Arithmetic versus mathematics.

  • Context: High School 
  • Thread starter Thread starter JWHooper
  • Start date Start date
  • Tags Tags
    Arithmetic Mathematics
Click For Summary

Discussion Overview

The discussion revolves around the relationship between arithmetic and mathematics, exploring whether arithmetic is considered a part of mathematics and its necessity for higher mathematical concepts. Participants engage in a debate regarding the definitions and roles of arithmetic in the broader context of mathematical study.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that arithmetic is merely a set of calculations and not truly mathematics.
  • Others propose that while arithmetic is essential for understanding basic mathematical concepts, it is distinct from higher mathematics.
  • A participant cites a quote by Leopold Kronecker, suggesting that integers are fundamental to mathematics.
  • There is a suggestion that one can learn algebra without mastering arithmetic, although this claim is contested.
  • Some participants emphasize the importance of arithmetic as a foundational skill necessary for higher mathematics, including numerical analysis.
  • Confusion arises regarding the distinction between arithmetic as a part of mathematics and its necessity for advanced mathematical study.
  • References to Serre's "A Course in Arithmetic" are made to support differing views on the definition and scope of arithmetic.

Areas of Agreement / Disagreement

Participants express differing opinions on whether arithmetic is part of mathematics, with no consensus reached. Some believe they are distinct, while others argue for the integral role of arithmetic in mathematical education.

Contextual Notes

Participants highlight the ambiguity in the definitions of arithmetic and mathematics, as well as the varying interpretations of what constitutes higher mathematics. The discussion reflects a range of perspectives without resolving these complexities.

Is arithmetic part of mathematics?

  • Yes! Arithmetic is needed in order to do higher maths.

    Votes: 14 87.5%

  • No! You can learn how to do algebra without any arithmetic at all.

    Votes: 2 12.5%
  • Total voters
    16
JWHooper
IMO, I don't really think arithmetic is really mathematics. It's just pure calculations, that's all.
 
Mathematics news on Phys.org
Some arithmetic is an essential part of Mathematics. You certainly do not need full mastery of arithmetic in order to study "elementary algebra", but you still must have basic understanding of most of arithmetic in order to effectively begin studying "elementary algebra".

Interesting: Why do some people do well with Arithmetic in grades 1 through 7, and then struggle so hard with Introductory Algebra?
 
JWHooper said:
IMO, I don't really think arithmetic is really mathematics. It's just pure calculations, that's all.

TOTALLY WRONG... how can you build real numbers? without real numbers you cannot have an algebra well defined or at least the usual one ...


quote from a genus:

God made the integers; all else is the work of man.
Leopold Kronecker

regards
marco
 
"Is arithmetic part of mathematics?" No, not really. I've always considered them distinct.

"Arithmetic is needed in order to do higher maths." Oh certainly, just like math is needed to do physics.

"You can learn how to do algebra without any arithmetic at all." Not really.
 
I refer you to Serre's "A course in arithmetic" since you do not seem to understand the meaning of the word.

https://www.amazon.com/dp/0387900403/?tag=pfamazon01-20

Hardcover: 132 pages
Publisher: Springer; 1st ed. 1973. Corr. 5th printing edition (October 10, 1996)
Language: English
ISBN-10: 0387900403

Serre's A Course in Arithmetic is a concentrated, modern introduction to three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms.
 
Last edited:
I am confused. I see two distinct and non-mutually-exclusive questions here:
1] Is arithmetic part of mathematics? (your title and your post)
2] Is arithmetic needed to do higher order math? (your poll)

Which question do you want the answer to?
 
mathwonk said:
I refer you to Serre's "A course in arithmetic" since you do not seem to understand the meaning of the word.

Meh. That meaning of "arithmetic" was old fashioned even back when the book was published.
 
Arithmetic is the most useful and therefore the most important part of mathematics. You don't need to be fast or good at it, but you do need it before you can do higher maths.
 
CRGreathouse said:
"Is arithmetic part of mathematics?" No, not really. I've always considered them distinct.

"Arithmetic is needed in order to do higher maths." Oh certainly, just like math is needed to do physics.

"You can learn how to do algebra without any arithmetic at all." Not really.
Hello, CRGreathouse! This is johnny from computer science and math forum. Nice meeting you in this forum! I hope to see you around in here as well, as far as I need help on my physics homework!
 
  • #10
Numerical analysis requires arithmetic, does that count as higher mathematics? Certain aspects certainly do, IMO.
 
  • #11
Dragonfall said:
Arithmetic is the most useful and therefore the most important part of mathematics. You don't need to be fast or good at it, but you do need it before you can do higher maths.

I'd say the same about high-school algebra and physics.

Gib Z said:
Numerical analysis requires arithmetic, does that count as higher mathematics? Certain aspects certainly do, IMO.

Ah, that's a good point.
 

Similar threads

High School Confused about ciphers in the book 'Arithmetic for the Practical Man'
  • · Replies 13 ·
Replies
13
Views
3K
High School Arithmetic progression, Geometric progression and Harmonic progression
  • · Replies 5 ·
Replies
5
Views
2K
High School Is Each Stage of Pascal's Triangle Special?
  • · Replies 11 ·
Replies
11
Views
2K
Is mathematics invented or discovered?
  • · Replies 64 ·
3
Replies
64
Views
4K
High School Rabbit and Turtle Race: A Mathematical Analysis of Infinity and Probability
  • · Replies 17 ·
Replies
17
Views
4K
High School Understanding the Relationship Between a Function and Its Inverse
  • · Replies 11 ·
Replies
11
Views
2K
High School Three Squares Problem
  • · Replies 10 ·
Replies
10
Views
2K
High School Creating Log Tables: Briggs' 400-Year-Old Accomplishment
  • · Replies 10 ·
Replies
10
Views
3K
High School A proper comprehensive rule for arithmetic operation precendence
  • · Replies 1 ·
Replies
1
Views
2K
High School Extending the Fundamental Theorem of Arithmetic to the rationals
  • · Replies 35 ·
2
Replies
35
Views
5K