Mathematics in Our World

Overview: What is mathematics?

Mathematics originates from the Greek term "mathemata," encompassing all knowledge or subjects of study.
It involves the study of quantitative or spatial issues.
Numeration is the earliest form of mathematics.
Possible explanation for the development of numeration systems:
- Ancient tribesmen were hunters.
- Climate changes forced them to shift their living patterns.
- Hunters transitioned into farmers, focusing on harvests and herds.
- They needed to determine land dimensions.
- Farmers also observed seasonal changes.
- Self-sufficient agricultural communities gradually evolved into larger units with a single government.
Mathematics arose from the need to address practical quantitative necessities.

Mathematical Platonism posits:
- The existence of abstract objects (nonspatiotemporal, nonphysical, and nonmental).
- The existence of true mathematical sentences that accurately describe these objects.
- Various formulations, reformulations, and antimotions are attributed to Platonism.
Three theses of mathematical platonism:
- Existence: Mathematical objects exist.
- Abstractness: Mathematical objects are abstract.
- Independence: Mathematical objects are independent of intelligent agents, their language, thought, and practices.

Founded by philosopher Immanuel Kant.
Mathematics originates from the human mind, not the physical world.
The mind possesses forms of space and time, called modes of perception or intuition.
Metaphysical Foundations of Natural Science (1786).
The world of science consists of sense impressions arranged and controlled by the mind.
Led by Dutch mathematician Luitzen Egbertus Jan Brouwer in the early 20th Century.
Every mathematical construction (real numbers, proofs, theorems, etc.) is a mental construction.
Infinite constructions can never be completed, but arbitrarily large finite initial parts can.
Intuitionism rejects non-constructive existence proofs.

Spearheaded by English philosophers Bertrand Russell and Alfred North Whitehead.
Logicism asserts that everything in mathematics is derivable from principles of logic.
Logicians view mathematics as an activity to be developed.
Russell and Whitehead authored Principia Mathematica – Foundation of Mathematics.
Logicians argue that logic can provide definitions of primitive concepts, from which first principles can be derived.
Strong logicism states that all mathematical truths in a particular branch are logical truths, while weak logicism isolates truth only within the scope of a theorem.

Founded by German mathematician David Hilbert.
Mathematics should be developed through axiomatic systems.
Hilbert asserts that whole numbers are inherently involved in the development of logic.
Numbers can be symbols, and physical objects can represent numbers.
Mathematics cannot be deduced from logic alone; self-evident statements (postulates or axioms) are necessary for systematic development.
Philosophically, Mathematics stands on the establishment of reality and truth.

Arithmetic
Numeration (including Hind-Arabic, Roman, Greek, Egyptian, Babylonian, Chinese, and Magar systems)
- Examples of numeration in different systems (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 50, 100)

Election
Census Report
Construction Project
Task Scheduling
Crime Statistics
Price Setting
Tax Collection
Outreach Programs
Expenses in the Market
Travelling to Community Establishments
Mathematics is a tool to address particular problems or concerns in our everyday living.