The subject of language, logic and proofs… MATHEMATICS The subject of language, logic and proofs…

Is Math a discovery or an invention? Discuss in your table groups and prepared to present your argument.

What is the balance to making new discoveries in math?

Pure vs. Applied Math Pure Mathematics: Pure Mathematicians prove theorems about new ideas or concepts. Discovering patterns, puzzles, and abstractions. Application examples: problems related to relativity or quantum mechanics Applied Mathematics: Applied Mathematicians construct theories based on real- world uses Application examples: Engineering, economics, physics, finance, biology, astronomy

In the 19th Century, mathematicians became obsessed tith proofs In the 19th Century, mathematicians became obsessed tith proofs. They wanted to create a system that could separate truth from falsehood, which could with perfect accuracy and utter permanence, describe our foundation of knowledge about the world.

The philosopher Kurt Godel proved that no matter what axioms you choose to start with, any system will eventually run into statements that can’t be proven either way. Not true or false. They just… are.

Throughout our year together, we will find many mathematical statements that we may think are true… or false…. Be sure to use pure math to prove it is true, and applied math to show how it can be used!

Trial and Error?

The history of counting…

Alien Based Counting Create a new alien civilization. Your goal is to: Describe their origin and their way of life Explain what they look like Based on their number of fingers, demonstrate their counting system. Provide examples of 10 different numbers in your counting system. Criteria Be creative! Try not to copy an idea that already exists in terms of alien societies. You must demonstrate their counting system.

Human - Counting Evolution: Humans evolved from a furry, banana eating species. When we believed we knew better, we dominated and crushed our prior existence to ensure the continual growth and domination of our species. However, over time, we began to understand our emotions and develop compassion and empathy towards our planet and other people. Description: We are of different skin colors, hair colors, and eye colors, but we stand tall on two legs with random patches of fur in peculiar locations. We are usually symmetrical, having two feet, two hands, two arms, and two legs, which connect to our torso, leading up to our head. We continue to become taller and more intellectual with each generation of evolution. The more we learn about our existence, the more we develop our understanding of the limitations and possibilities that exist for our species. Counting System: We developed a system of counting based off our 10 fingers and 10 toes. We call this the base 10 system and it is the foundation of all mathematics. We create benchmarks at 10^0=0, 10^1=10, 10^2=100, 10^3=1000, etc.

Counting Using Base-10 Number 10^3=1000 10^2=100 10^1=10 10^0=0 1 432 873 8 7 927 9 1289