Friday, August 11, 2023

Students Unravel Widely Believed Math Conjecture

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NUMBER THEORY | ALL TOPICS

 

Two Students Unravel a Widely Believed Math Conjecture

By MAX G. LEVY

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.

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EVOLUTION

 

Even Synthetic Life Forms With a Tiny Genome Can Evolve

By YASEMIN SAPLAKOGLU

By watching "minimal" cells regain the fitness they lost, researchers are testing whether a genome can be too simple to evolve.

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Related: 
Most Complete Simulation of a Cell
Probes Life's Hidden Rules

By Yasemin Saplakoglu (2022)

EXPLAINERS

 

Math's Famous Map Problem: The Four-Color Theorem

Video by JOY NG

Can you fill in any map with just four colors? The famous four-color theorem says you can. But a proof eluded mathematicians for more than a century.

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Related: 
The Colorful Problem That Has
Long Frustrated Mathematicians

By David S. Richeson

ALGORITHMS

 

Risky Giant Steps Can Solve Optimization Problems Faster

By ALLISON PARSHALL

New results break with decades of conventional wisdom for the gradient descent algorithm.

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Related: 
Computer Scientists Discover
Limits of Major Research Algorithm

By Nick Thieme (2021)

ASTRONOMY

 

Exoplanets Could Help Us Learn How Planets Make Magnetism

By JONATHAN O'CALLAGHAN

Astronomers made the first detection of what appears to be a magnetic field made by a rocky exoplanet.

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Related: 
A Dream of Discovering
Alien Life Finds New Hope

By Joshua Sokol (2022)

Around the Web

Ready, Set, Math
The ancient game of Set is based on rich mathematics. For Numberphile, the mathematician Catherine Hsu explains the modular arithmetic at the heart of the game and some more challenging extensions of Set that she helped invent. In Set, players try to find special triples of cards in a deck. It's possible for a collection of cards to have no such triples, but the largest possible size of such a "cap set" is 20 cards. In 2016, Erica Klarreich wrote for Quanta about a new proof that placed bounds on cap sets for larger extensions of the game.

Sun-ergy
Astronomers found that our sun blasts out a surprising amount of high-energy radiation. Their theoretical models can't account for the wealth of photons at those energies, reports Monisha Ravisetti for SPACE.com. The new measurement follows up on previous surprising findings from when astronomers examined the sun's radiation at slightly lower energies. Natalie Wolchover reported on the mystery of the sun's excess gamma radiation in 2019. In February, Katie McCormick reported for Quanta on the new measurement at higher energies. The measurement also revealed the energy at which the plethora of photons steeply drops off. That cutoff might hint at what's going on.
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