Several fields of mathematics have developed in total isolation, using their own “undecipherable” coded languages. In a new study published in Proceedings of the National Academy of Sciences, Tamás Hausel, professor of mathematics at the Institute of Science and Technology Austria (ISTA), presents “big algebras,” a two-way mathematical ‘dictionary’ between symmetry, algebra, and geometry, that could strengthen the connection between the distant worlds of quantum physics and number theory.
ChatGPT creator OpenAI on Thursday released a new series of artificial intelligence models designed to spend more time thinking—in hopes that generative AI chatbots provide more accurate and beneficial responses.
The new models, known as OpenAI o1-Preview, are designed to tackle complex tasks and solve more challenging problems in science, coding and mathematics, something that earlier models have been criticized for failing to provide consistently.
Unlike their predecessors, these models have been trained to refine their thinking processes, try different methods and recognize mistakes, before they deploy a final answer.
Someone went through Paul Erdos’ FBI files and found that all suspicious activities was really just him doing math.
A Hungarian born in the early 20th century, Paul (Pal) Erdős, mathematician, was well-known and well-liked, the sort of eccentric scientist from the Soviet sphere that made Feds’ ears perk up in mid-century America. His lifetime generated over 500 scholarly papers and a cult of collaborators. The Erdős number has become a mathy merit badge, and for those that don’t hold a coveted Erdős number of 1, there are resources to determine just how many degrees of celebrity separation exist between the man himself and other technical paper bylines.
But, try as they might, the Federal Bureau of Investigation was never able to find much motivation behind his movements and acquaintances beyond the math of it all.
His political criticisms applied equally to both sides of the Cold War crowd.
During the worst days of the COVID-19 pandemic, many of us became accustomed to news reports on the reproduction number R, which is the average number of cases arising from a single infected case. If we were told that R was much greater than 1, that meant the number of infections was growing rapidly, and interventions (such as social distancing and lockdowns) were necessary. But if R was near to 1, then the disease was deemed to be under control and some relaxation of restrictions could be warranted. New mathematical modeling by Kris Parag from Imperial College London shows limitations to using R or a related growth rate parameter for assessing the “controllability” of an epidemic [1]. As an alternative strategy, Parag suggests a framework based on treating an epidemic as a positive feedback loop. The model produces two new controllability parameters that describe how far a disease outbreak is from a stable condition, which is one with feedback that doesn’t lead to growth.
Parag’s starting point is the classical mathematical description of how an epidemic evolves in time in terms of the reproduction number R. This approach is called the renewal model and has been widely used for infectious diseases such as COVID-19, SARS, influenza, Ebola, and measles. In this model, new infections are determined by past infections through a mathematical function called the generation-time distribution, which describes how long it takes for someone to infect someone else. Parag departs from this traditional approach by using a kind of Fourier transform, called a Laplace transform, to convert the generation-time distribution into periodic functions that define the number of the infections. The Laplace transform is commonly adopted in control theory, a field of engineering that deals with the control of machines and other dynamical systems by treating them as feedback loops.
The first outcome of applying the Laplace transform to epidemic systems is that it defines a so-called transfer function that maps input cases (such as infected travelers) onto output infections by means of a closed feedback loop. Control measures (such as quarantines and mask requirements) aim to disrupt this loop by acting as a kind of “friction” force. The framework yields two new parameters that naturally describe the controllability of the system: the gain margin and the delay margin. The gain margin quantifies how much infections must be scaled by interventions to stabilize the epidemic (where stability is defined by R = 1). The delay margin is related to how long one can wait to implement an intervention. If, for example, the gain margin is 2 and the delay margin is 7 days, then the epidemic is stable provided that the number of infections doesn’t double and that control measures are applied within a week.
New research shows that the “superluminal observer” needs three separate time dimensions for a warp-speed math trick that would please even Galileo.
TL;DR
The concept of superluminal observers, proposed by Andrzej Dragan’s team, explores how faster-than-light travel might unify general relativity and quantum mechanics. By introducing three dimensions of time alongside one dimension of space, this research challenges our current understanding of the universe. Quantum phenomena, such as superposition and indeterminism, could be reinterpreted through the lens of a superluminal observer, where space and time swap roles at warp speeds. This theoretical framework suggests that the laws of physics remain consistent even at superluminal speeds, potentially paving the way for a unified field theory that reconciles these two fundamental branches of physics.
How did a giant impact 4 billion years ago affect Jupiter’s moon, Ganymede? This is what a recent study published in Scientific Reports hopes to address as a researcher from Kobe University investigated the geological changes known as a “furrow system” that Ganymede has exhibited since being struck by a giant asteroid in its ancient past, along with confirming previous hypotheses regarding the size of the asteroid. This study holds the potential to help scientists better understand how the very-active early solar system not only contributed to Ganymede’s but how such large impacts could have influenced the evolution of planetary bodies throughout the solar system.
“The Jupiter moons Io, Europa, Ganymede and Callisto all have interesting individual characteristics, but the one that caught my attention was these furrows on Ganymede,” said Dr. Naoyuki Hirata, who is an assistant professor in the Department of Planetology at Kobe University and sole author of the study. “We know that this feature was created by an asteroid impact about 4 billion years ago, but we were unsure how big this impact was and what effect it had on the moon.”
For the study, Dr. Hirata used a series of mathematical calculations to ascertain the size of the object that impacted Ganymede billions of years ago along with the angle of impact that produced the furrow system. In the end, Dr. Hirata determined that the impactor’s radius was approximately 93 miles (150 kilometers) and the angle of impact was potentially between 60 to 90 degrees, resulting in the furrows that overlay a significant portion Ganymede’s surface. For context, Ganymede is not only the largest moon in the solar system at a radius of 1,637 miles (2,634 kilometers), but it is also larger than the planet Mercury.
From the article:
When Saha and Sinha took a closer look at the resulting equations, they realized that they could express the number pi in this way, as well as the zeta function, which is the heart of the Riemann conjecture, one of the greatest unsolved mysteries in mathematics.
Two physicists have come across infinitely many novel equations for pi while trying to develop a unifying theory of the fundamental forces.
The number pi (π) appears in the most unlikely places. It can be found in circles, of course—as well as in pendulums, springs and river bends. This everyday number is linked to transcendental mysteries. It has inspired Shakespearean thought puzzles, baking challenges and even an original song. And pi keeps the surprises coming—most recently in January 2024, when physicists Arnab Priya Saha and Aninda Sinha of the Indian Institute of Science presented a completely new formula for calculating it, which they later published in Physical Review Letters.
More details of OpenAI’s secretive Project Strawberry have dropped, including its expected release date and the areas it will specialize in.
A recent report in The Information quotes “two people who have been involved in the effort”, and goes on to say that Project Strawberry could drop this Fall, and be better at math and programming than any chatbot we’ve seen so far.