Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

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Chapel Dome at the US Naval Academy

Monday Microsofty 97:  Mad Hatters Flip Their Lids

What are the chances that all of the naval academy graduates would find their own hats in a random toss?

There is more than one solution to last week’s Queens Problem because the board can be rotated — but we present one here.

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Cosmic Geometry: A Celestial Blueprint

Top Mathematicians Issue Letter Warning About a Rush to AI

Fields Medalists are concerned that a rush to produce answers could come at the expense of careful explanation and shared understanding

AI can solve a problem without understanding the proofs so the question arises, was anything learned that can be passed on?

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Close-up of computer screen displaying code at night.

What Exactly Was AI’s Breakthrough in Hard Math?

Claude translated an already proven theorem into a detailed computer-related derivation, which is much more difficult than, say, translating it into Cantonese

Meanwhile, some are asking if Claude’s Navier–Stokes proof really originated with a researcher and a math prof using the system.

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reforestation set of young trees trunks in pots

Monday Microsofty 94:  A Tree Planting Dilemma

This week's puzzle sounds simple but it involves thinking in terms other than squares

The answer to last week’s “count the squares” puzzle can be turned into a formula that can be applied to any number of dimensions.

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Abstract background 3D, many cubes with neon purple blue glow on black interesting science technology background, 3D render illustration.

Monday Microsofty 93: Square Dance With the Mathematicians!

How do we determine how many squares there are in squares of squares? Or cubes of cubes?

Hint for the handshake problem in Microsofty 92: Friedrich Gauss (1777–1855) provided a formula for this.

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two very nerd brains office workers

Monday Microsofty 92: When the Nerd Enters a Room…

Shaking hands is expected. Here’s a math question about the custom, to delight the true nerds among us

A hint for Microsofty 91: Where might Jimmy the Mooch have found some spare energy?

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Abstract multiverse with galaxies in the background. Generative Ai

Searching for Any World at All in the Many-Worlds Interpretation

If the many-worlds interpretation (multiverse theory) originated by Hugh Everett is understood realistically as it was intended to be, it can easily be rejected

While an interpretation might survive many difficulties, it cannot survive the failure to provide the one thing it promises — and even after seventy years, “many worlds” has yet to produce even one.

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Close up of old English dictionary page with word vocabulary

Monday Micro Softy 89:  Double Negatives are a No-No

Actually, they do have their uses — for example, if politicians are trying to correctly state views while making them hard to understand

To solve last week’s puzzle: you are told how many heads there are so start by flipping that number of coins.

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Stack of american gold coins background. US half Dollar coin with eagle. Concept of a stable banking system and economy.

Monday Micro Softy 88:  Flipping Gold Coins

Computer programmers must be good at math. The solution to this week's Micro Softy uses math — but you don’t need to know the math to impress your friends

The answer to Micro Softy 87 depends on understanding which number a given sequence of the code represents.

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Group of the small termite on decaying timber. The termite on the ground is searching for food to feed the larvae in the cavity.

Monday Micro Softy 81: Termites Are Surprisingly Smart

Provided we agree to count swarm intelligence, which we also use in computer science

Swarm intelligence enables the colony to converge on the shortest and most efficient path to food without any individual being especially smart.

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AI and math concept

What AI Has and Hasn’t Solved Recently in Math

We need to look at the distinction between horizontal and vertical innovation

AI displays very impressive horizontal integration (integrating existing concepts) but not vertical integration (entirely new inventions).

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Mathematician Deciphers Mathematical Equations Defining the Universe's Structure

Monday Microsofty 79: The Last Digits in Fermat’s Last Theorem

Did Andrew Wiles really prove Fermat’s Last Theorem? Today we offer you a chance to decide

About last week’s MicroSofty: Think of the probability issue as just a distraction…

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Abstract Numbers background - Mathematical, Numbers concept. 3d rendering

Micro Softy 56:   Elon Musk Parody’s Circle of Numbers

The circle of numbers looks pretty simple until you start thinking about it...

If you suspected that last week’s talk of baseball was just a distraction from the real puzzle hint, now you can find out.

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A Collage of Baseball Players and Memorabilia

Monday Micro Softy 55: “It Happens Every Spring”

Baseball, that is. Here’s a puzzle that takes in baseball's favorite season, summer

To solve last week’s puzzle, you don’t need to know the distance. Check the problem again for the number you do need to know.

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Two Commercial Airliners Pass Each Other at High Altitude

Micro Softy 54: A Plane Problem for Aspiring Engineers

The senator is leaving Washington to avoid the governor and their planes are headed in opposite directions

Today’s Micro Softy tests whether you are clever enough with math to code computers or be an engineer. Here’s the story: Senator Kornn did not like Governor Friar. Both were from Texas. When Kornn learned that Governor Friar was visiting Washington, DC, Kornn said “This town’s not big enough for the both of us.”  So Kornn decided to leave DC for that period. Kornn and Friar get on planes at the same time. One was at Reagan International Airport in DC and the other was at the Dallas Fort Worth (DFW) Airport. So each was flying to the other’s airport. Both planes took off at the same time. After a while, Kornn looked out of his first-class window and saw Read More ›

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Protecting Balance Between Percentage And House Model

Home Ownership: Madness Over 30-Year Mortgages

It is tempting to put borrowing and investment decisions in separate mental buckets, but they are intimately related

When considering a mortgage, the correct comparison is not total payments but the return on the borrowed money versus the loan’s annual percentage rate.

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