The Simplest Math Problem Could Be Unsolvable
The Collatz conjecture has plagued mathematicians for decades—so much so that professors warn their students away from it
Stories by Manon Bischoff
Manon Bischoff is a theoretical physicist and editor at Spektrum, a partner publication of Scientific American.
Surreal Numbers Are a Real Thing. Here’s How to Make Them
In the 1970s mathematicians found a simple way to create all numbers, from the infinitely small to infinitely large
How String Theory Solved Math’s Monstrous Moonshine Problem
A concept from theoretical physics helped confirm the strange connection between two completely different areas of mathematics
A Wild Claim about the Powers of Pi Creates a Transcendental Mystery
Mathematicians cannot determine whether multiplying pi by itself repeatedly might produce a whole number
AI Does Math as Well as Math Olympians
Until now computers have failed to solve mathematical problems. But the AI program AlphaGeometry has succeeded in finding proofs for dozens of theorems from the International Mathematical Olympiad
Simple Math Creates Infinite and Bizarre Automorphic Numbers
Squaring numbers can have surprising consequences
How Cryptographic ‘Secret Sharing’ Can Keep Information Safe
One safe, five sons and betrayal: this principle shows how shared knowledge can protect secrets—without having to trust anyone
Simple Formula Makes Prime Numbers Easy, but a Million-Dollar Mystery Remains
A generator equation can spit out many prime numbers, but it leaves important mathematical questions unanswered
All Natural Numbers Are Either Happy or Sad. Some Are Narcissistic, Too
The number 1 is among the happiest numbers, 4 is sad, and both are narcissistic
Mathematicians Think Saudi Arabia’s Ambitious ‘Line’ City Should Be a Circle
Despite efforts to make a planned city in the Saudi Arabian desert sustainable, its layout could create problems
Candy Crush Is Complicated—Even from a Mathematical Point of View
Don’t be annoyed if you fail at a certain level of the popular game Candy Crush Saga; computers also have their problems with it
How Recommendation Algorithms Work—And Why They May Miss the Mark
Huge data sets and matrices help online companies predict what you will click next
$1 Million Will Go to the Mathematician Who Busts the ‘ABC Conjecture’ Theory
The founder of a Japanese media company has offered a large cash prize to anyone who can find a flaw in an unusual proof
Why Do Cats Land on Their Feet? Physics Explains
As it turns out, felines can survive a fall from any height—at least in theory
Infinity Is Not Always Equal to Infinity
There are infinite real and natural numbers—yet real numbers exceed natural numbers thanks to the mind-bending logic of infinities
Discovery of Elusive ‘Einstein’ Tile Raises More Questions Than It Answers
A surprisingly simple answer to a mathematical puzzle intrigues the math world
New Tool Reveals How AI Makes Decisions
Large language models such as ChatGPT tend to make things up. A new approach now allows the systems to explain their responses—at least partially
Here’s How Hackers Steal Your Password and How You Can Create a Safer One
To craft a better password, first learn how people crack them
Gift Wrapping Five Oranges Has Outwitted the Best Minds in Mathematics for Generations
Perfectly wrapping spherical objects together seems trivial, but it’s a task that has stumped mathematicians for centuries
These Are the Most Bizarre Numbers in the Universe
Most real numbers are unknown—even to mathematicians
Why the ‘Sleeping Beauty Problem’ Is Keeping Mathematicians Awake
A thought experiment that’s dividing mathematicians can help illuminate how belief shapes rational decisions
How Much Does ‘Nothing’ Weigh?
The Archimedes experiment will weigh the void of empty space to help solve a big cosmic puzzle
Information Theory Finds the Best Wordle Starting Words
Information theory can help people mathematically calculate the best starting guess for a popular online game
Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern
A new shape called an einstein has taken the math world by storm. The craggy, hat-shaped tile can cover an infinite plane with patterns that never repeat.