Teylers Museum in Haarlem, the Netherlands’ oldest museum, offers a rare journey through 250 years of science, from giant fossils and early physics to its historic Oval Room.

As I walked along the peaceful banks of the Spaarne River in Haarlem, a historic Dutch city located just fifteen minutes by train from Amsterdam, an elegant neoclassical facade caught my eye. To a casual passerby, the grand entrance might look like just another historic manor. Stepping through its heavy doors, I felt like I had walked right into another century. This is the Teylers Museum, the oldest museum in the Netherlands, founded in 1778.

At a time when science and art were seen as sister disciplines rather than opposing worlds, Pieter Teyler van der Hulst, a wealthy cloth merchant and banker, decided to do something extraordinary. Inspired by Enlightenment ideals that people should discover the world independently through reason and hands-on investigation, he left his immense fortune to establish a public center for knowledge. Teylers Museum was designed not as a dusty storehouse for old relics, but as a living “temple of the muses.” It became a welcoming space where researchers, students, and everyday curious visitors could gather under one roof to witness live physics experiments, study fossilized secrets of the Earth, and admire master drawings.

The Heart of the Enlightenment

Inside the Oval Room Stepping into the museum’s historic core, the Oval Room, felt like walking directly into an eighteenth century laboratory. Completed in 1784, this double-tiered hall features carved wooden showcases, brass scientific instruments, and a balcony library filled with leather bound encyclopedias, all bathed in soft natural light flowing through an ornate ceiling skylight.

In the late 1700s, this room served as a high tech science hub. Martinus van Marum, the museum’s legendary first director, used the space to host public demonstrations that fascinated scholars and visitors alike. Van Marum firmly believed that science needed to be seen to be truly understood. To explore the mysterious nature of electricity, he commissioned John Cuthbertson in 1784 to build the largest electrostatic generator in the world.

From giant electrostatic machines and rare fossils to Hendrik Lorentz’s physics cabinet, Teylers Museum preserves the history of science in a remarkably intimate setting.

Equipped with two massive glass discs over five feet in diameter, Van Marum’s generator could produce sparks over two feet long, generating artificial lightning that left audiences completely amazed. As I stood before this colossal machine, I couldn’t help but think back to Van Marum’s original notes from his high voltage trials. He noticed that these massive electrical discharges left behind a distinct, sharp smell, an observation that quietly laid crucial groundwork for the later discovery of ozone gas.

Fossils, Physics, and the Foundations of Modern Science

Moving beyond the Oval Room led me into the scientific galleries, where cabinet after cabinet reveals the real origins of modern paleontology and physics. Long before Charles Darwin published his theories on evolution, early naturalists were struggling to make sense of prehistoric remains.

In 1802, Van Marum purchased a famous fossil, originally unearthed in Öhningen in southern Germany, known at the time as “Homo diluvii testis”, or “the witness of the Flood.” Theologians of the era believed it to be the skeletal remains of a human who perished in Biblical waters. Years later, French naturalist Georges Cuvier examined the specimen and identified it as the fossilized giant salamander ‘Andrias scheuchzeri’. That discovery helped overturn centuries of religious assumptions, proving that entire species could actually become extinct over time.

Teylers Museum also houses one of the rare specimens of Archaeopteryx, the famous primeval bird fossil that provided the crucial missing link between feathered dinosaurs and modern birds. Walking past these display cases felt like watching the early building blocks of science come together.

The museum’s dedication to physics continued well beyond the 18th century. In 1910, theoretical physicist and Nobel laureate Hendrik Lorentz was appointed Curator of Teylers Physics Cabinet. Lorentz, whose mathematical equations laid the groundwork for Albert Einstein’s theory of special relativity, conducted experiments on electromagnetism, optics, and atomic physics within these very walls for nearly two decades. When Einstein visited his friend Lorentz in Haarlem, he described the city and its scientific atmosphere as a sanctuary of pure thought.

A Center for Curiosity

Dutch Museum Culture Across Generations Exploring the galleries, I was repeatedly struck by an aspect of the experience that feels deeply rooted in Dutch culture. In the Netherlands, museums are rarely treated as rigid, solemn monuments reserved only for academics. Instead, they are active, community centered gathering places designed to spark curiosity across every stage of life.

Around me, multi-generational discovery was happening in real time. I watched a young child look wide-eyed at a display of polished mineral specimens, pointing out bright colors to a grandparent who was patiently explaining how crystals form. A few yards away, a group of students stood engrossed near a collection of early optical instruments, casually debating how light bends through glass lenses.

This spirit of accessibility gives Dutch museum culture its vitality. From toddlers interacting with physical phenomena to lifelong learners examining centuries old manuscripts, people of all ages come together to ask questions and explore. Teylers Museum reflects this philosophy naturally. It doesn’t feel like a dusty home for old artifacts, but a place where centuries old ideas still inspire people today.

Timeless Wonder in a Physical World

What makes Teylers Museum stand out today is its complete preservation. While modern science centers rely heavily on interactive touchscreens and digital simulations, Teylers offers something far rarer: authentic, untouched history. The brass dials of the barometers, the hand blown vacuum tubes, the polished mahogany cases, and the handwritten labels remain virtually untouched, arranged exactly as they were over two centuries ago.

Standing among these collections, the experience feels less like viewing a static display and more like walking into a researcher’s active workplace, as if the scientists have merely stepped out for a short break.

As I walked out into the quiet streets of Haarlem, I couldn’t help but feel that the real magic of the place was not just in its old collection. It was in the reminder that science is not about having all the answers, but about never losing the urge to keep looking.

India’s research and development (R & D) spending has more than doubled in absolute terms, but R&D intensity remains below 1% of GDP. As India approaches 2047, the bigger question is whether its investment in science is sufficient to build the technologies and industries needed for technological independence.

When India became independent in 1947, the country had only 17 universities and 636 colleges serving about 2.38 lakh students. Literacy was around 14%. Nearly eight decades later, India has built a vastly larger education and research system. The country had 1,168 universities, 45,473 colleges and 12,002 standalone higher-education institutions in 2021–22, according to the All India Survey on Higher Education.

But as India looks towards its centenary of Independence in 2047, its scientific ambitions are running into a persistent question: is the country investing enough in research and development to build the technologies it will need? India’s R&D spending has increased sharply in absolute terms. Yet as a share of the economy, it has remained below 1%.

India’s R&D Spending Remains Below 1% of GDP

India’s gross expenditure on research and development rose from ₹60,197 crore in 2010–11 to ₹1,27,381 crore in 2020–21, according to the Department of Science and Technology. However, R&D expenditure as a share of GDP was 0.64% in 2020–21. The corresponding figure was 0.66% in both 2018–19 and 2019–20.

This means that while India’s research spending more than doubled over the decade, R&D intensity remained at roughly two-thirds of 1% of GDP. The latest detailed official figure available for India is therefore 0.64% for 2020–21. WIPO’s Global Innovation Index 2025 uses an R&D intensity figure of 0.65%, based on 2020 data. One of the most commonly used measures of a country’s research effort is R&D intensity—the amount a country spends on research and development as a percentage of its gross domestic product (GDP). It allows researchers to compare the relative priority given to R&D across economies of very different sizes.

There is currently no single internationally comparable R&D figure for every country for 2026. UNESCO’s new global R&D data collection is still underway, with the resulting data scheduled for release in November 2026.

Government Still Funds the Larger Share

The issue is not only how much India spends on R&D, but who pays for it. Government accounted for 59.2% of India’s gross expenditure on R&D in 2020–21, while business enterprises accounted for 40.8%, according to DST data.

The figures point to India’s continuing dependence on public funding for research. That becomes significant as research moves into areas such as semiconductors, biotechnology, artificial intelligence, quantum technologies, advanced materials and clean energy. These fields can require expensive infrastructure, specialised equipment and long development cycles before research produces commercially viable technologies.

Increasing private-sector participation is therefore likely to be as important as increasing the overall R&D budget.

India is Producing More Patents and Research

Despite its relatively low R&D intensity, India has become a significant contributor to global research and innovation. The latest Nature Index data, covering April 2025 to March 2026, records 3,565 research articles from India in the journals tracked by the index.

Patent activity has also grown rapidly. Indian applicants filed 76,470 patent applications worldwide in 2024, according to the World Intellectual Property Organization. This was a 19.2% increase over 2023 and placed India sixth among origins for worldwide patent applications.

The growth marks the sixth consecutive year of double-digit growth in patent applications from India-based applicants, according to WIPO. But patent filings do not necessarily mean that inventions reach the market.

A patent can protect an invention without it becoming a commercially manufactured product. For research to generate wider economic value, it has to move through several stages—from discovery to patent, prototype, product and eventually large-scale deployment. That transition remains one of the important challenges for India’s innovation ecosystem.

India Ranks Higher on Innovation Than Its R&D Spending Suggests

India’s relatively low R&D intensity has not prevented it from performing strongly on broader measures of innovation. WIPO’s Global Innovation Index 2025 ranked India 38th among 139 economies. India was also ranked first among lower-middle-income economies and first in Central and Southern Asia.

WIPO identifies India as an innovation overperformer, citing strengths including ICT services exports, venture-capital activity and the country’s ability to translate scientific knowledge into commercial impact. The contrast is significant.

India is generating considerable innovation despite spending a relatively small share of its GDP on R&D. But that does not necessarily mean that the existing level of investment is enough to support the next generation of technologies. As research becomes more capital-intensive, countries seeking technological leadership require sustained investment in infrastructure, specialised researchers and long-term development.

China Spends Four Times India’s Share

The gap becomes clearer when India is compared with major research economies. WIPO’s latest internationally comparable estimates for 2024 put R&D intensity at 6.33% of GDP in Israel and 5.32% in South Korea. Japan and the United States were both at 3.45%, while Germany stood at 3.11%.

China’s R&D intensity reached 2.65%. By comparison, India’s latest available figure is about 0.65%. China therefore spends roughly four times India’s share of GDP on R&D. Other emerging economies also show different levels of research intensity. WIPO estimates Brazil at 1.15%, Thailand at 1.16%, Türkiye at 1.42%, Vietnam at 0.42%, the Philippines at 0.32% and Indonesia at 0.28%.

The figures are not all based on the same data year, making direct comparisons imperfect. However, the broad difference between India and the world’s leading research economies remains clear.

Government Changing The Funding Model

India has begun introducing policies aimed at expanding research funding and encouraging greater industry participation. The Anusandhan National Research Foundation was established through legislation in 2023, with a planned five-year outlay of ₹50,000 crore for 2023–28.

The foundation is intended to strengthen research across universities, colleges and research institutions and encourage collaboration between academia, industry and government.

In July 2025, the government also approved a ₹1 lakh crore Research, Development and Innovation Scheme. The scheme is intended to encourage private-sector investment in high-risk and high-impact R&D, particularly in strategic and emerging areas.

The initiatives reflect an attempt to address a longstanding problem: India’s research system needs greater private-sector participation if overall R&D investment is to rise substantially.

What Would Higher R&D Spending Change?

There is no fixed relationship between R&D spending and the number of patents, papers or technologies a country will produce. Reaching a particular percentage of GDP cannot guarantee scientific breakthroughs.

But higher sustained investment could expand the country’s research capacity. Moving from 0.64% to 1% of GDP would represent an increase of about 56% relative to India’s current R&D intensity. It could provide greater resources for research grants, laboratory infrastructure, doctoral training and advanced equipment.

At 2%, India would move much closer to China’s current R&D intensity and have a substantially larger pool of resources for research in areas such as biotechnology, advanced manufacturing, AI, semiconductors and clean energy. At 3%, India would enter the range of several major research economies. The outcome, however, would depend on how effectively that money is used.

From Research Papers to Technologies

For India, the next phase of science policy may therefore need to focus as much on the movement of research into the economy as on increasing research output. Universities need stronger research infrastructure and stable funding. Public laboratories need effective technology-transfer mechanisms. Companies need stronger incentives to conduct R&D domestically. Researchers need access to advanced equipment and long-term funding.

Success could also be measured through indicators beyond publications and patents: technologies licensed to companies, university spin-offs, industry-funded research, prototypes entering production and revenue generated from publicly supported research. This is particularly important for technologies that could shape India’s economic future.

A semiconductor process developed in an Indian laboratory, a new pharmaceutical platform, an energy-storage technology or an agricultural innovation can have an economic impact far beyond the research paper that first describes it. At the same time, basic research cannot be judged only by immediate commercial returns. Some of the technologies that eventually transform economies begin as discoveries with no obvious market.

India therefore faces a two-part challenge: expand research that pushes scientific boundaries while building the institutions and industrial capacity needed to convert discoveries into technologies.

The Science Challenge India Faces in 2047

The scientific challenge India faced in 1947 was largely about building capacity. The country needed universities, laboratories, trained researchers and institutions capable of supporting scientific inquiry. Much of that foundation now exists.

The challenge approaching 2047 is different. India is no longer simply trying to establish a scientific system. It is trying to use that system to compete in technologies that will determine economic and strategic strength. That will require more sustained investment, greater participation from industry and stronger links between research institutions and the market.

As India approaches 100 years of Independence, the question is therefore no longer only how much science the country produces. It is whether India can invest enough in that science—and build the systems around it—to turn research into technologies, technologies into industries and scientific capability into technological independence.

2026 Fields Medal winners Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang were honoured for solving mathematical problems that had challenged researchers for decades. From Hilbert’s Sixth Problem to the Kakeya conjecture, their breakthroughs are reshaping modern mathematics.

Every four years, the International Mathematical Union hands out the closest thing mathematics has to a Nobel Prize. The Fields Medal comes with a modest cheque — 15,000 Canadian dollars, worth about US$10,600, a sum untouched since 2006 — and a gold medal stamped with the head of Archimedes. Nobody wins it for the money. They win it because a committee of the world’s leading mathematicians has decided that, sometime before their 40th birthday, they cracked something the rest of the field had been stuck on for years, sometimes decades.

This year’s ceremony, held on 23 July at the International Congress of Mathematicians in Philadelphia — the first time the congress has met in the United States since 1986 — went to four mathematicians: Yu Deng of the University of Chicago, John Pardon of Stony Brook University, Jacob Tsimerman of the University of Toronto, and Hong Wang of New York University and the Institut des Hautes Études Scientifiques in France. Wang is only the third woman to win the medal since it was first awarded in 1936, following Maryam Mirzakhani in 2014 and Maryna Viazovska in 2022. Deng and Wang are also the first Chinese-born mathematicians to win since Shing-Tung Yau in 1982.

2026 Fields Medal Winners: Four Mathematicians Who Solved Decades-Old Problems

Each of the four solved a problem that had outlasted its original solvers by a human generation or more. Here is what they actually did, and why it matters.

Yu Deng: connecting Newton to the weather

In 1900, the mathematician David Hilbert drew up a list of 23 problems he thought would define the coming century of mathematics. The sixth asked for something that sounds almost philosophical: a way to show, with full mathematical rigour, that the everyday physics of gases and fluids can be derived from the motion of individual particles bouncing off each other according to Newton’s laws.

Physicists had a working answer since the 1870s. Ludwig Boltzmann proposed an equation describing how a cloud of colliding particles settles into predictable statistical behaviour, and decades later, other equations described how that gas behaves as a continuous fluid — the same mathematics used to model weather systems and airflow over a wing. The trouble was the middle step. Nobody could prove that Boltzmann’s equation actually follows from Newton’s laws once you let the collisions run for a realistic length of time. An attempt in 1975 by the mathematician Oscar Lanford got partway there, but only for a fleeting initial period, before particles had the chance to collide with each other more than once.

Deng, working with Zaher Hani and Xiao Ma, closed that gap. Starting from a large number of hard spheres bouncing elastically inside a bounded space, they showed that even once particles start colliding with each other repeatedly — which happens constantly in any real gas — the overall statistical picture Boltzmann predicted still holds. They then carried the argument one step further, showing it leads to the equations that describe fluids as a continuous medium. For the first time, a straight mathematical line runs from a box of colliding billiard balls to the equations meteorologists use to predict tomorrow’s weather.

Deng had built toward this for years, having already proved — with Hani — that a related equation describing ocean and atmospheric waves emerges correctly from the underlying wave physics. Colleagues describe his working method as having less to do with sudden insight than with total command of the calculation: one collaborator recalled him reciting 200 pages of computation from memory. The Fields committee cited him for “the rigorous derivation of the Boltzmann equation from hard-sphere dynamics for rarefied gases,” alongside his work on wave equations and the mathematics of the Schrödinger equation.

John Pardon: curves, knots, and a 20-year-old disagreement

Pardon’s Fields Medal recognises work spread across several corners of geometry and topology, but the throughline is a knack for finding exactly the right structure to settle an argument that had stalled.

His first major result came as a Princeton undergraduate, when he answered a question the mathematician Mikhail Gromov had posed about how badly a knot can be distorted — essentially, how much you have to stretch and twist a loop of string to untangle it — a problem that had sat unsolved for more than two decades. He wrote the proof after a walk in an English park during a summer break; his Stony Brook colleague Simon Donaldson has said it is short enough to sit down and read in one sitting.

His most recent major achievement is in a very different area: counting curves. In string theory, physicists model the extra, curled-up dimensions of the universe using shapes called Calabi–Yau threefolds. Mathematicians had developed several competing methods for counting the curves that can be drawn on these shapes, and in 2006 a group of researchers — Maulik, Nekrasov, Okounkov and Pandharipande — conjectured that two of these methods, despite looking completely different, always produce the same answer. Pardon proved they were right, closing a conjecture that had stood for nearly 20 years and that touches on questions in representation theory and quantum physics as well as pure geometry.

In between, Pardon built new mathematical machinery — including a rigorous way to define “virtual fundamental cycles,” a technical tool symplectic geometers had relied on informally for years without a fully solid foundation — and made progress on the 70-year-old Hilbert–Smith conjecture, about which kinds of mathematical groups can act on ordinary space. The Fields committee’s citation runs through all of it: “achievements in symplectic geometry including new approaches to virtual fundamental cycles, Fukaya categories of certain manifolds and counting holomorphic curves,” and contributions to “group actions on 3-manifolds and knot theory.”

Jacob Tsimerman: finding order in scattered points

Tsimerman’s medal centres on a problem he first encountered as a Princeton graduate student and never really left: the André–Oort conjecture, which concerns certain “special points” that turn up inside geometric spaces used to encode deep arithmetic information — the kind of spaces number theorists use to study elliptic curves and modular forms. The conjecture predicted that these special points can’t scatter randomly; wherever they cluster, there has to be a hidden algebraic reason.

Proving it meant reaching outside number theory entirely, into a branch of mathematical logic called o-minimality, which had mostly been used to describe well-behaved geometric shapes rather than to prove theorems in arithmetic. Tsimerman, working with several collaborators over more than a decade, showed that o-minimal methods could be turned into genuine tools for algebraic and arithmetic geometry — recasting a fairly obscure logical framework into one of the sharper instruments in the field. Along the way, he and his collaborators Benjamin Bakker and Yohan Brunebarbe also proved the Griffiths conjecture, a separate longstanding problem about when certain geometric maps must be algebraic rather than merely analytic, and developed a set of techniques nicknamed “o-minimal GAGA” that let mathematicians detect hidden algebraic structure in spaces that don’t obviously have any.

Colleagues describe him as unusual in combining two different temperaments: he is, as his doctoral adviser Peter Sarnak put it, both “a problem solver and a theory builder” — someone who chases a specific hard question to the end, and also builds the general-purpose machinery that outlives the original problem. The Fields committee credited him “for his contribution in the recasting of o-minimality as a fundamental method of arithmetic and complex algebraic geometry, and his role in the proof of many central conjectures including Griffiths’ conjecture… and the André–Oort conjecture for Siegel modular varieties.”

Hong Wang: how small can a needle’s path be?

The Kakeya problem started as a puzzle. In 1917, the Japanese mathematician Sōichi Kakeya asked: what is the smallest area in which you can rotate a needle a full 180 degrees, so that it points in every direction at some point during the rotation? The surprising answer, worked out not long after, is that the area can be made arbitrarily small — the needle can sweep through every direction while confined to a spiky, star-shaped region with almost no area at all.

That answer only deepened the underlying question, which mathematicians have spent a century turning into one of the hardest open problems in the field: if a set has to contain a full line segment pointing in every possible direction, how “thin” can it possibly be? In three-dimensional space, the conjecture held that such a set could have zero volume, but could never be less than three-dimensional in a more technical sense involving something called Hausdorff dimension — it could be thin, but not too thin. Despite real progress by several mathematicians over the decades, including some announced proofs that were later found to contain errors, a full proof in three dimensions had eluded everyone who tried it.

In February 2025, Wang and her collaborator Joshua Zahl posted a 127-page proof settling the three-dimensional case. Wang had picked up the trail during the pandemic, working from a strategy the mathematician Terence Tao had sketched in a 2014 blog post but never carried through. She and Zahl spent months quietly checking their own argument — sending it to a handful of trusted colleagues before making it public, still worried less that it contained an error than that it might simply be unclear. It wasn’t. Nets Katz, another mathematician who had spent years on the same problem, called it “a once-in-a-century kind of result.”

The proof’s significance runs beyond the needle puzzle itself. The Kakeya conjecture sits at a junction between geometric measure theory, harmonic analysis, and number theory, and results in one area often unlock progress in the others — number theorists studying prime numbers and analysts studying how waves focus and spread have both drawn on Kakeya-type reasoning before. The Fields citation recognises Wang for “her major advances in Fourier restriction and the Kakeya problem,” building on a body of work that, colleagues say, has already reshaped how both fields are studied.

A prize built around a deadline

What ties these four together isn’t a shared subject. Deng works in the mathematics of fluids and waves, Pardon in geometry inspired by string theory, Tsimerman in the arithmetic of number theory, Wang in the geometry of how shapes fill space. What they share is the medal’s defining constraint: all the work being honoured happened before each of them turned 40, a rule the medal’s namesake, the Canadian mathematician John Charles Fields, set deliberately when he funded the prize from the surplus of the 1924 mathematics congress in Toronto. Fields wanted a prize that rewarded not just what a mathematician had already done, but the likelihood that their best work was still ahead of them.

Three of the four — Deng, Pardon, and Tsimerman — did their doctoral work at Princeton, under different advisers and in different decades, a detail that says as much about how mathematical talent gets identified and trained as it does about any one institution. All four, notably, solved problems that had been sitting in plain sight for a long time: Hilbert’s sixth problem waited 125 years, the MNOP conjecture 20, the André–Oort conjecture more than three decades, and the three-dimensional Kakeya conjecture the better part of a century. None of the four found a shortcut. Each built, over years, the specific tools their problem needed — and then used them.