Questions tagged [number-theory]

A field of mathematics studying numbers, their properties and structures that arise from them.

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57
votes
1answer
6k views

What's the famous story about a mathematician who gave a talk without saying a word?

Years ago, I read a story about a mathematician who found a numerical counterexample to some conjecture long believed to be true. He gave a talk during which he didn't utter a single word but simply ...
25
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4answers
4k views

Irrationality of the square root of 2

We know that Pythagoreans in Ancient Greece discovered that the square root of two is an irrational number. Why was that discovery historically significant? What value was that knowledge to the ...
7
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1answer
2k views

Was there a very early culture that's number system was 12-based, like ours is 10-based?

There are several uses of 12 in some old systems of measurement. Some of them make sense given current context (There are 12 lunar cycles per year), however some of them seem to be arbitrarily chosen. ...
23
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4answers
8k views

Ancient Chinese numbering system

It has been said that the invention of zero was a great leap forward, not only in abstract understanding, but in the ability to introduce place value notation and do computations; computing using ...
3
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2answers
667 views

Can Numerology be said to be the precursor of Number Theory?

My understanding is that alchemy was a precursor to modern chemistry. Some might say that numerology, similarly, was an earlier form of what is now known as number theory, but I feel like it's a more ...
67
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3answers
9k views

What evidence is there that Fermat had a proof for his Last Theorem?

Aside from the fact that Fermat was a genius, is it probable that he actually did have a proof? Some specifics that I think would point one way or another: Would the mathematics of his day allow him ...
8
votes
1answer
459 views

What Is the Origin of the Twin Primes Conjecture?

Is there any written work by Euclid about consecutive primes differing by two? What work was done on the problem from the time of Euclid about 2,300 years ago to the time of Polignac in 1849?
20
votes
0answers
528 views

What is the modern significance of Theaetetus's classification of quadratic irrationals?

Before Eudoxus's theory of proportion there was a theory of irrationals based on continued fraction expansions, which Fowler calls anthyphairesis. Theaetetus is said to develop a classification of ...
5
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1answer
671 views

Is there a translation of Gauss' work on Gaussian integers?

Gauss introduced the Gaussian integers in an 1832 Latin work named Theoria residuorum biquadraticorum. I believe there is a German translation available. Is there an English, or possibly French ...
8
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1answer
138 views

How did Mersenne discover Mersenne primes?

So, I was wondering, how did Mersenne come up with the formulae $2^p-1$? Do we have any ideas of how it came to be?
7
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1answer
987 views

Why is the Sophie Germain Identity called thus?

Several authors (z.B.: Arthur Engel in his Problem-Solving Strategies, Alexander Bogomolny in this entry of the Cut the Knot website) refer to the following (straightforward) consequence of the ...
14
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6answers
2k views

Have numbering systems other than base ten ever been used or popular?

Base ten makes a lot of sense as a numbering system, given the number of digits humans typically have on their hands. That said, some older money systems weren't based on the number of fingers we ...
6
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1answer
1k views

What is the most ancient civilization that used base-16 (hexadecimal) number system?

What is the first or most ancient civilization to use a base-16, hexadecimal number system?
4
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1answer
198 views

What changes in mathematics resulted in the change of the definition of primes and exclusion of 1?

Why 1 is not prime? I read in this article that G.H Hardy explicitly included 1 as a prime in the first 6 editions of "A Course in Pure Mathematics", published between 1908-1933. He updated ...