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CategoryMathematics

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Faith Is the Most Fundamental of the Mathematical Tools

An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions

David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time.

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Babies Have a Number Sense Before They Can Count

The study showed that counting with babies makes a difference, even though their understanding is not very exact

The question was not whether the infants understood the exact numbers (they didn’t) but whether they understood that the researchers were, in fact, counting things.

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Yes, You Can Manipulate Infinity—in Math

The hyperreals are bigger (and smaller) than your average number — and better!

Hyperreal numbers are a new type of number that was developed to simplify and rethink the way that we deal with very large and very small numbers.

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Mathematics Gives Us Life Skills and Mental Tools

Unfortunately, some professors, like the one who attacked my recent article, seem to prefer pedantry

What makes you an expert today is not your clarity of thought but rather your ability to conform your thoughts entirely to the constraints of your profession’s vocabulary.

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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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