Is (nearly) all mathematics addition?

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SUMMARY

The discussion centers on the hypothesis that nearly all mathematics can be reduced to addition. Participants provide various examples, including the simplification of subtraction to addition of negative numbers, multiplication as repeated addition, and division as the inverse of multiplication. While some agree that basic arithmetic operations can be expressed through addition, others argue that more complex mathematical concepts, such as logarithmic functions, calculus, and abstract algebra, cannot be simplified in this manner. The conversation highlights the limitations of the hypothesis and the complexity of mathematical structures beyond basic arithmetic.

PREREQUISITES
  • Understanding of basic arithmetic operations: addition, subtraction, multiplication, and division.
  • Familiarity with mathematical concepts such as exponents and logarithms.
  • Knowledge of calculus, including Taylor series expansions and limits.
  • Basic understanding of abstract algebra and set theory.
NEXT STEPS
  • Explore the properties of logarithmic functions and their relationship to addition.
  • Study Taylor series and their applications in approximating functions.
  • Investigate the fundamentals of abstract algebra, focusing on groups and operations.
  • Learn about the principles of calculus, particularly differentiation and integration.
USEFUL FOR

Mathematicians, educators, students, and anyone interested in the foundational concepts of mathematics and their interrelations.

  • #31
cmcraes said:
Division: 1/Multiplication
You are saying, Division : Division.
How does that save you from doing division?
 
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  • #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.
 

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