Ben Green and collaborators discover that the well-known "birthday paradox" has its equivalent in the divisors of a typical integer.

"The well-known "birthday paradox'' states that if you have 23 or more people in a room - something difficult to achieve nowadays without a very large room - then the chances are better than 50:50 that some pair of them will share a birthday. If we could have a party of 70 or more people, the chance of this happening rises to 99.9 percent.

Oxford Mathematician Christopher Hollings and Oxford Egyptologist Richard Bruce Parkinson explain how our interpretation of Egyptian Mathematics has changed over the past two centuries and what that says about how historians of mathematics approach their subject.

In modern Cryptography, the security of every cryptosystem is required to be formally proven. Most of the time, such formal proof is by contradiction: it shows that there cannot exist an adversary that breaks a specific cryptosystem, because otherwise the adversary would be able to solve a hard mathematical problem, i.e. a problem that needs an unfeasible amount of time (dozens of years) to be concretely solved, even with huge computational resources.