Knowledge and Math

Question 1

What is it about math that enables mathematical results to remain unchanged over time?

Answer 1

Perspective

Question 2

Do math symbols have meaning in the same way words have meaning? Is personal exp important…

Answer 2

M&T

Question 3

Does math only yield knowledge about the real world when it is combined with other AOKs?

Answer 3

Scope

Question 4

Is progress harder to make in math than in other AOKs?

Answer 4

Perspective

Question 5

Why is Math so important in other areas of knowledge, particularly the natural sciences?

Answer 5

Scope

Question 6

How have technological innovations, such as developments in computing, affected the scope and nature of math as an AOK.

Answer 6

Scope

Question 7

Are all the AOKs in the TOK course themselves embedded in a particular tradition or bound to a particular culture?

Answer 7

Perspectives

Question 8

If math is created by humans, is it still possible to accept math truths as objective facts about the world?

Answer 8

Perspective

Question 9

Is math reasoning different from scientific reasoning in other AOKs?

Answer 9

M&T

Question 10

What are the five Forms of Knowledge in Math?

Answer 10

1. Peripheral: Foundational concepts to learn more
2. Evolutionary: Math is ongoing
3. Axiomatic: The starting point of reasoning
4. Logical: Using foundational knowledge “If, then”
5. Inferential: Using certainties

Question 11

What is the role of the mathematical community in determining the validity of a proof?

Answer 11

Perspective

Question 12

Is math better defined by its subject matter or its method?

Answer 12

Scope

Question 13

What does it mean to say that math is an axiomatic system?

Answer 13

M&T

Question 14

Should math be defined as a language?

Answer 14

Scope

Question 15

How significant have notable individuals been in shaping the nature and development of math as an AOK?

Answer 15

Perspectives

Question 16

What is the Bellman-ford algorithm?

Answer 16

• A formula used to promote discriminatory practices and predatory pricing online

Question 17

What is it meant by the term proof in math, and how is it similar to, or different from this in other AOKs

Answer 17

M&T

Question 18

What are the perspectives in math?

Answer 18

• Constructivist: The objects of math do not exist independent of us
• Platonist: Math exists independently of humans
• Applied: Math is used in other disciplines
• Pure: Math for its sake beauty

Question 19

Is math knowledge embedded in particular cultures or traditions?

Answer 19

Perspectives

Question 20

How is an axiomatic system of Knowledge different from, or similar to, other systems of Knowledge?

Answer 20

M&T

Question 21

Is absolute certainty attainable in math?

Answer 21

Scope

Question 22

What is an axiom and a theorem?

Answer 22

• Axiom: A statement or proposition which is regarded as being established, accepted, or self-evidently true
• Theorem: A general proposition not self-evident but proved by a chain of reasoning

Question 23

What is an additive identity?

Answer 23

An additive identity that is a number that, when added to a number equals that number

Question 24

Does personal exp play any role in the formation of claims in math?

Answer 24

Perspectives

Question 25

What are some base Methods and tools in math?

Answer 25

- Notation - Sets and mapping - Fractals - Algebra - Theorems, proofs, laws - Necessary, Contingent

Question 26

How do mathematicians reconcile the fact that some conclusions seem to conflict with our intuitions?

Answer 26

M&T

Question 27

Is there a distinction between truth and certainty in math?

Answer 27

Scope

Question 28

What is the golden record?

Answer 28

- In 1977, spacecraft carried it as a unique time capsule into interstellar space with instructions on how to play it, how to find space, and its time in space.

Question 29

Is there a hierarchy of AOks in terms of their usefulness in solving problems?

Answer 29

Scope

Question 30

How do Axioms tie in proof?

Answer 30

- Axioms don't need proof, they aren't true or false, just a matter of reality - Theorems are the inevitable implications of axioms that define the system.

Question 31

What is the general scope of Math?

Answer 31

- A symbolic representation of real life - Helps yields understanding, generalizations, and understanding - Applied to real life problems - Establishes sets and maps connections between them - Practical applications