Mind Matters News and Analysis on Natural and Artificial Intelligence

TagMathematics

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Architectural curves

Don’t Leave Home Without These Three Curves

Three mathematical curves explain a lot of what happens—and doesn’t happen—in everyday life

One of the problems with modern secondary mathematics education is that it teaches lots of details about how to solve problems but provides very little insight into how to understand problems. You may have learned to solve a quadratic equation but you may not have learned what life situations generate a quadratic equation.

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Girl pushing big stone hard, impossible and useless concept

Doing the Impossible: A Step-by-Step Guide

Often, in life as in calculus, when our implicit assumptions as to why something can’t be done are made explicit, they can be disproven
Calculus textbooks are the most dry and boring presentations of mathematics I have ever seen, even though calculus offers some of the most amazing insights. Unfortunately, most mathematics texts teach only the mathematics, never the insights. Read More ›
Old calculator
Detail of an old office machine used for calculations

Machine Learning Dates Back To at Least 300 BC

The key to machine learning is not machines but mathematics

Machine learning is not a new technique, but is simply a modern extension of a tool that we have had in our toolbox since the days of the Babylonians. It continues to serve us well to help us extrapolate our data to estimate the value of unknown results and to help find the signal in noisy data.

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A pen on top of several math equations

Walter Bradley Center Fellow Discovers Longstanding Flaw in an Aspect of Elementary Calculus

The flaw doesn't lead directly to wrong answers but it does create confusion.

The lead author, Jonathan Bartlett, noted that the likely source of the bad notation was a philosophical issue. Because no one wanted to give differentials that same ontological status as other numbers, everyone presumed that the notational problems were simply the result of this fact, and no one pursued it further.

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blue digital binary data on computer screen
blue digital binary data on computer screen. Close-up shallow DOF

The Flawed Logic behind “Thinking” Computers, Part II

There is another way to prove a negative besides exhaustively enumerating the possibilities

I am publishing, in three parts and with his permission, an exchange with Querius, who is looking for answers as to whether computers can someday think like people. In the first part, we discussed why human thinking cannot be indefinitely compressed. Here is the second part: Recapping for myself what I said in Part I and mulling it over: “If all symbol strings do have a shorter representation, then so must their shorter representations. Thus, we’d end up concluding that all symbol strings can be represented by nothing, which is incoherent.” Wait, I’m getting lost. “Therefore, we conclude that only some symbol strings have a compressed representation. As a consequence, compression intelligence is only true if the physical effects of Read More ›

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STEM Education 7: Sell the Sizzle

The mathematics underlying our world is fascinating and full of surprises

In my experience, true STEM nerds are always pursuing some type of sizzle even in their spare time. Generally, the higher the academic degree, the greater the freedom STEM nerds have to pursue their sizzle of choice.

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Boy and blackboard filled with math formulas
boy in glasses, blackboard filled with math formulas background

STEM EDUCATION 2. Not Everyone Is Lucky Enough to be a Nerd

How do you identify extroverted nerds? When you are talking to them, they look at YOUR shoes
If I am made to confess that college courses in Shakespearean sonnets will make me a better person, then English literature majors had better confess that calculus makes them better people. Read More ›