! Nothing could be further from the truth,” one might say, borrowing the emphatic tone of Sherlock Holmes after eliminating the impossible.

India’s Social Stock Exchange (SSE) is a relatively recent institutional innovation. The Securities and Exchange Board of India (SEBI) formally notified the regulatory framework on 25 July 2022, followed by the issuance of a detailed operational framework on 19 September 2022. The SSEoperates as a separate segment of a recognised stock exchange, enabling eligible social enterprises to register, make prescribed disclosures and raise funds within a regulated framework. Its most distinctive innovation is the Zero Coupon Zero Principal (ZCZP) instrument.

In an ordinary bond, the investor earns interest and expects the principal to be repaid at maturity. A Zero Coupon Zero Principal instrument is fundamentally different: it offers neither interest nor repayment of principal. The contributor provides funds for a clearly defined social purpose, and the ‘return’ lies entirely in the social value created. Yet the instrument is issued within a regulated framework, supported by prescribed disclosures, reporting requirements and accountability. It may therefore be understood as a donation supported by the discipline of the capital market.

Consider a cancer foundation seeking ₹2 crore to operate mobile screening units in underserved districts. Under the traditional model, it may have to approach companies, charitable trusts and individual donors separately, preparing different proposals and complying with different reporting requirements. Funding may arrive irregularly, making it difficult to sustain a programme that depends on specialised equipment, trained personnel, digital data systems, diagnostic referrals and continuous patient follow-up. Such an undertaking requires not only generosity, but also a dependable funding pipeline.

Through the Social Stock Exchange, the foundation can present the programme as a clearly defined project, specifyingthe population to be covered, the personnel and equipment required, the duration, the budget, the referral pathway and the expected outcomes. It can then raise funds by issuing ZCZP instruments for that project. A company may contribute ₹50 lakh, a philanthropic institution ₹25 lakh, and numerous smaller contributors the balance. A mission beyond the capacity of any one donor can thus be supported collectively by many.

The contributors receive neither interest nor repayment, but they gain visibility into how the funds are used, whether the stated targets are achieved, how many suspected cases are identified and referred, and what measurable difference the programme makes. The exchange neither operates the screening units nor guarantees their success. Its role is to provide a transparent and regulated platform that connectsthose who possess resources  with organisations that have the experience and capacity to address social needs.

Corporate Social Responsibility (CSR) enters the picture here. Under Section 135 of the Companies Act, 2013, qualifying companies are required to spend at least two per cent of their average net profits of the preceding three financial years on eligible CSR activities. On 27 May 2026, the Ministry of Corporate Affairs expanded this framework by recognising subscriptions to eligible ZCZP instruments listed on the Social Stock Exchange as permissible CSR expenditure. Companies may use this route for up to ten per cent of their total CSR expenditure in a financial year. The SSE does not replace conventional CSR; it provides an additional regulated channel through which companies can join other contributors in supporting clearly defined social projects.

The value of the SSE lies in four interconnected strengths: trust, visibility, aggregation and accountability. Registration and standardised disclosures establish a common threshold of transparency, allowing a credible social organisation—even one working in a remote district—to reach a much wider community of contributors.

Aggregation can be equally transformative. A public health, education, nutrition or livelihood programme may be beyond the capacity of any single contributor, yet entirely feasible when hundreds or thousands participate. Scattered streams of generosity can thus converge into a river capable of sustaininga major social mission.

Above all, the SSE shifts attention from expenditure to impact. Traditional philanthropy may sometimes measure success by the amount spent, the activities conducted or the number of people reached. The more demanding question is: What actually changed in the lives of the intended beneficiaries?

The central question is not how much money was spent, but what changed as a result. A training programme should be judged by whether participants acquired useful skills and improved their livelihoods. A cancer screening programme should track abnormal findings, referrals, confirmed diagnoses, treatment linkages and, ultimately, lives extended or saved. Data must show not merely that an activity took place, but whether it produced meaningful change. Digital systems and artificial intelligence (AI) can strengthen such accountability at scale.

The SSE should not, however, be romanticised. Listing on the exchange cannot guarantee social transformation. Smaller organisations may struggle with documentation and compliance, and not every valuable outcome can be reduced to a number. Dignity, confidence, solidarity and freedom from fear resist easy measurement. Funding must not therefore flow only to causes whose results are easiest to quantify.

People seek not only wealth, but also meaning. Wealth finds its deepest purpose when it creates a legacy that endures beyond one lifetime. The Social Stock Exchange offers a way to convert generosity into sustained social action by preserving purpose, measuring outcomes and building institutions that endure.

The listing of organisations such as Grace Cancer Foundation is therefore more than a financial milestone. It points to a new social compact in which corporations provide resources, civilsociety organisations contribute field experience, regulators foster trust and citizens participate in measurable public good. The SSE does not put a price on compassion. It gives compassion a platform, a structure and a means of demonstrating what it has achieved.

Grace Cancer Foundation’s dream of deploying 1,000 mobile screening buses across India’s hinterlands can now move closer to reality. Properly channelled, compassion can flow like rain across the countryside, reaching every field rather than only those with their own source of water.

Hats off to these aggregators of compassion. I have encountered few ideas in the social sector that appear so credible, hopeful and potentially transformative. When compassion is aggregated, organised and made accountable, it ceases to be an occasional act of charity and becomes a sustained force for social change.

Recently, my son Amol brought me Ceylon tea from Sri Lanka, and my biomedical engineering pupil, Deepti Sai Prasad, presented me with an elegant Queen Elizabeth box of tea bags she brought from London. They could hardly have chosen a gift that would have delighted me more.

I love tea. Whenever I am asked, “Tea or coffee?”, my answer comes without a moment’s hesitation: “Tea.”

I grew up drinking tea. In my native Meerut, tea is not merely brewed; it is almost cooked. Strong black tea leaves—typically the robust Assam variety—are boiled vigorously with milk and generous quantities of sugar, with two teaspoons per cup being the norm. Ginger and cardamom are added as the mixture simmers, allowing their flavours to infuse the tea. The entire house becomes fragrant. Tea is not only consumed; it is announced.

Years later, after moving to Hyderabad, I encountered another marvel—Irani tea. It belongs to an altogether different tradition. A robust black tea blend, usually rich in Assam CTC leaves, is brewed into a concentrated decoction, while the milk is simmered separately for hours, developing a natural sweetness through gentle caramelisation. The two meet only at the moment of serving. The result is velvety, aromatic, and almost meditative—a cup that rewards patience as much as craftsmanship. A plate of Osmania biscuits, lightly dipped into the tea before each bite, completes the experience. It feels less like drinking tea than performing a small daily ritual of contentment.

That cup also awakened my curiosity. Every beverage carries not only a flavour but a civilisation. Behind its aroma lie journeys across continents, encounters between cultures, and centuries of commerce, conquest and adaptation. The more I reflected on tea, the more I realised that it is not merely a drink but one of history’s most remarkable travellers.

There is a great deal of history behind tea. Tea never grew naturally in England; the climate required for the evergreen shrub simply does not exist there. Tea is native to China, where it had been cultivated and cherished for centuries before Europe discovered its allure. Yet England became its most influential global promoter because it understood something larger than agriculture: a product can be culturally appropriated by those who control its trade, shape its image, and weave it into the fabric of everyday life.

The British East India Company played a decisive role in transforming tea from a Chinese luxury into a global commodity. It first imported tea on a vast scale and, when dependence on China became commercially inconvenient, encouraged the development of tea plantations in Assam, Darjeeling, the Nilgiris and Sri Lanka (formerly Ceylon). Yet Britain’s greatest achievement lay not in growing tea but in giving it a distinctive cultural identity. Through afternoon tea, fine porcelain, etiquette, conversation, and the rituals of domestic hospitality, tea came to symbolise refinement and social order. Carried by empire, commerce and literature, this distinctly British way of drinking tea spread across much of the world.

The English transformed tea from an agricultural product into a social institution. They refined not only its trade but also its preparation. Though the British did not invent tea drinking; they transformed it into a distinctive social ritual. Water is brought almost to the boil, loose leaves are allowed to infuse in a teapot, and warm milk is poured into the cup first—a practice said to have protected delicate porcelain from cracking—before adding the strained tea. The ritual possesses an elegance born of centuries of repetition.

Tea punctuates the English day. It begins with the first cup on waking and continues through breakfast, mid-morning, afternoon tea with sandwiches or scones, and the traditional late-afternoon gathering, usually at five o’clock. High tea, despite its aristocratic reputation, was originally the hearty evening meal of the working classes, served at a high dining table with substantial fare and tea. For many households, the day ends with yet another comforting cup.

The world of tea has its own aristocracy. Earl Grey, delicately scented with bergamot, is perhaps the most celebrated blend, while English Breakfast draws its strength from teas grown in Assam, Kenya and Sri Lanka. Darjeeling, cultivated on the mist-covered slopes of the Himalayas, is often called the ‘Champagne of teas’ for its floral aroma and muscatel notes. Ceylon teas are bright and brisk, Kenyan teas add colour and body, and Assam provides the rich malty depth that anchors many of the world’s favourite blends.

Exploring these varieties inevitably raises another question. If tea possesses such extraordinary diversity, why do so many people still reach instinctively for coffee? The two beverages occupy neighbouring places in our daily lives, yet they arrive at their flavours by remarkably different paths. Tea reveals the character of a leaf; coffee is transformed by fire. Hundreds of volatile aromatic compounds are formed as coffee beans are roasted at high temperatures, producing flavours ranging from chocolate and caramel to toasted nuts and smoke.

A fresh tea leaf contains several thousand naturally occurring chemical compounds. During withering, rolling, oxidation (often called fermentation in the tea trade), and drying, these compounds rearrange themselves into an astonishing spectrum of aromas and flavours. Scientists have identified well over 600 volatile compounds that contribute to tea’s aroma, while thousands of other compounds influence its colour, taste, mouthfeel and potential health benefits. Polyphenols, such as catechins and theaflavins, contribute to tea’s antioxidant activity, while amino acids—especially L-theanine—produce a gentle sweetness and promote an unusual state of relaxed alertness.

Both beverages contain caffeine, and the caffeine molecule is chemically identical whether it comes from tea or coffee. The difference lies not in the molecule but in its company. A typical cup of tea contains less caffeine than a cup of coffee and also provides L-theanine, an amino acid found almost exclusively in tea. Together with tea’s naturally occurring polyphenols, L-theanine appears to modulate the subjective effects of caffeine, promoting a state of calm alertness rather than intense stimulation. Many tea drinkers, therefore, experience a steadier, more sustained wakefulness, without the pronounced surge—and, for some, the subsequent slump—that often follows a strong cup of coffee. Tea does not so much propel the mind as gently prepare it: awake, attentive and yet unhurried. Perhaps that is why the act of drinking tea so easily becomes a small ceremony of reflection, opening a quiet space in which ordinary things begin to reveal their depth.

Reading Virginia Woolf taught me that the deepest truths often arrive disguised as the smallest moments. A room, a window, a flower in a vase, the quiet ceremony of making tea—such things do not interrupt life; they are life. I often think of her while waiting for tea leaves to unfurl in hot water. Their fragrance cannot be hurried; it asks only for stillness. Then, almost imperceptibly, the mind loosens its grip on the day’s clamour. Thoughts that had been jostling for attention drift apart like clouds after rain, and an inward silence begins to gather. My own ritual is equally simple. Every morning around seven, and again at four in the afternoon, I prepare a cup of strong black tea, briefly boiling the leaves in water while warming the milk separately before the two meet in the cup. I have long since abandoned sugar. If a guest happens to arrive—which is less frequent these days—I gladly brew another pot. For all its chemistry and ceremony, tea remains, above all, a companion: to thought when one is alone, and to conversation when one is not.

Perhaps that is why tea is more than a beverage; it is a way of inhabiting time. A cup demands neither urgency nor distraction. The warmth against the palms, the rising fragrance, the deepening colour, the first sip, and the lingering aftertaste gently draw the wandering mind back to the present moment. One cannot hurry good tea; it quietly teaches patience. For a few unhurried minutes, yesterday’s regrets and tomorrow’s anxieties surrender their hold. The mind returns to the only place where life is ever lived—the present. If there is any philosophy in my daily cup, it is simply this: happiness rarely arrives with fanfare. More often, it unfolds quietly, like the fragrance of freshly brewed tea.

I was invited to address nearly 500 students during their first week at GITAM University in Hyderabad. I was hosted by Dr. Motahar Reza, Director of the GITAM School of Science. A native of Murshidabad in West Bengal, Dr. Reza trained at IIT Kharagpur, worked across computational fluid mechanics, machine learning and data science, and joined GITAM in 2020. His journey from fluid dynamics to artificial intelligence made him an ideal host for a conversation about how learning itself is changing.

GITAM began in Visakhapatnam in 1980 as the Gandhi Institute of Technology and Management. The acronym has since become an educational brand, with campuses in Visakhapatnam, Hyderabad and Bengaluru. This year, the university is home to 28,000 full-time students—young, energetic, curious and ambitious. Yet scale alone does not define a university. What struck me was its carefully curated environment: orderly without being oppressive, ambitious without appearing anxious, and imbued with the Tagorean aspiration, ‘Where the mind is without fear, and the head is held high.’

I chose ‘The Three Habits in the AI Era’ as the subject of my address. My message was simple: do not fear artificial intelligence; form habits that help it amplify your intelligence. The three habits were: Ask, Speak and Write.

Ask AI one meaningful question every day. Once a week, select one idea that arises from those questions and speak about it for three minutes. Let AI transcribe the recording and polish the language. Then study the polished version: What became clearer? Did the machine improve the grammar, or alter the thought? Finally, write the improved version by hand in a dated notebook.

Asking cultivates curiosity; speaking reveals gaps in thought; writing consolidates learning and strengthens memory. The student also learns to inspect rather than passively accept an AI output. Sustained through four years, the notebook can become a personal intellectual autobiography—perhaps a 200-page book authored before graduation.

The students received the idea warmly. Afterwards, Dr. Reza hosted lunch with faculty colleagues and Dr. S. Chandrasekhar, one of the finest green chemists of our time and a former Secretary of the Government of India’s Department of Science and Technology. Despite his eminence, he possesses the warmth and humility of a true scholar. A university is revealed as much by conversations around a table as by lectures in an auditorium.

During lunch, my thoughts returned to mathematics. Mathematics has always fascinated me, although I could never claim mastery of it. During my master’s programme at G. B. Pant University, I chose Tensor Methods in Continuum Mechanics as an elective and only just secured a B grade. Yet the course gave me a sufficient grounding in matrix algebra to prove invaluable later in operational research and mechanical vibrations. During discussions at DRDL on six-degree-of-freedom modelling—the three translational and three rotational motions of a missile—I found myself unexpectedly confident and vocal.

This experience taught me that mathematical education cannot be judged only by marks secured at the moment of instruction. A concept imperfectly grasped today may become the instrument through which one understands a real-life system years later. Education deposits structures in the mind; application activates them.

I therefore asked Dr. Reza, “How do young students see mathematics today, and how is AI affecting its teaching and learning? Mathematics has always required a heady combination of rigour and intuition. Does AI strengthen that combination—or quietly undermine it?”

The answer lies not in the intelligence of the machine, but in the wisdom with which we choose to wield it.

Mathematics contains four interacting layers. The conceptual layer concerns meaning: What is a derivative, a vector or an eigenvalue? The procedural layer concerns operations such as differentiation and integration. The representational layer connects equations with graphs, tables, simulations and physical phenomena. The metacognitive layer concerns thinking about one’s own thinking. It asks: Why did I choose this method? Where could it fail? Is the answer logically, dimensionally and physically plausible?

Traditional classrooms often overemphasise procedure because it is easiest to demonstrate and examine. AI can perform many procedures rapidly. That does not make mathematics obsolete; it reveals that procedure was never the whole of mathematics. Done till here

A large language model is most useful at the conceptual and linguistic interface. It can explain an idea through an analogy, a graph, a physical example or simpler language. It can help students whose English is functional rather than fluent, generate graded examples, compare alternative methods, and ask Socratic questions. A computer algebra system manipulates symbols; a numerical solver approximates solutions that resist closed-form expression; a visualisation engine reveals parameter sensitivity; and a proof assistant verifies that deductions follow from stated axioms. Mathematical literacy now includes knowing which technology to trust for which task.

This is a neuro-symbolic partnership. Neural models excel at pattern recognition, language and analogy; symbolic systems are stronger at exact manipulation and formal verification. The human must still choose the assumptions, formulate the model, interpret the results and decide whether the answer is relevant.

The distinction matters because a language model generates plausible sequences, while mathematics demands valid relationships. A convincing explanation is not a mathematical proof. A confident derivation may contain a sign error, an unstated assumption or an invalid cancellation. One recent evaluation found that although 90 per cent of AI tutoring dialogues appeared instructionally strong, only just over half were mathematically correct throughout. OECD analyses likewise warn that generative AI may improve task performance without producing genuine learning when students outsource the intellectual work.

The pedagogical principle should therefore be:

AI may assist the struggle, but it must not abolish productive struggle.

A sound mathematics lesson in the AI era might follow five stages: Conjecture – Attempt – Dialogue – Verification – Reconstruction.

First, the student predicts what should happen. Second, the student attempts the problem unaided. Third, AI offers a hint, questions an assumption, presents an alternative representation or constructs a counterexample—without immediately supplying the answer. Fourth, the result is checked through substitution, limiting cases, dimensional analysis, numerical testing or formal proof. Fifth, the student reconstructs the argument in their own words and, where appropriate, by hand.

This is an AI sandwich: human effort before AI, critical interaction with AI, and human synthesis afterwards.

Teachers therefore cease to be mere transmitters of worked examples. They become designers of mathematical encounters, diagnosticians of misconceptions and guardians of epistemic standards. Instead of asking only whether the student obtained the answer, they ask whether the student can explain the method, identify the weakest step, test a boundary case, distinguish an exact result from an approximation, and justify the conclusion.

Assessment should evolve accordingly. Students can critique an AI-generated solution, locate a deliberately inserted error, compare methods, defend their assumptions orally, annotate a proof or maintain a handwritten reasoning journal. The trace of thought becomes more important than the final answer.

My three habits fit mathematics particularly well. Ask becomes the habit of forming a precise mathematical question. Speak becomes the ability to articulate a chain of reasoning and hear where it breaks. Write becomes the disciplined conversion of intuition into symbols, definitions and proof. AI can accompany all three, but it cannot assume responsibility for any of them.

The real danger is not that AI will make students weak at mathematics. It is that institutions will continue teaching mathematics as the production of answers when machines have become excellent answer-producing partners. The opportunity is to restore mathematics to its deeper purpose: modelling reality, detecting structure, reasoning under uncertainty and learning to recognise when one is wrong.

The classroom board will not disappear. Nor will the notebook. They will stand beside the bot. The university’s task is to ensure that the machine supplies speed and range while the human being retains curiosity, judgement and the courage to ask:

“Is this merely a convincing answer—or is it mathematically true?”

That question stayed with me as I made my way home. In my mind’s eye, Dr. Reza’s infectious smile returned, seeming to carry the simplest possible reply:

“It can be both.”

My blog, Solidified Air, received an unexpectedly enthusiastic response. Readers remarked that it had drawn attention to something that everyone sees every day but very few consciously notice. Air surrounds us so completely that we almost forget it exists. Yet compressed air becomes steel-cutting power, lifts aircraft into the sky, drives industries, and sustains every breath we take.

The arrival of the first monsoon showers each year evokes a similar feeling. We celebrate the rain and welcome the relief from summer’s relentless heat. Yet very few of us pause to ask an astonishing scientific question. Every year, billions of tonnes of water leave the oceans, travel thousands of kilometres as clouds, and finally descend upon the Indian subcontinent. Why does that enormous mass of water not simply fall back into the sea from which it arose? Why does it remain suspended in the sky throughout its long journey? And what finally persuades it to release itself over land – from Kerala to the Gangetic plains?

The word monsoon itself tells a fascinating story. Derived from the Arabic word mausim, meaning ‘season’, it later came to signify the seasonal reversal of winds observed by Arab sailors navigating the Indian Ocean. For centuries, these predictable changes in wind direction determined the rhythm of maritime trade between Arabia, East Africa, India and Southeast Asia. Long before satellites or weather models existed, navigators understood that the winds themselves possessed a seasonal memory.

Every summer, the Indian subcontinent undergoes one of the most intense seasonal land-heating events anywhere on Earth. Land responds to solar heating far more rapidly than the oceans. While the vast Indian Ocean warms only gradually because water has an exceptionally high heat capacity, the Indian landmass heats quickly under the tropical sun. During May and June, temperatures across northwestern India and adjoining regions frequently exceed 45°C.

As the land becomes intensely hot, the air above it warms as well. Warm air expands, becomes less dense, and rises, creating a broad region of relatively low atmospheric pressure across much of the subcontinent. Nature abhors imbalance. Air naturally moves from regions of higher pressure to regions of lower pressure in an attempt to restore equilibrium.

South of the equator, over the southern Indian Ocean, relatively cooler and denser air occupies a region of higher pressure. This air begins its long journey northwards towards the low-pressure system over India. Because the Earth rotates continuously, the moving air does not travel in a straight line. Instead, it is deflected by the Coriolis effect. After crossing the Equator into the Northern Hemisphere, the winds are deflected to the right, causing them to curve and eventually approach the Indian subcontinent as the moisture-laden south-westerly winds that define the Indian summer monsoon.

The scale of this transport is almost beyond imagination. Every day during the peak monsoon season, atmospheric rivers carry quantities of water comparable to the discharge of many of the world’s largest rivers combined. Yet almost all this water remains suspended high above the ocean without falling back into it. This is where the real wonder begins.

The clouds that eventually darken the skies over Kerala, Hyderabad, Mumbai, Kolkata, or Delhi are not bags filled with water waiting to burst. Nor are they simply floating masses of liquid water. They are extraordinarily delicate physical systems in which microscopic droplets, ice crystals, water vapour, temperature, pressure and atmospheric motion exist in a state of dynamic balance. Each cloud is a masterpiece of fluid physics.

The first misconception we must set aside is that clouds are collections of large water droplets floating through the sky. If that were true, every cloud would empty itself almost immediately under the pull of gravity.

Instead, a cloud is an astonishingly delicate suspension of unimaginably tiny droplets of water, each typically only about 10 to 20 micrometres in diameter. To appreciate how small that is, consider a human hair. A single strand of hair is roughly 70 micrometres thick. Most cloud droplets are, therefore, only about one-fifth to one-sixth the diameter of a human hair. Millions of them could comfortably fit inside a teaspoon.

Because each droplet is so extraordinarily small, gravity has surprisingly little influence upon it. The downward pull of gravity exists, of course, but the droplet is so light that the resistance offered by the surrounding air almost completely balances its weight. Instead of falling like raindrops, these microscopic droplets behave more like tiny specks of dust floating in a sunbeam. The slightest upward movement of air is sufficient to keep them suspended.

This is the first secret behind the long journey of clouds. They are not carrying rivers through the sky. They are carrying an invisible multitude of microscopic droplets so small that the atmosphere itself can support them. But where do these droplets come from?

Every droplet needs a tiny foundation upon which to form. The atmosphere is never perfectly clean. Floating everywhere are microscopic particles of sea salt, desert dust, pollen grains, industrial aerosols, and so on. These minute particles, known as condensation nuclei, provide the tiny surfaces on which water vapour condenses, allowing droplets to form. They serve as nature’s scaffolding for billions of cloud droplets. But if clouds contain such enormous quantities of water, why do they not gradually become heavier until gravity inevitably wins?

The atmosphere is remarkable for its dynamism. A cloud is an ever-changing physical system. Every second, billions of droplets are formed while billions of others disappear. Water molecules continuously pass between the vapour and liquid states. The cloud that appears unchanged to our eyes is, in reality, undergoing ceaseless renewal.

The journey from the Arabian Sea to Hyderabad, or from the Bay of Bengal to the Himalayas, is, therefore, not undertaken by a fixed collection of water droplets. The cloud is continually rebuilding itself as it travels. The cloud survives because the overall balance remains remarkably stable. This delicate equilibrium can persist for hundreds or even thousands of kilometres. Only when the droplets begin to grow beyond their microscopic size does gravity slowly reclaim its authority.

However, one question still remains: why does so much of this rain fall only after the clouds reach India?

Stretching like a giant wall roughly parallel to India’s western coast stand the Western Ghats. Moist air approaching these mountains has only one option—it must climb. As the air is forced upwards, it expands and cools rapidly. Condensation accelerates. Droplets grow. Clouds thicken. Rain begins.

But the story does not end there. After shedding much of their moisture on the windward slopes, the monsoon winds continue their journey across the Indian peninsula. Here, the great mountain systems of central India—the Satpura and Vindhya ranges, together with the Maikal Hills and the hills of Odisha—act not only as barriers but also as guides and sculptors of the monsoon. Each encounter with rising terrain cools the air anew, triggering fresh condensation and another burst of rainfall. Finally, the Himalayas prevent moist tropical air from escaping into Central Asia and force the remaining moisture to rise, cool, condense, and fall over northern India.

India’s rainfall is a magnificent collaboration between the seas, the winds, and the mountains. The seas, warmed by the Sun’s energy, continuously supply vast quantities of water through evaporation. The monsoon winds carry this invisible water vapour across the subcontinent. When these moisture-laden winds encounter mountain ranges, they are forced to rise, cool, and condense, producing rain. This remarkable partnership gives rise to some of the wettest places on Earth, including Mawsynram and Cherrapunji in the Khasi Hills, while equally nourishing the forests of the Western Ghats, the tea gardens of Agumbe, and countless rivers, fields and villages across the country. What an extraordinary interplay of the seas, the winds, and the mountains! The more we understand, the more extraordinary the ordinary becomes.