Cushing and CP’s Random Talks, number 1

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.