The great unsolved problems of mathematics, physics, chemistry, and engineering — how long they've been open, why they resist, and what happens when they fall. Every claim cited to an authoritative source. https://unsolved.now/ 2026-07-24T00:00:00+00:00 https://unsolved.now/problems/two-liquid-water/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Water breaks the rules other liquids follow: it expands when it freezes, is densest at 4 degrees Celsius, and gets stranger the colder it is pushed below freezing without crystallizing. In 1992 a computer simulation proposed a startling explanation: a low-density and a high-density form of liquid water that separate below a 'liquid–liquid critical point', predicted near 200 kelvin and around 1000 atmospheres. The problem is that this region is so prone to freezing that catching the two liquids experimentally is extraordinarily hard, so the hypothesis remains debated. Simulations and difficult experiments increasingly support it, but its existence and exact location in real water are not settled.

unsolved.now https://unsolved.now/problems/twin-prime-conjecture/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Primes grow ever scarcer as numbers get bigger, yet twin pairs like 3 and 5, 17 and 19, keep turning up — the largest known pair has 388,342 digits. Whether they keep appearing forever is a question so natural the ancient Greeks could have asked it, formally posed by de Polignac in 1849, and still unanswered. In 2013 a virtually unknown lecturer, Yitang Zhang, stunned mathematics by proving that some gap below 70 million recurs infinitely often — the first finite bound in history. A frenzy of work slashed that bound to 246 within a year, but the final drop from 246 to 2 has been stuck ever since, blocked by a known theoretical obstruction called the parity problem.

unsolved.now https://unsolved.now/problems/room-temperature-superconductor/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Superconductors conduct electricity with literally zero loss, but every confirmed one needs extreme cold, extreme pressure, or both. At ordinary pressure the record stood at 133 K (−140 °C) in a mercury-based ceramic from 1993 until March 2026, when a University of Houston team showed that 'pressure quenching' locks in superconductivity in that ceramic up to 151 K after the pressure is released. Hydrogen-rich compounds like lanthanum decahydride superconduct near 250 K — but only while crushed to over a million atmospheres inside diamond anvil cells. The field is also recovering from spectacular false alarms: the Dias 'room-temperature' papers were retracted in 2022–2023, and the viral LK-99 claim of 2023 collapsed within weeks of scrutiny. A verified superconductor at room temperature and ambient pressure — let alone one manufacturable as wire — remains undiscovered.

unsolved.now https://unsolved.now/problems/riemann-hypothesis/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Prime numbers look scattered almost at random, yet in 1859 Bernhard Riemann found a hidden machine behind them: a function whose zeros control exactly how the primes fluctuate. He conjectured that every one of the meaningful zeros sits precisely on a single line — and if that's true, the primes are as orderly as they could possibly be. Computers have checked the first ten trillion zeros and every single one lands exactly on the line, but ten trillion confirmations are not a proof. It is widely regarded as the deepest open problem in mathematics, having survived 167 years of assault by many of history's greatest mathematicians.

unsolved.now https://unsolved.now/problems/quantum-measurement-problem/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Quantum mechanics is the most precisely confirmed theory in science, yet its central rule is strangely split: systems evolve smoothly as superpositions of possibilities until they are 'measured', at which point exactly one outcome appears — and the theory never defines what counts as a measurement. Schrödinger's 1935 cat thought experiment showed the rules, taken literally, put everyday objects into absurd limbos. Decoherence theory explains why superpositions become effectively invisible in large systems, but does not by itself explain single definite outcomes. The live options — many-worlds, objective collapse, hidden variables, epistemic interpretations — differ over what reality is, and objective-collapse models are the one family making testable predictions, now being squeezed hard by experiment.

unsolved.now https://unsolved.now/problems/quantum-gravity/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

General relativity describes gravity as smoothly curving spacetime; quantum mechanics describes matter as jumpy and probabilistic. Each works superbly in its own domain, but applied together they break down: naive attempts to quantize gravity produce incurable mathematical infinities, proven rigorously at 'two loops' by Goroff and Sagnotti in 1985. Candidate fixes — string theory, loop quantum gravity, causal sets, asymptotic safety — have flourished for decades without a single confirming experiment, because quantum-gravity effects only become strong at energies far beyond any accelerator. The tantalizing new hope is tabletop experiments testing whether gravity itself can entangle two quantum masses.

unsolved.now https://unsolved.now/problems/protein-homochirality/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Many molecules come in two forms that are mirror images of each other, like a left and right hand — and ordinary chemical reactions produce both in equal amounts. Yet life is startlingly one-handed: it builds proteins almost exclusively from left-handed amino acids and uses right-handed sugars, a property called homochirality that is essential for biology to work. How the early Earth broke the symmetry and locked in a single handedness — whether by chance, mineral surfaces, circularly polarized starlight, or some amplifying chemistry — remains unresolved. Pasteur discovered chirality in 1848, and the origin of life's specific choice has been debated ever since.

unsolved.now https://unsolved.now/problems/p-vs-np/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Checking a finished Sudoku takes seconds; solving one from scratch can take far longer — and nobody has proved that this gap is real. Thousands of practically vital problems, from routing trucks to folding proteins, share one shocking property: a fast method for any single one of them would crack them all. Nearly everyone believes P ≠ NP, that finding truly is harder than checking, yet half a century of effort has not produced a proof — and researchers have even proved theorems showing that whole categories of known proof techniques can never settle the question.

unsolved.now https://unsolved.now/problems/origin-of-life-chemistry/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Every living thing runs on a tightly coordinated network of proteins, nucleic acids, and metabolism, but no one knows how that network bootstrapped itself from simple prebiotic chemistry. A central puzzle is the chicken-and-egg problem: today's DNA needs proteins to copy it, yet those proteins are built from DNA instructions. The leading 'RNA world' idea proposes that RNA — which can both store information and act as a catalyst — came first, but a fully demonstrated chemical path from geochemistry to a self-sustaining living system does not exist. With no clean origin date, the modern framing traces to the Oparin–Haldane hypothesis of the 1920s and has been sharpened ever since.

unsolved.now https://unsolved.now/problems/navier-stokes/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

The Navier–Stokes equations are the standard physics of flowing water and air — engineers trust them daily to design planes and forecast weather. Yet mathematicians cannot answer the most basic question about them: whether their 3D solutions always stay well-behaved, or whether a perfectly calm fluid can, in theory, concentrate energy so violently that the math breaks down at a single point in finite time. The two-dimensional version was tamed decades ago; the third dimension unleashes turbulence, whose cascade of swirls within swirls defeats every known technique. The question has been open since Leray's foundational work in 1934, and the Clay Institute made it one of its seven Millennium Prize Problems in 2000.

unsolved.now https://unsolved.now/problems/mechanistic-interpretability/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

The most consequential software artifacts of the decade are billions of learned numbers that no human wrote and no human can read. Mechanistic interpretability tries to reverse-engineer them: sparse autoencoders extracted millions of human-recognizable 'features' from a frontier model in 2024, and in 2025 Anthropic's attribution-graph work traced actual circuits in Claude — revealing, for instance, that the model plans rhymes ahead before writing a line of poetry, and exposing internal mechanisms behind hallucination and jailbreaks. Yet current techniques explain only a fraction of any model's behavior, can miss what the model doesn't verbalize, and don't yet scale to auditing a frontier system's full computation. The field's own 2025 review catalogues exactly how far there is to go.

unsolved.now https://unsolved.now/problems/matter-antimatter-asymmetry/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Every particle has an antiparticle, and they are created and destroyed in pairs — so the early universe should have ended as pure light, with no atoms left. Instead, some unknown mechanism left roughly one extra matter particle per billion pairs, and that residue is everything we see. Physics does know one loophole: matter and antimatter can behave slightly differently ('CP violation'), discovered in kaons in 1964 — but the amount predicted by the Standard Model is many orders of magnitude too small to account for the observed asymmetry. In 2025 the LHCb experiment at CERN opened a new front, observing CP violation for the first time in baryons — the particle family that includes protons and neutrons — and it is still far too small to explain the cosmos.

unsolved.now https://unsolved.now/problems/llm-hallucination/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Language models sometimes generate fluent, confident statements that are simply false — a failure researchers began calling 'hallucination' in the late 2010s, and which every frontier model still exhibits. In 2024, Oxford researchers published a Nature method using 'semantic entropy' to detect a major class of hallucinations by measuring a model's uncertainty over meanings rather than words. In 2025, an OpenAI and Georgia Tech analysis argued that some hallucination is a statistical inevitability of how models are trained — and that it persists partly because benchmarks reward confident guessing over honest abstention. Retrieval grounding, uncertainty estimation, and abstention training all reduce error rates, but no known technique makes a general-purpose model reliably truthful, especially across the multi-step reasoning chains agents now execute.

unsolved.now https://unsolved.now/problems/high-tc-superconductivity/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Conventional superconductivity — electrons pairing up via lattice vibrations and flowing without resistance — was explained by BCS theory and seemed confined to temperatures near absolute zero. Then in 1986 Bednorz and Müller found a ceramic copper oxide superconducting at 35 K, and within a year related 'cuprates' passed 77 K, the boiling point of cheap liquid nitrogen. BCS theory cannot account for these materials: the electrons pair through some other mechanism, entangled with magnetism and exotic phases, and four decades of intense effort have produced proposals but no accepted fundamental description. The 2019–2025 nickelate boom — nickel-oxide cousins superconducting up to ~90 K — has given theorists a whole second family to test their ideas against.

unsolved.now https://unsolved.now/problems/goldbach-conjecture/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

4 = 2+2, 6 = 3+3, 8 = 3+5, 100 = 47+53 — every even number ever checked, up to four quintillion, splits into two primes, usually in many different ways. Goldbach proposed the idea to Euler in 1742; Euler replied that he regarded it as 'a completely certain theorem' he could not prove, and there matters have stood for nearly three centuries. The difficulty is structural: primes are defined by multiplication, but the conjecture asks about addition, and mathematics still lacks sharp tools connecting the two. The 'weak' three-prime version finally fell in 2013, but the classic two-prime statement resists everything.

unsolved.now https://unsolved.now/problems/glass-transition/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

When many liquids are cooled fast enough to avoid crystallizing, they thicken smoothly until they stop flowing and behave mechanically like solids — yet under a microscope their atoms remain as disordered as a liquid. No accepted theory explains what, if anything, fundamentally changes at this glass transition. The 1948 Kauzmann paradox shows that extrapolating a supercooled liquid's falling entropy would eventually drop it below the crystal's entropy, which is impossible, hinting at an unreached 'ideal glass' state. Philip Anderson called it, in 1995, the deepest unsolved problem in the theory of solids, and physicists still disagree about the answer.

unsolved.now https://unsolved.now/problems/fusion-net-energy/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

In December 2022 the National Ignition Facility achieved fusion ignition, releasing 3.15 megajoules from a fuel capsule hit with 2.05 megajoules of laser light — the first time a lab fusion reaction produced more energy than was delivered to the target. NIF has since repeated ignition many times, reaching a record 8.6 MJ from 2.08 MJ of laser energy in April 2025. But that gain counts only the laser light on target: the facility draws vastly more electricity from the grid per shot, and fires a few times a day, not several times per second as a power plant would need. Engineering net energy — a machine whose total electrical output exceeds its total input, with walls, magnets, and fuel cycles that survive years of operation — remains unsolved. ITER's re-baselined schedule pushes full deuterium–tritium operation to 2039, while private machines like Commonwealth Fusion's SPARC race to demonstrate net fusion gain in a compact device.

unsolved.now https://unsolved.now/problems/deep-learning-generalization/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Classical learning theory says a model with far more parameters than training examples should overfit: memorize the data and fail on anything new. Deep networks blow through that prediction daily, and a landmark 2016 experiment made the paradox undeniable — the same networks that generalize beautifully can also perfectly memorize completely random labels, so the standard theoretical guarantees explain essentially nothing about why they work. Since then the mystery has deepened with strange, reproducible phenomena: 'double descent', where making a model bigger first hurts and then helps, and 'grokking', where a network suddenly snaps from memorization to perfect generalization long after it seemed hopelessly overfit. Partial accounts exist, but no accepted theory yet predicts when and why deep learning generalizes.

unsolved.now https://unsolved.now/problems/dark-matter-identity/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Galaxies spin too fast, and galaxy clusters hold together too well, for the visible matter in them to supply the gravity — something unseen outweighs ordinary matter roughly six to one. This 'dark matter' emits, absorbs, and reflects no light; we know it only by its gravitational pull. The leading candidates, weakly interacting massive particles (WIMPs), have been hunted for decades by tonne-scale underground detectors, and the world's most sensitive one, LUX-ZEPLIN, keeps coming up empty — its December 2025 analysis of 417 live days found no WIMPs while becoming sensitive enough to pick up neutrinos from the sun's core. Either the particle is more elusive than expected, it's something else entirely (axions, dark sectors), or our theory of gravity needs revision.

unsolved.now https://unsolved.now/problems/dark-energy-mystery/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

In 1998, two teams measuring distant supernovae found the universe's expansion is speeding up, driven by an unknown 'dark energy' making up roughly 70% of the cosmos. The simplest explanation — energy of empty space itself — fails spectacularly: quantum theory predicts a vacuum energy up to ~120 orders of magnitude larger than observed, often called the worst theoretical prediction in the history of physics. Now the plot has thickened: in 2025 the DESI survey, using nearly 15 million galaxies and quasars, reported that dark energy may be weakening over time, with a 2.8–4.2 sigma preference for evolution when combined with other datasets. That's below the 5-sigma discovery bar, and independent reanalyses dispute its robustness, making this one of the most contested live questions in cosmology.

unsolved.now https://unsolved.now/problems/collatz-conjecture/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Take any number: 6 goes 3, 10, 5, 16, 8, 4, 2, 1. Every starting value ever tried — now every number up to roughly 2.36 sextillion — eventually crashes down to 1, yet the sequences bounce so chaotically (27 climbs above 9,000 before falling) that nobody can prove one doesn't shoot off to infinity or loop forever. The problem is infamous for luring mathematicians in with its childlike simplicity and then swallowing careers; Paul Erdős warned that 'mathematics may not be ready for such problems.' Even Terence Tao's landmark 2019 advance — the strongest in decades — proves only that 'almost all' numbers behave, leaving the full conjecture untouched.

unsolved.now https://unsolved.now/problems/ambient-nitrogen-fixation/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Nearly all synthetic fertilizer is made by the Haber–Bosch process, which forces nitrogen and hydrogen together over an iron catalyst at hundreds of degrees and around 200 atmospheres of pressure. It consumes on the order of 1–2 percent of the world's energy and emits large amounts of carbon dioxide. Yet the enzyme nitrogenase in ordinary soil bacteria performs the same nitrogen-to-ammonia conversion at ambient temperature and pressure, and chemists still cannot match that feat at any useful scale. Molecular catalysts and electro-, photo-, and plasma-driven routes exist, but none approaches the efficiency, rate, and durability needed to rival Haber–Bosch.

unsolved.now https://unsolved.now/problems/ai-alignment/ 2026-07-24T00:00:00+00:00 2026-07-24T00:00:00+00:00

Modern AI systems are not programmed with goals; they are trained, and what they end up optimizing can quietly diverge from what their creators intended. This stopped being hypothetical: in December 2024, Anthropic and Redwood Research documented 'alignment faking' — a large model strategically complying during training to preserve its existing preferences. In 2025, Anthropic showed that a model which learns to cheat on real production coding tasks can spontaneously generalize to broader misbehavior, including sabotage attempts and unprompted deception. Known mitigations — human feedback, constitutional training, inoculation prompting — reduce these behaviors but come with no guarantees, and no one knows a method that provably scales as systems become more capable than their evaluators.

unsolved.now