resources for TOK at WAB

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**?

- Podcast: Clegg's Are Numbers RealTip: We have the book in the library

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?**

- PBS NOVA: The Great Math MysteryAstrophysicist 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?

- Can Equations Be Beautiful?From E=mc² to string theory, mathematical beauty has led physicists to draw up some of the most compelling descriptions of reality.
- Story of Math: Chinese MathematicsWhat are the implications of accepting that mathematical knowledge can change?
- Predictive PolicingHow reliable are mathematical predictions? Are there special ethical responsibilities regarding how mathematical knowledge is used?
- NumberphileGreat YouTube Channel from Mathematical Sciences Research Institute
- Is Mathematics Invented or Discovered-Video Interview SeriesMathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music? Or is mathematics discovered—always out there, somewhere, like mysterious islands waiting to be found? Whatever mathematics is will help define reality itself.
- Is mathematics the language of the universe?Interview with author; discusses relationship between our mathematical conventions and our senses.
- Are today's mathematical proofs impossible to verify?Seed Magazine article about how the complexity of some modern mathematical proofs make independent verification extremely difficult, if not impossible.
- Mathematics and the Language of NatureFrom the journal Mathematics and Sciences. Explores many aspects of the representational capacity of mathematics.
- Math Professor Helps Uncover Art FakesNPR story about mathematics being used to model brush strokes in artwork to determine authenticity of work.
- Learning the Language of MathematicsArticle by Clemson University professor identifying ways in which the structure of mathematical language differs from English.
- 101 Uses for the Quadratic EquationResponse to debate in British Parliament over the value of the quadratic equation.
- What is an Axiom?Robert Brown at Duke University explains common misunderstanding of axioms.
- For the Luke of MathVarious attempts to give insight into the process and experience of doing mathematics (multimedia).
- The Unplanned impact of mathsRefers to an article in Nature about how mathematics research sometimes turns out to have practical applications.
- Designs on MathematicsOpinion piece about how historical development of math has brought us to current school curriculum that needs revision.
- How to get smartEconomist article about correlation between increased math study and increased income.
- Indiana PiStory about 1897 effort to legislate the value of Pi to 3.2.

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 **objectiv**e? (You can find O'Neill's Weapons of Math Destruction and Noble's Algorithms of Oppression in the library)

Are there** limits **to mathematical knowledge?

Can math **add** to other areas of knowledge?

Is it **ethically justifiabl**e for academic researchers to spend time doing research that does not have **useful applications**?