**An Alternative to Conventional Neural Networks Could Help Reveal What AI Is Doing behind the Scenes**

Despite their performance, current AI models have major weaknesses: they require enormous resources and are indecipherable. Help may be on the way

**Manon Bischoff** is a theoretical physicist and editor at *Spektrum*, a partner publication of *Scientific American*.

MathMay 28, 2024

**An Alternative to Conventional Neural Networks Could Help Reveal What AI Is Doing behind the Scenes**

Despite their performance, current AI models have major weaknesses: they require enormous resources and are indecipherable. Help may be on the way

MathematicsMay 7, 2024

The Mathematical Case for Monkeys Producing Shakespeare—Eventually

An infinite number of random events can produce just about anything if you have quintillions of years to wait

Artificial IntelligenceMay 6, 2024

AI Could Help Find a Solution for String Theory

String theory could provide a theory of everything for our universe—but it entails 10^{500 }(more than a centillion) possible solutions. AI models could help to find the right one

MathematicsApril 18, 2024

Mathematicians Explain Why Some Lengths Can’t Be Measured

Can you assign a size to every object? The surprising answer is no

MathematicsMarch 12, 2024

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

MathematicsFebruary 14, 2024

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

MathematicsFebruary 5, 2024

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

MathematicsJanuary 24, 2024

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

Artificial IntelligenceJanuary 17, 2024

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

MathematicsJanuary 11, 2024

Simple Math Creates Infinite and Bizarre Automorphic Numbers

Squaring numbers can have surprising consequences

MathematicsDecember 7, 2023

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

MathematicsNovember 16, 2023

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

MathematicsOctober 24, 2023

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

MathematicsSeptember 13, 2023

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

MathematicsSeptember 12, 2023

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

MathematicsAugust 17, 2023

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

MathematicsJuly 28, 2023

$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

MathematicsJuly 24, 2023

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

MathematicsJuly 13, 2023

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

MathematicsJuly 1, 2023

Discovery of Elusive ‘Einstein’ Tile Raises More Questions Than It Answers

A surprisingly simple answer to a mathematical puzzle intrigues the math world

Artificial IntelligenceJune 15, 2023

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

MathematicsJune 13, 2023

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

MathematicsJune 6, 2023

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

MathematicsMay 23, 2023

These Are the Most Bizarre Numbers in the Universe

Most real numbers are unknown—even to mathematicians