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| The Ulam spiral: when arranging numbers in a spiral, highlighting prime numbers, they produce the (yet not fully understood) pattern showed above |
Deep connection between prime numbers proved: “If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century.” says Dorian Goldfeld, a mathematician at Columbia University, New York. Mathematician Shinichi Mochizuki of Kyoto University, Japan claims to have proved the abc conjecture. It was one of the unsolved problems in number theory. The abc conjecture needs the concept of radicals to be understood. A radical of a number $n$, $rad(n)$ is the multiplication of the prime numbers dividing $n$ (e.g. $ 360 = 2^3 \cdot 3^2 \cdot 5$, then $rad(360) = 2 \cdot 3 \cdot 5 = 30$). The abc conjecture then states that, given three integers $a$, $b$, and $c$, such that $a+b=c$, the number $ \frac{rad(abc)^r}{c} $ is always greater than 0 for any $r>1$. The proof of this theorem is split between 4 papers and is based on many others, so it might take a while to verify, but Mochizuki was known for his deep mathematics proof and provides lot of confidence. The proof of this theorem will not only help solving similar problems in future, but also solves many other problems, such as the famous Fermat's Last Theorem.
First visible-light evidence for gravitational waves: before this discovery, an evidence for the general theory of relativity in strong gravitational fields was the measurements of binary pulsars' (a bright x-ray source) periodicity. This was achieved measuring the shrink in the period of revolution, given by the loss of gravitational waves. For the first time, the model including Einstein's general relativity has been tested in a pair of white dwarves, which has spectrum in the visible light and a significantly lower mass. Direct detection of gravitational waves could be possible with an ambitious experiment involving building an interferometer into space with arms separated a million kilometers, but connected through lasers.
Proximity-induced high-temperature superconductivity using Scotch tape: Scotch tape is proving to be a good friend to physicists, lately. After the discovery (following a Physics Nobel Prize in 2010) of an easier production of graphene, using Scotch tape, by Andre Geim, a research group from University of Toronto discovered another use of Scotch tape. High-temperature superconductivity is a property of a few materials only, which allows them to show superconductive properties at room temperature, without overheating and losing energy. Cuprates show this property, but were believed to be impossible to be incorporated as superconductors. Then, other techniques, as proximity effects were used to induce superconductivity (from Cuprates) into semiconductors, but this requires the two materials to be close in nearly perfect contact. Cuprates cannot be fabricated that way (chemically), hence here comes the tape: the team used it to tape glass slides and Cuprates to topological insulators, known to have semiconducting properties as a whole, but to be very metallic on the surface. This induced semi-conductivity into the the topological insulators, making it a first. These semi-conductors can be used to improve energy efficiency in quantum computation.
Heisenberg's uncertainty might not be that uncertain: the Heisenberg's uncertainty principle is one of the biggest pillars of quantum mechanics. A team from University of Toronto built a new experiment involving entangled photon pairs in order to try to determine the "indeterminacy" of quantum mechanics. Heisenberg is still right, but the quantitative aspect of the uncertainty was never singularly tested. According to results, the "outcome" blurred out less than expected.
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