Explore the nature of math, the methodologies used to study it, and the power and limitations of its use.
Key questions:
Do mathematical symbols convey the same type of meaning as conventional language?
Was mathematics discovered or invented?
Does basing decisions on algorithms create solid ethical knowledge?
Is "proof" in mathematics different or similar to this term in other AOKs?
Is personal experience more or less important in mathematics compared to other AOK's?
Does mathematics only yield knowledge about the real world when it is combined with other areas of knowledge?
How significant have notable individuals been in shaping the nature and development of mathematics as an area of knowledge?
Is mathematical knowledge always abstract?
Is mathematical reasoning different from scientific reasoning or reasoning in other areas of knowledge?
What is "proof" to mathematicians? Is this different from proof in other AOKs?
Is mathematics invented or discovered? Is mathematics better defined by its subject matter or its method?
Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond. It all leads to the ultimate riddle: Is math a human invention or the discovery of the language of the universe?
Does emotion play a role in mathematical knowledge?
If numbers and mathematical objects are mere mental constructs, something invented by us, then why does mathematics work so well and seem to describe the world? On the other hand, if mathematical entities are "out there" in some sense waiting to be discovered, then what is their status and how do we get knowledge of them?
Is math objective? (You can find O'Neill's Weapons of Math Destruction in the library)
Are there limits to mathematical knowledge?
Can math add to other areas of knowledge?
Is it ethically justifiable for academic researchers to spend time doing research that does not have useful applications?
Fibonacci
From E=mc² to string theory, mathematical beauty has led physicists to draw up some of the most compelling descriptions of reality.
What are the implications of accepting that mathematical knowledge can change?
How reliable are mathematical predictions? Are there special ethical responsibilities regarding how mathematical knowledge is used?
Great YouTube Channel from Mathematical Sciences Research Institute