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Tag: Graph Theory

New Breakthrough Brings Matrix Multiplication Closer to Ideal | Quanta Magazine

IntroductionComputer scientists are a demanding bunch. For them, it’s not enough to get the right answer to a problem — the goal, almost always,...

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A Triplet Tree Forms One of the Most Beautiful Structures in Math | Quanta Magazine

IntroductionMost people are only familiar with a handful of numbers that can’t be written as fractions, like $latex sqrt{2}$ or $latex pi$. But such numbers,...

The Hidden Connection That Changed Number Theory | Quanta Magazine

IntroductionThere are three kinds of prime numbers. The first is a solitary outlier: 2, the only even prime. After that, half the primes leave...

Complexity Theory’s 50-Year Journey to the Limits of Knowledge | Quanta Magazine

IntroductionIn the first week of the fall semester in 2007, Marco Carmosino dragged himself to a math class required for all computer science majors...

Math That Lets You Think Locally but Act Globally | Quanta Magazine

IntroductionIn math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of...

To Move Fast, Quantum Maze Solvers Must Forget the Past | Quanta Magazine

IntroductionImagine you visit a maze with some friends. You emerge from the exit shortly after going in, and wait around for hours before your...

Mathematicians Discover New Way to Predict Structure in Graphs | Quanta Magazine

IntroductionIt has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field...

The Simple Geometry That Predicts Molecular Mosaics | Quanta Magazine

IntroductionOn a Saturday afternoon in the fall of 2021, Silvio Decurtins was leafing through a paper with a title that could have been pulled...

How Math Has Changed the Shape of Gerrymandering | Quanta Magazine

IntroductionUntil recently, gerrymandered districts tended to stick out, identifiable by their contorted tendrils. This is no longer the case. “With modern technology, you can...

A Very Big Small Leap Forward in Graph Theory

IntroductionOn March 15, intriguing seminar announcements sent rumblings through the field of combinatorics, the mathematical study of counting. Three collaborators planned to give coordinated...

Advancements in Graph Theory: A Significant Breakthrough in Small-Scale Progression

Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to model relationships between objects....

How Randomness Improves Algorithms

IntroductionSince the very first days of computer science — a field known for its methodical approach to problem-solving — randomness has played an important...

The Colorful Problem That Has Long Frustrated Mathematicians

IntroductionOne of the great episodes in the history of mathematics began on October 23, 1852. In a letter to Sir William Rowan Hamilton, Augustus...

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