- How can popular math be useful and important?
- Showing the general public that math is valuable.
- Making people (especially students) interested in learning math.
- Inpsire students to persue degrees and careers in math.
- Remind undergrads like us about how awesome math is, and why we have chosen to study it.
- Why is it not done more? (A common saying is that the content of higher math is one of the world's best kept secrets)
- No economical incentives.
- The that rigor is super important, and the idea that popular math requires you to be extremely non-rigorous.
- The idea that higher math math is "too difficult" to be explained to the general public. (Not necessarily true, since really advanced and abstract physics like quantum mechanics or relativity are very popular subjects).
- How is it done well?
- Pick the right topic, focus on the right things. (Don't fall into the trap of structuring the presentation in the same way as a mathematical paper.)
- Use metaphors.
- Use graphics and animations.
- Emphasize the creative, inventive and explorative aspects of mathematics.
- Be careful about confirming prejudices or stereotypes about mathematics (for example that it's confusing hocus-pocus).
- Avoid saying things that are false and that might cause problems later in a viewers math education. Don't be afraid of putting up warning-signs when you gloss something over.
- How did the video approach the topic?
- Who is it aimed at? What are they trying to accomplish?
- What did (or didn't) we understand?
- Can anyone explain the difficult bits for others?
- Did we like this approach or not?
- What did we like (or not like) about it?
- How did the video portray mathematics as a field?
- How does it work for certain audiences inside/outside the math community?
- Where is this on a scale from 1-10?
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Adding Past Infinity (minutephysics, 47 seconds)
"Math trolling". Probably intended to show that "crazy" math can be useful in physics, even if it's not entirely rigorous. -
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12 (Numberphile, 8 mins)
This runs the risk of confirming peoples ideas of math as being mysterious and incomprehensible. -
What does it feel like to invent math? (3blue1brown, 15 mins)
There is a newer video! -
Why -1/12 is a gold nugget (Numberphile, 15 mins)
Highlights the creative nature of math by bringing up examples from math history. Great comparason to complex numbers. -
Ramanujan Summation (singingbanana, 9 mins)
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Ramanujan: Making sense of 1+2+3+... = -1/12 and Co. (Mathologer, 34 mins)