World Solve

Once deployed, a model could be subtly altered or poisoned without obvious signs, potentially changing its behavior in harmful ways. There's no simple, universal way yet to verify a model is exactly as it was originally trained.

Countless websites, articles, and pages vanish permanently when companies shut down or servers go offline. Without better and more complete web archiving, we risk losing large chunks of internet history.

Even experienced teams regularly introduce bugs into complex software, some of which cause expensive failures. Languages or tools that can mathematically guarantee certain classes of bugs can't exist would be a major step forward.

Homes filled with gadgets from different brands often struggle to talk to each other properly, frustrating users and limiting real automation. A shared, open standard would fix this fragmentation.

These particles carry more energy than anything we can produce on Earth, and we still don't know exactly what cosmic event launches them our way. Identifying the source could reveal entirely new astrophysical processes.

This period, known as cosmic inflation, is widely accepted as a concept but the exact physical mechanism driving it remains unproven. Confirming it would close a major gap in our understanding of the universe's first moments.

The leading theory involves a massive collision with early Earth, but several details still don't perfectly match the evidence we've collected from lunar samples. A fuller explanation would clarify Earth's own early history too.

Some outer moons hide liquid oceans beneath thick ice, and possibly conditions that could support life. Getting real data from beneath that ice remains a major unsolved engineering and mission challenge.

Fast radio bursts flash briefly and then vanish, and we still don't fully understand what causes them. Some theories point to exotic stars, but no explanation is fully confirmed yet.

Low gravity and different light conditions slow plant growth and change nutrient uptake in ways we don't fully understand yet. Solving this is essential for any long-duration space mission that needs fresh food.

This mismatch is part of the evidence for dark matter, but the details of how it shapes galaxy rotation are still not fully worked out. A better model would sharpen our understanding of galaxy formation.

We've confirmed thousands of exoplanets, but identifying which ones could truly support life requires data we mostly don't have yet. A clearer count would refocus the search for life beyond Earth.

Earth's magnetic field protects us from solar radiation, but the dynamo process that generates it deep underground is still only partly understood. This matters for predicting how long that protection will last.

If P equaled NP, countless hard problems in logistics, cryptography, and optimization could be solved efficiently, but most computer scientists suspect they can't. This remains the most famous open question in computer science.

Gödel's incompleteness theorems already showed some truths escape any fixed formal system, but the full boundary between provable and unprovable truths remains an active area of exploration. This shapes how we understand the limits of formal reasoning itself.

This weaker cousin of Goldbach's Conjecture illustrates how even modest-sounding claims about primes can remain unproven for centuries. It highlights how little we still understand about the raw arithmetic of prime numbers.

This difficulty is exactly what keeps most modern encryption secure, since multiplying primes together is easy but reversing the process is not. If an efficient method were found, it could upend the security of the internet as we know it.

Mathematicians have many tools for distinguishing knots, but no single method works perfectly and efficiently for every possible case. This unsolved problem sits at the heart of the mathematical field of knot theory.

This question, closely related to the once-open Poincaré Conjecture, has been resolved in three dimensions but opens further mysteries in higher-dimensional analogues. Exploring these generalizations remains an active area of topology.

Some sequences and structures appear chaotic without ever settling into repetition, and proving whether repetition is truly avoidable in specific systems remains unresolved. This connects deeply to dynamical systems and number theory.