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 theoryThe probabilistic methodSwiss cheeses, rational approximations and universal plane curves (The one with the excellent bibliography)A cheaper Swiss cheeseAlice in Switzerland: The life and mathematics of Alice RothMeromorphic functionCarrots for dessertOrange peels and Fresnel integralsCake Cutting MechanismsThe University of Auckland has lots of kiwis in its logo. Newcastle University only has one lion.
Computer analysis of Sprouts with nimbersNimbersOn Numbers and GamesHow to eat 4/9 of a pizzaOn the Cookie Monster Problem100 Essential Things You Didn’t Know You Didn’t KnowGarfield’s proof of the Pythagorean theoremNapoleon’s theoremArithmetic derivativeDavid really does have a big tattoo of $\pi$ on his chest.Tukey tallyingThere 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 DameThe 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 numberMatrix determinant factDeterminants and Matrices by A.C. Aitken (possibly shonky PDF copy)PfaffianThe 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.