Maths in Europe: Seven cosmic messengers

Let us suppose we travel from Earth to the furthest observable point in the universe. We have seven satellites on our spacecraft, used to keep communications between us and the Earth. Let’s suppose that the speed of the satellites coincides with that of light, or in any case equal to a speed whose difference with c is negligible, while the speed of the spacecraft is $v = 2 / 3c$. The satellite, once it reaches Earth orbit, transmits the information we have loaded into its memory, then heads back to us to collect the new information. Meanwhile, within 24 hours of each other, we launch all the satellites.
The time each probe takes will be given by the formula \[t = \frac{y_1+y_0}{c}\] where $y_0$ is the distance traveled on the outward journey (or if you prefer the relative position of the spacecraft respect to the Earth at the time the first probe was launched), $y_1$ the distance of the return (or the position of the spacecraft when the first probe returns) and c is the speed of the probe.

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Maths in Europe: John Conway

Card Colm Mulcahy, an irish mathematician and John Conway's friend, on 11 april 2020 published on twitter the news of the death of Conway. His source was a close associate of his and confirmed by the family.
I written a little post in his honour on Maths in Europe, a ahort article about the free will theorem.
The theorem was proposed by Conway with Simon Kochen, inspired by the question about the interpretation of quantum mechanics. The statement is:

If the choice of directions in which to perform spin 1 experiments is not afunction of the information accessible to the experimenters, then the responsesof the particles are equally not functions of the information accessible to them.

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Maths in Europe: The ultimate question

If you are a reader of the Hitchhiker's guide to the galaxy, you probably know that 42 is the answer to the Ultimate Question of Life, the Universe, and Everything. The choice of the number by Douglas Adams was quite random, excluding the simple fact that the number liked the writer. Yet the 42 was the protagonist of a recent news related to one of the open problems of mathematics:

Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes?

To find an answer to this question, mathematicians used numerical methods. In particular, Andreas-Stephan Elsenhans and Jorg Jahnel using a particular vector space, searched solutions of the following diophantine equation:

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Maths in Europe: Lunar Arithmetic

One of the most popular expressions in Italy for giving strength to numbers is mathematics is not an opinion. The expression is exclusively Italian and mathematicians don't agree with this opinion, since they have fun inventing a large number of different mathematics. For example, a curious mathematics is what today called lunar arithmetic. In this kind of arithmetic, the sum between two digits gives the largest digit, while the product between two digits gives the smallest one. A particular consequence of the multiplication rule is the definition of prime numbers: in base 10 a lunar prime number is a number divisible only by itself and by 9, because the neutral element of lunar multiplication is 9.

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