Prime Minister Narendra Modi on Sunday said wars are fought by attacking economies, urging protection for India’s banking system from cyber terrorists. He said, “We need modern infrastructure and a skilled workforce to meet these challenges effectively.” The PM spoke while inaugurating the RBI Data Centre and Cybersecurity Training Institute.
Wars target economies, must protect India’s banking from cyber terror: PM
Syllabus:
Preliminary Examination: Current events of national and international importance
Mains Examination: General Studies III: Basics of Cyber Security
What’s the ongoing story: Prime Minister Narendra Modi on Sunday said wars are fought not only conventionally but also by attacking economies, as he emphasised the need to protect India’s banking system and digital infrastructure from ‘cyber terrorists’ and emerging challenges.
Key Points to Ponder:
• What are the recent cyber-attacks on Indian banks?
• What did you understood by the statement “modern wars are increasingly fought by targeting economies rather than through conventional weapons alone”?
• Why has the protection of India’s banking system against cybercriminals and cyberterrorists become a national priority?
• What is Cyberterrorism and cyberterrorists?
• Why did the Prime Minister Narendra Modi emphasise the need for modern infrastructure, updated training systems and skilled human resources to address emerging cyber threats?
• How does the expansion of formal banking services to small entrepreneurs, traditional artisans, street vendors and workers in the unorganised sector reflect the changing reach of India’s banking system?
• How the Reserve Bank of India’s new data centre can contribute to the security, efficiency and reliability of India’s banking and payment infrastructure?
Key Takeaways:
• Amid growing concerns over cyber fraud and digital threats as India’s digital payments ecosystem expands, Modi, while addressing a gathering in Bhubaneswar while inaugurating the RBI Data Centre and Cybersecurity Training Institute, said: “We all know that wars today are not fought with weapons alone. A country can also be weakened by attacking its economy. As India grows stronger economically, safeguarding our banking system against cybercriminals and cyberterrorists has become equally essential”.
• On emerging cybersecurity challenges, Modi said the nature of cyber threats was evolving rapidly and could not be tackled with outdated systems, traditional training methods and old training tools. “We need modern infrastructure and a skilled workforce to meet these challenges effectively. The role of the new cybersecurity training institute is significant in this context,” he added.
Do You Know:
According to UNODC,
• Information and communication technology (ICT) can be used to facilitate the commission of terrorist-related offences (a form of cyber-enabled terrorism) or can be the target of terrorists (a form of cyber-dependent terrorism).
• Specifically, ICT can be used to promote, support, facilitate, and/or engage in acts of terrorism. Particularly, the Internet can be used for terrorist purposes such as the spreading of “propaganda (including recruitment, radicalization and incitement to terrorism); [terrorist] financing; [terrorist] training; planning [of terrorist attacks] (including through secret communication and open-source information); execution [of terrorist attacks]; and cyberattacks”.
• The term cyberterrorism has been applied by some to describe the use of the Internet for terrorist purposes.
Other Important Articles Covering the same topic:
📍As AI poses threat to critical financial systems, how regulators are stepping up vigil
Previous year UPSC Prelims Question Covering similar theme:
1) The terms ‘WannaCry, Petya and Eternal Blue’ sometimes mentioned in the news recently are related to (UPSC, CSE, 2018)
(a) Exoplanets
(b) Cryptocurrency
(c) Cyber attacks
(d) Mini satellites
Politics
Creamy layer row: ‘Centre awaiting SC directions for CSE service allocation’
Syllabus:
Preliminary Examination: Indian Polity and Governance-Constitution, Political System, Panchayati Raj, Public Policy, Rights Issues, etc.
Mains Examination: General Studies II: Welfare schemes for vulnerable sections of the population by the Centre and States and the performance of these schemes; mechanisms, laws, institutions and Bodies constituted for the protection and betterment of these vulnerable sections.
What’s the ongoing story:The Foundation Course for every batch of civil servants recruited through the Civil Services Examination (CSE), conducted by the Union Public Service Commission (UPSC) every year, usually begins at the Lal Bahadur Shastri National Academy of Administration (LBSNAA) in Mussoorie by late August or early September, and concludes in December.
Key Points to Ponder:
• What is creamy layer?
• Why has the service allocation of 958 candidates who cleared the Civil Services Examination 2025 been delayed?
• What is the Supreme Court’s March 11, 2026 judgment?
• Who will benefit from the Supreme Court ruling?
• Why did the Supreme Court hold that parental salary income alone cannot be the sole criterion for determining whether an OBC candidate belongs to the creamy layer?
• Why was the creamy layer introduced?
• What are the criterion for deciding creamy layer for OBC reservation?
• What was the SC ruling in the Indra Sawhney v. Union of India (1992)?
• How Article 14, 15, and 16 of the Constitution indirectly associated with affirmative action?
• What are the DoPT OM of 1993 and the clarification of October 2004?
• What was the impact of the DoPT clarification?
Key Takeaways:
• Its commencement this year, for the 958 candidates who cleared CSE 2025, was listed in the LBSNAA’s calendar as the last week of August. However, the training course has still not begun.
• This is the first time since Independence that the Foundation Course has been stalled, leaving an entire batch of future administrators in the cold.
• After the Supreme Court’s March 11, 2026 judgment on the determination of “equivalence” with regard to the Other Backward Classes (OBC) creamy layer, the Centre moved the apex court on August 24 — barely three weeks before the six-month deadline for the implementation of the court’s order was to expire — seeking certain clarifications.
• On September 24, the top court reserved its order on the Centre’s plea. Consequently, the service allocation and the Foundation Course for the new recruits have been suspended.
Do You Know:
• On March 11 this year, hearing an appeal by one of the candidates, Rohith Nathan, a Division Bench of Justices P S Narasimha and R Mahadevan ruled that income cannot be the sole criterion for determining the creamy layer among OBCs. The Court said: “The object of excluding the creamy layer is… not to create artificial distinctions between equally placed members of the same social class… unequal treatment of similarly placed OBC candidates would not only be legally erroneous but constitutionally impermissible.”
• It further held that treating the children of those employed in PSUs or private employment as excluded from reservation benefits solely on the basis of salary income, without reference to the nature of their posts (Group A, B, C or D), “would certainly lead to hostile discrimination between parties who are similarly placed and would amount to equals being treated unequally, thereby attracting the rigour of the equality doctrine under Articles 14, 15 and 16”.
• The Centre has argued that SC’s March 11 judgment came five days after the final result of CSE-2025 was declared. Delay in finalisation of the category-wise merit and allocation list would have a cascading effect — from training to seniority and pay fixation of the incoming batch.
• The matter traces its origins to a DoPT letter of October 14, 2004, clarifying an Official Memorandum (OM) of September 1993 on the creamy layer criterion for OBCs. The 1993 OM had excluded income from salary and agricultural sources from the income/wealth test used to determine creamy layer status. However, the 2004 clarification said the salary income of employees in public sector undertakings (PSUs) and the private sector would be a criterion.
Other Important Articles Covering the same topic:
📍SC verdict on parental income as OBC creamy layer criterion: What has court said, what changes
Previous year UPSC Mains Question Covering similar theme:
📍Whether the National Commission for Scheduled Castes (NCSC) can enforce the implementation of constitutional reservation for the Scheduled Castes in the religious minority institutions? Examine. (UPSC CSE 2018)
The Ideas Page
We need to address the issue of soil health. Four steps can improve the situation
Syllabus:
Preliminary Examination: Economic and Social Development
Mains Examination: General Studies III: Indian Economy and issues relating to planning, mobilization, of resources, growth, development and employment.
What’s the ongoing story: Ashok Gulati, Ritika Juneja Writes-The subsidy budget for 2026-27 is Rs 1.71 lakh crore. The disruption in the Strait of Hormuz could push the subsidy bill to between Rs 2.5 lakh crore and Rs 3 lakh crore
Key Points to Ponder:
• What is the health of the soil?
• What is meant by balanced nutrient application in agriculture?
• What is the Nutrient-Based Subsidy (NBS) scheme, introduced in 2010?
• Why Nutrient-Based Subsidy (NBS) scheme failed to correct the imbalance in the use of nitrogen (N), phosphorus (P) and potassium (K)?
• What does the article reveal about the changes in nitrogen, phosphorus and potassium use in India between 2009–10 and 2024–25?
• Soil health and its relationship with food security and human health-connect the dots
• How tailored soil nutrition strategies can help India move from food security to nutrient security?
• Know the role of the Soil Health Card Scheme in transforming India’s agricultural and health landscape.
• How a paradigm shift in fertiliser management can support sustainable agriculture, soil health, and ecosystem resilience in the context of the Green Revolution’s legacy.
• Compare Indian soil-health challenges with global initiatives in crop and human nutrition.
Key Takeaways:
Ashok Gulati, Ritika Juneja Writes-
• Crops, like humans, need a balanced meal. ICRIER’s recent policy brief, ‘Repurposing India’s Fertiliser Policy towards Nutrient Optimisation’, compares actual nutrient use in 20 major states with crop- and irrigation-specific norms between 2009-10 and 2024-25, neatly bracketing the NBS reform of 2010.
• The results are sobering. Nationally, nitrogen use has moved from 7 per cent below its recommended dose to 6 per cent above it. The phosphorus deficit has narrowed only from 29 to 22 per cent, while the potassium deficit has deepened from 48 to 72 per cent: Farmers apply just 9 kg of potash per hectare against a need of 32 kg. The N:P:K ratio stands at 10.5:4.1:1, against a derived normative 2.8:1.5:1. Eleven of 20 major states, led by Jharkhand (72 per cent) and Punjab (65 per cent), overuse nitrogen. Every state under-applies potash; Haryana and Jharkhand apply barely a tenth of what their crops need.
• Why has a reform meant to fix the imbalance made it worse? Simple economics. NBS let the prices of phosphatic and potassic fertilisers float with world markets, but kept urea out at a fixed price. Between 2010-11 and 2024-25, DAP prices nearly tripled to Rs 54/kg, and MOP rose six-fold to Rs 52/kg, while the price of nitrogen in urea rose by just 1 per cent. Farmers respond to relative prices. Nitrogen also makes the crop look green, while the damage from missing potash shows up later, and quietly. So, nitrogen’s share in NPK use is back to about 67 per cent — the 1970-71 level.
• The damage runs from the soil to the plate. Of the 96 lakh samples tested under the Soil Health Card scheme in 2025-26, 72 per cent were low in nitrogen, 52 per cent in organic carbon, 42 per cent in boron and 37 per cent in zinc. Low nitrogen despite its overuse is no paradox: Carbon-starved soils cannot hold what is poured on them, and crops take up only 30-40 per cent of the nitrogen applied. Part of the rest escapes into the air as nitrous oxide, a greenhouse gas 273 times as potent as carbon dioxide; Punjab’s fertiliser-related emissions are nearly double the national average. Some of the chemical leaches into groundwater: Nitrate above safe limits has been found in parts of 502 districts and carries the risk of “blue baby syndrome” in infants and chronic illness in adults.
• Potassium deficiency weakens resistance to drought and disease and lowers grain quality; phosphorus shortage delays flowering. When soils lack zinc and other micronutrients, the grains they yield do too, fuelling the hidden hunger that afflicts millions. All this also comes at a steep fiscal price. The subsidy budget for 2026-27 is Rs 1.71 lakh crore. The disruption in the Strait of Hormuz could push the subsidy bill to anywhere between Rs 2.5 lakh crore and Rs 3 lakh crore, with the urea subsidy amounting to two-thirds of this. The benefits are skewed, too: Punjab gets about Rs 25,700 of nitrogen subsidy per hectare, 10 times what Kerala gets. Add MSP-based procurement and subsidised power, and the rice-wheat rotation gets locked in. All this hurts aquifers.
Do You Know:
Ashok Gulati, Ritika Juneja Writes-Four steps can improve the situation.
• One, move from input price subsidy to a direct benefit transfer on a per-hectare basis and neutral across nutrients and crops. This will ensure that farmers face the market price of each nutrient and urea loses its artificial edge. AgriStack is creating digital farmer IDs linked to land records and crops sown, and a framework for fertiliser sale (FFS) will tie each purchase at the point of sale to that identity.
• Two, reward balance where decisions are made. PM-PRANAM was supposed to reward states that use fertilisers in a balanced way. But so far, nothing has been disbursed. The scheme needs fixing, and its implementation should be expedited.
• Three, plough the savings in fertiliser subsidy into drip irrigation and fertigation, and back product innovation. These include customised and coated fertilisers, triple super phosphate (TSP) — in place of DAP — biofertilisers, nano fertilisers, and gene-edited seeds using nitrogen more efficiently.
• Four, follow the 4Rs — right source, rate, time and place — with plot-level advice based on soil tests. Rotating cereals with pulses can cut the next crop’s nitrogen need by 20-30 per cent. But none of this will stick in Punjab and Haryana unless power pricing and procurement are reformed.
Other Important Articles Covering the same topic:
📍All is not well with soil
Previous year UPSC Mains Question Covering similar theme:
📍How far is the Integrated Farming System (IFS) helpful in sustaining agricultural production? (UPSC, GS3, 2019)
Nation
Odisha mobilises personnel, orders evacuations, braces for very severe cyclone
Syllabus:
Preliminary Examination: Indian and World Geography-Physical, Social, Economic Geography of India and the World.
Mains Examination:
• General Studies I: Important Geophysical phenomena such as earthquakes, Tsunami, Volcanic activity, cyclone etc., geographical features and their location-changes in critical geographical features and in flora and fauna and the effects of such changes.
• General Studies III: Disaster and disaster management
What’s the ongoing story: As Odisha braces for a very severe cyclonic storm that is expected to cross the Andhra Pradesh coast on October 28, the state government on Sunday stepped up preparations, mobilising personnel and equipment in vulnerable areas.
Key Points to Ponder:
• Cyclone Arnab-know in detail
• What are Key features of cyclone Arnab?
• What India Meteorological Department (IMD) says about cyclone Arnab?
• Odisha and Cyclone-connect the dots
• Why is Odisha prone to cyclone?
• How Odisha deals with cyclone?
• What are Odisha’s strategies for mitigating and managing cyclonic hazards?
• What you understand by Pre cyclone watch, Cyclone alert, Cyclone warning and Post landfall scenario?
• What are the major disaster risk reduction initiatives being taken by Odisha Government?
• What are the main priorities of the Sendai Framework?
• What can the world learn from the Odisha government’s approach to dealing with Cyclones?
• Classification of cyclonic disturbances-how they are classified?
• Cyclone and Super Cyclone-Compare and Contrast
• Cyclone and Anti-Cyclone-Compare and Contrast
• Types of Cyclones or Classification of Cyclones-Know in detail
• What are the Stages of Formation of Cyclones?
• Structure of Tropical Cyclone-Know in detail
• What are Air Masses and Fronts? How they associated with the formation of Cyclones?
• What is eye of the Cyclone?
• What is the average lifespan of a cyclonic storm?
• Storm Intensity, Expected Damage and Suggested Actions-Know in detail
• Deep Depression (DD), Cyclonic Storm (CS), Severe Cyclonic Storm (SCS), Very Severe Cyclonic Storm (VSCS), Extremely Severe Cyclonic Storm (ESCS) and Super Cyclone (SuCS)-how they are different?
• India’s Vulnerability to Cyclones-Know in Detail
Key Takeaways:
• In its latest bulletin, the India Meteorological Department (IMD) said a depression over the Bay of Bengal is likely to cross the Andhra Pradesh coast between Bapatla and Visakhapatnam as a very severe cyclonic storm, with maximum sustained winds of 115-125 kmph and gusts up to 140 kmph.
• The depression over the east-central and adjoining southeast Bay of Bengal remained practically stationary during the past three hours and lay centred at 0830 hours IST on October 25, 2026, over the same region, the bulletin said. “It is very likely to move nearly southwards, intensify into a deep depression and then gradually recurve west-northwestwards over the east-central and adjoining southeast Bay of Bengal on October 25,” it said.
Do You Know:
• The state government has formulated a disaster management policy with a focus on total risk management and vulnerability reduction, strengthening physical infrastructure, psychological as well as socio-economic status of people to reduce vulnerability. After super cyclone in 1999, Government of Odisha constituted Odisha State Disaster Management Authority (OSDMA) to have a systematic and planned approach to disaster mitigation and management in the state.
• State Government have constituted units of Odisha Disaster Rapid Action Force (ODRAF) being procured with equipment for use during disaster management.
• Government has implemented UNDP sponsored Disaster Risk Management Programme at multi-level and construction of Emergency Operation Centres or Control Room.
• A four stage warning system for tropical cyclone is followed by IMD since 1999. After the weakening of the cyclone into a depression stage, a final message on De-warning is issued
—Pre cyclone watch- a special bulletin is issued containing early information about the development of cyclonic disturbances.
—Cyclone alert –It is issued at least 48 hours in advance of the expected commencement of adverse weather over the coastal area.
—Cyclone warning – it is issued at least 24 hours in advance.
—Post landfall scenario-It is issued to cover the devastating impact of the cyclone in coastal areas.
Other Important Articles Covering the same topic:
📍Odisha’s turnaround in disaster management has lessons for the world
Previous year UPSC Mains Question Covering similar theme:
📍Discuss the recent measures initiated in disaster management by the Government of India departing from the earlier reactive approach. (UPSC, GS3, 2020)
📍Vulnerability is an essential element for defining disaster impacts and its threat to people. How and in what ways can vulnerability to disasters be characterized? Discuss different types of vulnerability with reference to disasters. (UPSC, GS3, 2019)
Explained
Why Loss & Damage Fund for Nepal matters beyond it
Syllabus:
Preliminary Examination: General issues on Environmental Ecology, Biodiversity and Climate Change – that do not require subject specialisation
Mains Examination: General Studies II: Important International institutions, agencies and fora- their structure, mandate.
What’s the ongoing story: A month after it raised a request, Nepal has been promised a sum of $20 million (around Rs 190 crore) to help it recover from the devastating flash floods in August this year. Though the amount is extremely small compared to an estimated need of about $4.75 billion (around Rs 44,600 crore) in recovery and reconstruction costs, it marks the beginning of the implementation of a new international regime on loss and damage. This system seeks to provide financial assistance to developing countries affected by climate events.
Key Points to Ponder:
• What is the Fund for Responding to Loss and Damage (FRLD)?
• Why has Nepal become the first beneficiary of an allocation from the global Loss and Damage Fund?
• Why is the $20 million allocation to Nepal considered a significant milestone in the implementation of the international loss-and-damage financing mechanism?
• How does the estimated cost of Nepal’s recovery and reconstruction compare with the amount provisionally allocated by the FRLD?
• What do you understand by the term ‘Climate justice’?
• ‘The Climate justice requires reconciling the principles of historical responsibility, present capability and vulnerability’—how far you agree?
• Do you think that the Nepal’s floods are Himalayan disasters and no longer purely national disasters?
• What are the challenges in establishing liability for climate-induced disasters?
• Why did Nepal seek financial assistance from the FRLD rather than relying exclusively on its domestic resources?
Key Takeaways:
• The allocation is a first from the Fund for Responding to Loss and Damage (FRLD), a new international financing instrument created in 2022 to address a long-pending demand from developing nations, particularly those small and vulnerable countries that face the maximum risk from climate events. These countries have contributed negligibly to creating the problem of climate change because of their extremely low emissions footprint, yet they disproportionately suffer its consequences.
• Developing countries also have fewer resources and happen to be among those least equipped to deal with major climate-related disasters.
• The allocation for Nepal, which still has to undergo some procedural formalities before being released, is by no means commensurate with the extent of damage inflicted by an event assessed to be triggered by climate change. But its importance lies in acknowledging the need for quickly mobilising financial resources. The decision to earmark $20 million for Nepal was taken at an emergency board meeting of the FRLD, following requests from Nepal and several other countries that supported it.
• The money for Nepal is an out-of-turn allocation by the FRLD, and essentially its first decision on applications made by countries. Operationalised in 2023 after receiving the first round of contributions from donor countries, the FRLD made its first call for applications during the annual climate conference in Brazil last year (COP30). By the time the window for applications closed on June 15 this year, 119 countries had submitted 176 funding requests.
• The total amount requested by countries added up to $2.8 billion — over three times what it currently has. The fund has so far received only $822 million from donors, and much of it is currently only at the commitment stage, with the actual amount yet to be delivered. Clearly, the fund has no capacity to accept every request even after capping each request at $20 million.
• As a result, the fund will have to prioritise these requests. A decision on these requests is scheduled for December, although Nepal’s case is a separate one. The flooding incident, in which more than over 1,300 people were killed and over 5,000 continue to be missing, happened in August, and an extraordinary request was made in September. Its acceptance underlines the need to provide emergency financial assistance to countries following a large-scale climate disaster.
• The success in disbursing funds to Nepal quickly, even though the amount is nominal, is likely to become a template for many such requests in future. Countries struck by a disaster would insist on immediate consideration of their request and quick access to money, which is how this mechanism was envisaged to work.
Do You Know:
According to the World Bank,
• In a historic decision at COP28, an agreement was reached by 198 countries to move forward with a fund to provide financial support to vulnerable countries hardest hit by climate impact. The purpose of the Fund for responding to Loss and Damage (FRLD) is to assist particularly vulnerable developing countries in responding to economic and non-economic loss and damage associated with the adverse effects of climate change, including extreme weather events and slow onset events. As a new channel for multilateral finance, the FRLD seeks to provide new, additional, predictable, and adequate financial resources to developing countries that are particularly vulnerable to the adverse effects of climate change and assist in mobilizing external finance to address loss and damage, while supporting achievement of sustainable development and the eradication of poverty.
Other Important Articles Covering the same topic:
📍Knowledge Nugget | Nepal floods and compensation: Why Loss and Damage Fund matters
Previous year UPSC Prelims Question Covering similar theme:
2) Consider the following statements with reference to India’s response to climate change: (UPSC, CSE, 2026)
I. India’s Long-Term Low Emission Development Strategy (LT-LEDS) is a crucial tool for achieving net-zero emissions by 2070.
II. India’s 4th Biennial Update Report (BUR-4) submitted in December, 2024 recorded around 8% decrease in Greenhouse gas emissions in 2020 over 2019.
III. Climate-resilient development necessarily depends on quick and short-term achievement of emission reduction targets.
Which of the following relationships among the above statements is/are correct?
1. Statement I is empirically supported by statement II.
2. Statement III contradicts the approach implicit in statement I.
3. Statement I and statement III together establish the premise of long-term sustainability.
Select the answer using the code given below:
(a) 1 only
(b) 1 and 2
(c) 2 and 3
(d) 3 only
Previous year UPSC Mains Question Covering similar theme:
📍‘Climate change’ is a global problem. How India will be affected by climate change? How Himalayan and coastal states of India will be affected by climate change? (UPSC, GS3, 2017)
As AI solves complex maths problems, proof lies in the proving
Syllabus:
Preliminary Examination: Current events of national and international importance.
Mains Examination: General Studies III: Awareness in the fields of IT, Space, Computers, robotics, nano-technology, biotechnology and issues relating to intellectual property rights.
What’s the ongoing story: The growing ability of artificial intelligence (AI) to solve mathematical problems is prompting researchers to rethink what constitutes progress in the field.
Key Points to Ponder:
• What is a mathematical proof?
• What are proofs in research mathematics?
• Why is proof verification important when artificial intelligence generates mathematical solutions?
• How is solving a mathematical problem different from demonstrating that its solution is correct?
• Why has the growing ability of artificial intelligence to solve complex mathematical problems prompted researchers to reconsider what constitutes progress in mathematics?
• What concerns did mathematician Terence Tao raise about an excessive focus on problem-solving in mathematics?
• What is the objective of China’s Yau Laboratory Alliance for Mathematics and Artificial Intelligence?
• Why does the ability of AI to generate mathematical proofs make their reliable verification increasingly important?
Key Takeaways:
• In a lecture at Caltech on October 9, Fields Medallist Terence Tao argued that solving problems, historically one of the most visible goals of mathematical research, is only a means to broader ends. “Further blind optimization of problem-solving alone is now actively harmful to the long-term health of mathematics,” he said in his presentation
titled Math 2.0.
• The debate comes as research institutions move to develop AI for mathematical discovery. On Sunday (October 11), China launched the Yau Laboratory Alliance for Mathematics and Artificial Intelligence at Tsinghua University, bringing together eight institutions and aiming to build a network of over 1,000 scientists working on specialised AI models for mathematics, proof formalisation, and conjecture generation.
• According to a report by the South China Morning Post, Fields Medallist Shing-Tung Yau noted during a Beijing launch event that China is falling behind the US in applying AI to advance frontier science.
• For researchers, the challenge is not simply whether AI can generate proofs, but whether those results can be verified, understood and used to advance mathematical knowledge.
Do You Know:
• In mathematics, it is not enough to find an answer. Researchers must also prove that it is correct.
• Take two even numbers: their sum will always be even. Trying this with a few numbers illustrates the pattern, but a proof explains why it must hold every time. Such proofs are the foundation on which mathematicians build new results. An error in one can undermine the work that follows.
• Yet, checking a proof can be surprisingly difficult. In his book The Proof in the Code, author Kevin Hartnett recounts how mathematician Tom Hales faced this challenge while proving the Kepler conjecture, which concerns the most efficient way to pack spheres together. Hales’s proof involved hundreds of pages of mathematical reasoning and extensive computer calculations. After years of review, referees at Annals of Mathematics were unable to certify the proof as a whole, prompting Hales to look for a way to have a computer check it.
• The idea draws on a connection between mathematics and computer science. Known as the Curry–Howard correspondence, it relates mathematical propositions to types in computing, and proofs to programs. It underpins tools called proof assistants, which allow mathematicians to encode arguments in a formal language that a computer can check.
• One such tool is Lean, a functional programming language and interactive theorem prover developed by Leonardo de Moura at Microsoft Research in 2013. It can be used to formalise mathematics and verify software. Mathematicians subsequently adopted it, building a shared digital library of definitions, theorems and proofs that others can reuse rather than start from scratch.
Other Important Articles Covering the same topic:
📍AI solved an 80-year maths problem. Here’s why this matters beyond mathematics
Previous year UPSC Prelims Question Covering similar theme:
3) With the present state of development, Artificial Intelligence can effectively do which of the following? (UPSC, CSE, 2020)
1. Bring down electricity consumption in industrial units
2. Create meaningful short stories and songs
3. Disease diagnosis
4. Text-to-Speech Conversion
5. Wireless transmission of electrical energy
Select the correct answer using the code given below:
(a) 1, 2, 3 and 5 only
(b) 1, 3 and 4 only
(c) 2, 4 and 5 only
(d) 1, 2, 3, 4 and 5
Previous year UPSC Mains Question Covering similar theme:
📍What is agentic Artificial Intelligence (AI) ? Explain its working. Describe its applications with suitable examples. Discuss the advantages, risks and challenges associated with agentic AI systems. (UPSC, GS3, 2026)
Economy
Agrivoltaics: Can India put solar panels on farms without hurting crop yields?
Syllabus:
Preliminary Examination: Economic and Social Development
Mains Examination: General Studies III: Major crops-cropping patterns in various parts of the country, – different types of irrigation and irrigation systems storage, transport and marketing of agricultural produce and issues and related constraints; e-technology in the aid of farmers and economics of animal-rearing.
What’s the ongoing story: The government this week announced plans to introduce agri-photovoltaics (PV) under the second phase of the Pradhan Mantri Kisan Urja Suraksha evam Utthaan Mahabhiyaan (PM-KUSUM), its flagship scheme to solarise irrigation. The approach combines solar power generation with crop cultivation on the same land, with the aim of allowing farmers to continue growing crops while earning additional income from electricity generation.
Key Points to Ponder:
• What is agrivoltaics?
• How agrivoltaics enable the simultaneous use of agricultural land for crop cultivation and solar power generation?
• What is the role of the second phase of the Pradhan Mantri Kisan Urja Suraksha evam Utthaan Mahabhiyan (PM-KUSUM) in promoting agrivoltaics?
• Why are solar panels installed on elevated structures in agrivoltaic systems?
• Which categories of crops have been found suitable for agrivoltaic systems, and which crops have not been found suitable in the government’s initial assessments?
• How can the additional income from solar power generation be evaluated against the full costs of agrivoltaic projects to determine their actual benefits for farmers?
Key Takeaways:
• Speaking at the Agrivoltaics World Conference 2026 – ‘Powering the Global South’ in New Delhi on Wednesday, Union New and Renewable Energy (MNRE) Minister Pralhad Joshi said the approach could help address the shortage of land for solar projects while allowing farming to continue beneath elevated panels. Citing estimates, Joshi said around 30% of India’s 160 million hectares of cropland could be suitable for agrivoltaic projects.
• Agri-photovoltaics (PV) involves installing solar panels on elevated structures over agricultural land, allowing farmers to continue cultivation underneath while generating electricity from the same plot. Technology-wise, photovoltaic is the same as that in conventional ground-mounted solar projects. The difference lies in the additional infrastructure required to elevate the panels and leave sufficient space for farming activities beneath them.
• Earlier this week, Santosh Kumar Sarangi, Secretary at MNRE, had told the media that agri PV panels are installed at a height of around 3.5 to 4 metres above the ground to allow farmers to carry out routine agricultural operations, including the movement of machinery, without interruption.
• With most of the agri-photovoltaic projects in India still at the pilot stage, the government faces the challenge of developing a policy framework that allows solar power generation to expand without compromising crop yields, soil health, or farmers’ livelihoods.
Do You Know:
Pralhad Joshi, Shivraj Singh Chouhan Writes in Harvesting the Sun, and powering the farm
• Agrivoltaics, or AgriPV, offers an opportunity to take that purpose forward by enabling farmers to produce clean electricity while continuing to cultivate their land. The successful efforts of the Government of India in the form of PM-KUSUM are already evident in the solarisation of irrigation. Further efforts are being made to accelerate the generation of solar energy through creation of separate space for AgriPV under the next phase of PM-KUSUM.
• Behind every harvest are months of effort, money invested and a family’s hopes. A good crop does not always bring a good income. Weather, input costs and market prices can unsettle the household budget. Public policy must help farmers strengthen their capacity to withstand these uncertainties and create additional opportunities to earn.
• Agrivoltaics combines cultivation and solar generation on the same land through structures and spacing suited to farming. It can give the cultivator an additional source of revenue from electricity. Where solar energy replaces diesel or purchased power, it can also reduce costs. The favourable microclimate under AgriPV provides additional protection against heat stress, drought, excessive solar radiation, and hail.
Other Important Articles Covering the same topic:
📍Farmers need a share of the solar boom
Previous year UPSC Prelims Question Covering similar theme:
4) With reference to solar power production in India, consider the following statements: (UPSC, CSE, 2018)
1. India is the third largest in the world in the manufacture of silicon wafers used in photovoltaic units.
2. The solar power tariffs are determined by the Solar Energy Corporation of India.
Which of the statements given above is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Previous year UPSC Mains Question Covering similar theme:
📍India has immense potential of solar energy though there are regional variations in its developments. Elaborate (UPSC, GS3, 2020)