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Archive for the ‘mathematics’ category

Oct 21, 2024

Srinivasa Ramanujan Was a Genius. Math Is Still Catching Up

Posted by in category: mathematics

Srinivasa Ramanujan embodies the myth of the self-taught genius.


Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.

Oct 17, 2024

Big Advance on Simple-Sounding Math Problem Was a Century in the Making

Posted by in category: mathematics

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.

Oct 16, 2024

Quantum theory is challenging long-standing ideas about entropy

Posted by in categories: mathematics, quantum physics

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.

By Karmela Padavic-Callaghan

Oct 16, 2024

CERN Just Found Ultra-Rare Particle, Which Is Creating New Physics

Posted by in categories: mathematics, particle physics

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.

Oct 14, 2024

Magnetic fields and electric currents around the dayside magnetopause as inferred from data-constrained modeling

Posted by in category: mathematics

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)).

Oct 13, 2024

Topology joke by henryseg

Posted by in categories: 3D printing, humor, mathematics

Model is featured in figure 5.4 of Visualizing Mathematics with 3D Printing. This is joint work with Keenan Crane.

Oct 13, 2024

Inside @ibm’s Quantum System Two, The World’s First Modular Utility Scale Quantum Computer

Posted by in categories: business, encryption, mathematics, quantum physics, robotics/AI

#ibm #heron #quantumcomputer #quantumphysics #softwareengineering #developers #programming #artificialintelligence #ai #neuralnetworks #machinelearning #explorepage #financialmarkets #cryptography #business #productdevelopment #researchanddevelopment #computerscience #qubit #engineering #technology #startups #science #mathematics #innovation #invention

Oct 13, 2024

Rutgers Professor Cracks Two of Mathematics’ Greatest Mysteries

Posted by in category: mathematics

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.

Oct 12, 2024

In double breakthrough, mathematician helps solve two long-standing problems

Posted by in categories: chemistry, computing, economics, engineering, mathematics, physics

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.

Oct 11, 2024

This is a Monumental Breakthrough… [Part 2]

Posted by in categories: mathematics, physics, robotics/AI

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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