Questions tagged [arithmetic]

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Are there any arithmetic problems studied by Euler still open?

Fermat's last theorem, which Euler had studied in the case of certain exponents, was only solved in the 1990s. Also, a counterexample to Euler's sum of powers conjecture has been found quite recently (...
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2 votes
1 answer

Is there a complete translation of "Arithmetices principia" by Peano?

If I understand correctly, Arithmetices principia: nova methodo exposita is one of the most important works covering the axiomatisation of arithmetic. I was surprised that no translation into English (...
14 votes
3 answers

What does this cover of a 1508 German book on arithmetic depict?

In a 1508 German book on arithmetic for merchants, this image appears on the cover (high resolution and context here): What is this depicting? Who are these people and what are their roles? In ...
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Does arithmetic go back before 2000 BC [duplicate]

There are various documents stating that arithmetic was first seen in 2000 BC, but wondered whether if there were any signs of it before?
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Is multiplication postulated axiomatically in Peano arithmetic?

I figured this question is better suited to this stackexchange. I give some mathematical details, but this is primarily an HSM question. According to this post, the existence of multiplication in ...
4 votes
2 answers

Why did the romans use IV and why doesn't it overcomplicate things?

Ok so if the Romans did not use things like IX and IV and XC etcetera then addition and subtraction would be almost as instant as it is in our number system. However with the new system it seems to me ...
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1 vote
1 answer

Was the idea that the result of division of positive number by negative number should be negative ever been controversial?

If we divide a positive number by another positive number, the result becomes greater as the divisor becomes smaller. If we continue this logic, division by a negative number should be greater than ...
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4 votes
0 answers

Where is First-Order Peano Arithmetic first clearly formulated?

I really should know this, but ... When/where/by whom was first-order Peano Arithmetic first clearly and explicitly formulated in a recognizably modern form (perhaps exact notation apart) -- with the ...
6 votes
2 answers

Did Archimedes view fractions as "numbers"?

For quite some time I had the wrong impression that classical Greek mathematicians didn't use fractions. (I don't remember where I had this from.) But I recently looked into Heath's book about ...
3 votes
2 answers

Who Invented The Number Line?

Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?