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A special anniversary episode where @reflectivemaths (Dave Gale) and I pick the brains of two special guests: Abel prize nominee @samuel_hansen (Samuel Hansen) and @peterrowlett (Dr Peter Rowlett, surprisingly).

"I think we should conclude that an argument has gone on long enough when Samuel Hansen is the voice of conciliation" - Peter Rowlett

- Introducing our podfathers!
- Why we're THE WORLD'S #1 ACTIVE PODCAST
- A second series of Relatively Prime? Samuel just needs $16,000 or so, so rummage around the back of your sofas.
- The glamorous career arc of a podcasting legend
- Dr Peter Rowlett listens to us! But only because we mention him every month. We ask the big questions!
- How fancy is your degree certificate?
- Why does $0! = 1$? And then what is $(-1)!$?
- Is $4 \times 6$ four groups of six (yes) or six groups of four (which only a poopyhead would believe)? Samuel says we're both wrong. Maybe he's the poopyhead. None of us can say 'commutativity' and Peter doesn't even try.
- Is Pythagoras part of trigonometry? Is wikipedia commutative? Did Samuel mean the "Pythagoras is the root of trigonometry" pun?
- Colin tries to wrap everything up... but it's a false ending! It's almost like listening to Bowie.
- Why study maths? (reprise). Should we have a Dr Gale's Basic Human Competence Test?
- Uncovering the next maths star and what's really pure maths
- What is mathematics? (reprise)
- Colin screws up the timezones, just to mess with Samuel's schedule, with a SH, and fails the DGBHCT.
- We run through some messages from @twentythree (Drew Barker) and @notonlyahatrack (Will Davies)
- Why do students hate 'show that' questions? Why do people think maths is about the right answer? How and whether to credit guesswork in exams? Dave's 'no marks for the answers' suggestion (the first thing he's got right all episode, frankly).
- Colin apologises for last month's puzzle, while blaming @tombutton (Tom Button) and @jussumchick (Jo Sibley), to which the answer was:

... (multiplied by $2\pi$ for an angle, of course), so well done if you got that. - A guest puzzle from @srcav (Cav in real life)
- What Samuel's been listening to (but NOT Wrong But Useful... yet).
- What continued fractions are for (thanks to @colinthemathmo (Colin Wright) and @njj4 (Nick Jackson) for their suggestions).
- What our guests don't understand, and Colin shills his books, as per.
- Samuel apologises for being a terrible guest, as if he were English or something.
- Peter invites everyone to the BCME conference, 14th-17th April 2014 at Nottingham University, and the post-conference MathsJam.

## Peter Rowlett

This run down makes it sound kind-of chaotic, not like the well-oiled machine that it was 😉

Thanks for having us, we had fun.

Peter.

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## Joshua Little

To beat a dead horse, the current literature for elementary/primary education in the U.S. has us teaching A x B is representing A as the number of groups and B as the number of objects.

I hate to agree with Mr. Hansen (after he asked me to hate him and berated me for listening to Math/Maths), but the idea of commutativity should take precedent over the discussion of which number is representative of group and which is representative of number in each group. While certainly commutativity (I can type it, but not say it) has its exceptions, I think the idea we need to “RAIL INTO THEIR HEADS” is that with simple arithmetic there are few exceptions to the rule.

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