David and I sat down again and talked about maths a bit more. I’m calling this number 1 because it suits both our counting systems: David can call this the first podcast of a new series, and I can say the one we put out under *All Squared* was number 0. Everyone wins!

Here follows a long rambly list of things we talked about, and some things we alluded to too. The button to actually play the podcast is down at the bottom of the post.

- Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
- The probabilistic method
- Swiss cheeses, rational approximations and universal plane curves (The one with the excellent bibliography)
- A cheaper Swiss cheese
- Alice in Switzerland: The life and mathematics of Alice Roth
- Meromorphic function
- Carrots for dessert
- Orange peels and Fresnel integrals
- Cake Cutting Mechanisms
- The University of Auckland has lots of kiwis in its logo. Newcastle University only has one lion.

- Computer analysis of Sprouts with nimbers
- Nimbers
- On Numbers and Games
- How to eat 4/9 of a pizza
- On the Cookie Monster Problem
- 100 Essential Things You Didn’t Know You Didn’t Know
- Garfield’s proof of the Pythagorean theorem
- Napoleon’s theorem
- Arithmetic derivative
- David really does have a big tattoo of $\pi$ on his chest.
- Tukey tallying
- There exist infinitely many twin primes iff there are infinitely many primes $p$ such that $(p^2)^{\prime\prime\prime} = 1$.
- The Princeton Companion to Mathematics (warning: auto-playing “podcast”)
- A CBE is not quite as worthy as a Knight or a Dame
- The book with the pictures of nudey ladies is
*Groupes Stables*, by Bruno Poizat. The French edition with the pictures is very hard to get hold of (we had to do an inter-library loan through the university), but the foreword to the English translation is superb, and basically boils down to “je ne regrette rien”. - The proof that $\sqrt[n+2]{2}$ is irrational because of Fermat’s Last Theorem, which was retold at MathsJam by Julia Collins.
- That came from the MathOverflow question, “Awfully sophisticated proof for simple facts”.
- Congruent number
- Matrix determinant fact
- Determinants and Matrices by A.C. Aitken (possibly shonky PDF copy)
- Pfaffian
- The 15 stupid proofs that the primes are infinite were published in the latest issue of
*Paradox*(PDF), the magazine of the Melbourne University maths and stats society. They’re on page 17.

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