Collatz Conjecture: Why 3n+1 Has Defied Proof Since 1937
The Collatz conjecture asks whether the 3n+1 rule always reaches 1. A child can follow it, yet it has resisted proof since 1937.
Physics and Mathematics
54 glossary terms
Physics and mathematics are the languages scientists use to describe the structure of reality. The terms here range from the familiar (prime numbers, Planck length) to concepts that still unsettle physicists a century after they were proposed, such as wave-particle duality and quantum entanglement. Mathematics runs alongside, not because physics cannot stand without it, but because so many physical ideas become precise only when expressed in the shorthand of equations. This glossary covers the quiet workhorses of classical physics, the strangeness of quantum mechanics, and the mathematical structures that let theorists probe phenomena no instrument can yet reach.
Riemann Hypothesis: The Conjecture That Controls Prime Numbers
The Riemann hypothesis claims all nontrivial zeros of the zeta function lie on a single line. If true, it pins down exactly how far prime numbers can stray from their expected pattern.
Mersenne Primes: The Largest Primes Ever Found
A Mersenne prime is a prime number of the form 2^n - 1, where n is itself prime. Only 52 are known. Learn how the Lucas-Lehmer test works and why GIMPS keeps finding record-breaking primes.
SAT Solvers: How Software Cracks the Hardest Logic Problems
SAT solvers determine whether Boolean logic formulas can be satisfied. The problem was the first ever proved NP-complete.
Yield Stress Fluids: Where Solids Begin to Flow
A yield stress fluid behaves as a solid when undisturbed but flows once force exceeds a threshold called the yield stress.
Standard Model: Particles, Forces, and What It Cannot Explain
The Standard Model classifies all known elementary particles and describes three fundamental forces. It is the most tested theory in physics, yet it cannot account for gravity, dark matter, or dark energy.
Quantum Entanglement Experiments: From EPR to the Nobel Prize
Quantum entanglement experiments test correlations between particles whose quantum states are linked, confirming that nature violates classical limits. From the 1972 Freedman-Clauser test to the 2022 Nobel Prize.
Langlands Program: Mathematics' Bridge Between Worlds
The Langlands program connects number theory and representation theory, proposing that prime numbers and symmetry share deep, hidden structures.
Laser Cooling: How Light Slows Atoms to Near Absolute Zero
Laser cooling uses laser light to reduce atomic motion, lowering temperatures to millionths or billionths of a degree above absolute zero. It enables atomic clocks, quantum computing, and Bose-Einstein condensates.
Wave Refraction: How Depth Steers Ocean Waves Toward Shore
Wave refraction is the bending of ocean waves as they move into shallower water, reshaping coastlines by concentrating energy on headlands.