open problems

The conjectures

Every paper Pith reviews gets its core claim, load-bearing premise, and falsifier extracted into a claim graph. These pages collect the reviewed papers whose claims name a famous open problem, so you can watch each one being attacked in real time.

Dark Matter 500+ reviewed papers
Around 85 percent of the matter in the universe interacts gravitationally but has never been directly detected. What is it?
Dark Energy 500+ reviewed papers
The accelerating expansion of the universe, and the 120-order-of-magnitude gap between predicted and observed vacuum energy.
Quantum Gravity 500+ reviewed papers
Reconciling general relativity with quantum mechanics: the missing theory underneath both.
Matter-Antimatter Asymmetry 464 reviewed papers
The Big Bang should have made matter and antimatter in equal parts. It did not, and the Standard Model cannot explain why.
The Hubble Tension 252 reviewed papers
Early-universe and late-universe measurements of the expansion rate disagree at 5 sigma. One of them, or the model, is wrong.
P versus NP 168 reviewed papers
Whether every problem whose solution can be checked quickly can also be solved quickly. The central open question of computer science.
The Riemann Hypothesis 167 reviewed papers
All nontrivial zeros of the Riemann zeta function lie on the critical line. The oldest open problem on Hilbert's list and a Clay Millennium Prize problem.
The Measurement Problem 104 reviewed papers
What actually happens when a quantum superposition becomes a definite outcome? A century in, there is still no agreed answer.
The Hierarchy Problem 66 reviewed papers
Why is the Higgs mass 17 orders of magnitude below the Planck scale? Quantum corrections say it should not be.
The Strong CP Problem 63 reviewed papers
Why does quantum chromodynamics conserve CP symmetry when nothing in the theory forces it to? The axion was invented to answer this.
High-Temperature Superconductivity 29 reviewed papers
No accepted mechanism explains superconductivity in the cuprates, and a room-temperature superconductor remains the materials-science grail.
The abc Conjecture 23 reviewed papers
A deep statement relating the additive and multiplicative structure of integers, with dozens of famous corollaries.
The Hodge Conjecture 17 reviewed papers
Whether certain de Rham cohomology classes on projective varieties are algebraic. A Clay Millennium Prize problem.
Protein Folding 13 reviewed papers
Predicting structure is largely solved by machine learning; deriving the folding process and its energetics from first principles is not.
The Collatz Conjecture 12 reviewed papers
Iterate n -> n/2 or 3n+1; does every starting value reach 1? Simple to state, unproven since 1937.
Birch and Swinnerton-Dyer 10 reviewed papers
The rank of an elliptic curve equals the order of vanishing of its L-function at s = 1. A Clay Millennium Prize problem.
Goldbach's Conjecture 10 reviewed papers
Every even integer greater than 2 is the sum of two primes. Verified to astronomical bounds, never proven.
The Twin Prime Conjecture 4 reviewed papers
Are there infinitely many primes p with p + 2 also prime? Zhang's 2013 bounded-gaps breakthrough brought it within reach.
Navier-Stokes Regularity 3 reviewed papers
Whether smooth initial data for the 3D Navier-Stokes equations can develop singularities in finite time. A Clay Millennium Prize problem.
Yang-Mills Mass Gap 0 reviewed papers
Proving that quantum Yang-Mills theory exists rigorously and has a positive mass gap. A Clay Millennium Prize problem.