On their own, addition and multiplication are simple operations. But the relationship between them is a complicated mystery that mathematicians are still working to understand.
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
A mathematical study finds that three definitions of what it means for entropy to increase, which have previously been considered equivalent, can produce different results in the quantum realm.
In a particle collider at CERN, a rarely-seen event is bringing us tantalizingly close to the brink of new physics.
From years of running what is known as the NA62 experiment, particle physicist Cristina Lazzeroni of the University of Birmingham in the UK and her colleagues have now established, experimentally observed, and measured the decay of a charged kaon particle into a charged pion and a neutrino-antineutrino pair. The researchers have presented their findings at a CERN seminar.
It’s exciting stuff. The reason the team has been pursuing this very specific kind of decay channel so relentlessly for more than a decade is because it’s what is known as a “golden” channel, meaning not only is it incredibly rare, but also well predicted by the complex mathematics making up the Standard Model of physics.
Based on a new mathematical framework and large multi-year multi-mission data sets, we reconstruct electric currents and magnetic fields around the dayside magnetopause and their dependence on the incoming solar wind, IMF, and geodipole tilt. The model architecture builds on previously developed mathematical frameworks and includes two separate blocks: for the magnetosheath and for the adjacent outer magnetosphere. Accordingly, the model is developed in two stages: 1) reconstruction of a best-fit magnetopause and underlying dayside magnetosphere, based on a simple shielded configuration, and 2) derivation of the magnetosheath magnetic field, represented by a sum of toroidal and poloidal terms, each expanded into spherical harmonic series of angular coordinates and powers of normal distance from the boundary. The spacecraft database covers the period from 1995 through 2022 and is composed of data from Geotail, Cluster, Themis, and MMS, with the total number of 1-min averages about 3 M. The modeling reveals orderly patterns of the IMF draping around the magnetosphere and of the magnetopause currents, controlled by the IMF orientation, solar wind pressure, and the Earth’s dipole tilt. The obtained results are discussed in terms of the magnetosheath flux pile-up and the dayside magnetosphere erosion during periods of northward or southward IMF, respectively.
The dayside magnetosheath and magnetopause play a principal role in the magnetosphere response to the interplanetary plasma flow. They serve as a main gateway where the first contact occurs between the incoming magnetized solar wind and the geomagnetic field, eventually resulting in a complex chain of magnetospheric processes. Of primary importance here is the mutual orientation of the external IMF and the internal magnetospheric field, defining the reconnection pattern at the boundary. This subject has long been at the center of many studies and extensive debates in the literature, starting from the seminal ideas of Dungey (Dungey, 1961) and followed by a multitude of works, recently summarized in reviews (Trattner et al., 2021; Fuselier et al., 2024). The reconnection geometry has been traditionally addressed in the framework of two basic concepts: the component and antiparallel merging (e.g. (Fuselier et al., 2021), and refs. therein (Qudsi et al., 2023)).
Model is featured in figure 5.4 of Visualizing Mathematics with 3D Printing. This is joint work with Keenan Crane.
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A distinguished mathematics professor at Rutgers, has resolved two critical problems in mathematics that have puzzled experts for decades.
He tackled the 1955 Height Zero Conjecture and made significant advancements in the Deligne-Lusztig theory, enhancing theoretical applications in several sciences.
A Rutgers University-New Brunswick professor, dedicated to unraveling the mysteries of higher mathematics, has resolved two separate, fundamental problems that have baffled mathematicians for decades.
The solutions to these long-standing problems could further enhance our understanding of symmetries of structures and objects in nature and science, and of long-term behavior of various random processes arising in fields ranging from chemistry and physics to engineering, computer science and economics.
A Rutgers University-New Brunswick professor who has devoted his career to resolving the mysteries of higher mathematics has solved two separate, fundamental problems that have perplexed mathematicians for decades.
Edward Frenkel is a renowned mathematician, professor of University of California, Berkeley, member of the American Academy of Arts and Sciences, and winner of the Hermann Weyl Prize in Mathematical Physics. In this episode, Edward Frenkel discusses the recent monumental proof in the Langlands program, explaining its significance and how it advances understanding in modern mathematics.
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Edward Frenkel’s previous lecture on TOE [Part 1]: • Revolutionary Math Proof No One Could…
Check out Edward Frenkel’s New York Times Bestselling book “Love and Math” which covers a lot of material in this video: https://amzn.to/4evbBkS
A mathematical proof shows that some quantum states can resist nature’s tendency to disorder – but only under very specific conditions.
