# Questions tagged [arithmetic]

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### Regula Pigri: How far does it date back?

Regula pigri, or rule of the lazy, is a method of multiplication of single-digit numbers. If one is to multiply 6 by 8, one would start by bending one's fingers like so: B B B B S　　　　　　　　B B S S S ...
1 vote
66 views

### When were Peano axioms formulated purely in first-order logic?

It is mentioned on the Wikipedia article about Peano axioms that: The ninth, final axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes ...
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### How did negative numbers “force themselves” onto Cardano, and was it analogous to how imaginary numbers were forced upon him?

I was reading “A brief history of numbers” by Corry, but I came across a part that confused me. Cardano accepted the law of signs for “subtractions” proposed by an older group of Italian ...
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### Did Rafael Bombelli write any commentary about his rules for arithmetic involving negative numbers?

Rafael Bombelli was the first European mathematician to write about the laws of arithmetic for negative numbers. On Wikipedia I read that he wrote: “Minus 5 times minus 6 makes plus 30”. I also read ...
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1 vote
158 views

### Is there any meaningful history behind harmonic mean?

I am trying to understand the origin of harmonic mean and get an intuitively feel for why it was invented in the first place. I have surfed the web but I keep seeing things like harmonic series / ...
280 views

### How was addition and multiplication of natural numbers defined before 1870 (Cantor and modern set theory)?

I know how to define addition and multiplication of natural numbers using set theory, but I think that before Cantor, mathematicians did not try to use set theory as a foundation for mathematics (I ...
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1 vote
149 views

### How did someone discover LCM?

How did someone came up with an idea that if we do prime factorization of two numbers and then multiply all the prime factors but including common ones only once, we will get a number that is the ...
• 11
86 views

### Did the Romans really use the binomial formula to calculate products?

I'm not quite sure if this is the right place to ask this question (in fact, I was redirected to this SE from the Math Stackexchange), but it's probably more fitting than the original posting place. I ...
85 views

### A text or YouTube channel with a comparison between pre-Cartesian with post-Cartesian mathematics

Is there some good book or YouTube channel that make a good comparison/distinctions between the mathematics before René Descartes, with the mathematics after Descartes? In the short article "The ...
163 views

### 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 (...
227 views

### 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 (...
4k views

### 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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1 vote
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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 ...
327 views

### 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 ...
298 views

### Has 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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### 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 ...
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