Is (nearly) all mathematics addition?

Click For Summary
The discussion centers on the idea that nearly all mathematics can be reduced to addition, with the original poster providing examples such as subtraction, multiplication, and division as forms of addition. While some participants acknowledge that basic arithmetic can be expressed in terms of addition, they argue that this reductionist view fails to encompass broader mathematical concepts like logarithms, calculus, and topology. Critics emphasize that many mathematical operations and theories cannot be simplified to addition alone, highlighting the complexity and diversity of mathematical fields. The conversation also touches on the limitations of this hypothesis, suggesting that while addition is foundational, it does not capture the entirety of mathematical thought. Overall, the notion that all mathematics can be reduced to addition is deemed overly simplistic and flawed.
  • #31
cmcraes said:
Division: 1/Multiplication
You are saying, Division : Division.
How does that save you from doing division?
 
Mathematics news on Phys.org
  • #32
phinds said:
How about these? Do you reckon they reduce to addition?

geometry
topology
abstract algebra
prepositional logic
Fourier analysis
Laplace transforms
differential equations
set theory
game theory

and those are just ones that come to mind and I don't know all that much about math even at the undergraduate level. I'm sure there are lots I'm leaving off that really have little or nothing to do with addition. Your hypothesis is seriously flawed.

Wow, I'm not sure who pissed in your cheerios but I'm pretty sure it wasn't the OP.
 

Similar threads

Exploring Unconventional Addition: Can Mathematics Embrace New Foundations?
  • · Replies 8 ·
Replies
8
Views
2K
A Question about intersection of coordinate rings
  • · Replies 1 ·
Replies
1
Views
796
I Zero raised to a positive real number
  • · Replies 12 ·
Replies
12
Views
2K
I Mutually disjoint sets of all integer powers?
  • · Replies 2 ·
Replies
2
Views
1K
I What is the role of geometry and dimensional operations?
  • · Replies 3 ·
Replies
3
Views
2K
I How to define addition and multiplication using Peano's axioms?
  • · Replies 12 ·
Replies
12
Views
4K
B Number of concepts of Multiplication and Addition
  • · Replies 14 ·
Replies
14
Views
2K
I The solution to a cubic equation
  • · Replies 2 ·
Replies
2
Views
2K
B The Paradox of 1 – 1 + 1 – 1 + 1 – 1 + …
  • · Replies 5 ·
Replies
5
Views
2K
I Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K