Lifeboat Foundation

Mathematician Bernhard Riemann was born #OTD in 1826.

Bernhard Riemann was another mathematical giant hailing from northern Germany. Poor, shy, sickly and devoutly religious, the young Riemann constantly amazed his teachers and exhibited exceptional mathematical skills (such as fantastic mental calculation abilities) from an early age, but suffered from timidity and a fear of speaking in public. He was, however, given free rein of the school library by an astute teacher, where he devoured mathematical texts by Legendre and others, and gradually groomed himself into an excellent mathematician. He also continued to study the Bible intensively, and at one point even tried to prove mathematically the correctness of the Book of Genesis.

Although he started studying philology and theology in order to become a priest and help with his family’s finances, Riemann’s father eventually managed to gather enough money to send him to study mathematics at the renowned University of Göttingen in 1846, where he first met, and attended the lectures of, Carl Friedrich Gauss. Indeed, he was one of the very few who benefited from the support and patronage of Gauss, and he gradually worked his way up the University’s hierarchy to become a professor and, eventually, head of the mathematics department at Göttingen.

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Australian physicists resolve time travel paradox, showing it could be possible according to einstein’s theory.

Australian physicists have demonstrated that time travel could be theoretically possible by resolving the classic grandfather paradox. By aligning Einstein’s theory of general relativity with classical dynamics, researchers at the University of Queensland showed that time travel scenarios, such as altering past events, can coexist without resulting in logical inconsistencies. They used a model involving the coronavirus pandemic to illustrate how events would adjust themselves to avoid paradoxes. This research suggests that time travel, while complex, does not inherently create contradictions and could be feasible according to current mathematical models.

After reading the article, a Reddit user named Harry gained more than 524 upvotes with this comment: Isn’t the problem with time travel that it is also space travel? The earth isn’t in the same spot now as it was when you first started reading my comment, the earth travels very fast in space so wouldn’t you also have to find out where in space the earth was in 1950 (chose random date) in order to physically travel there? And how could we know where in physical space the earth was in 1950?

Some big claims here: https://openai.com/index/learning-to-reason-with-llms/

OpenAI o1 ranks in the 89th percentile on competitive programming questions (Codeforces), places among the top 500 students in the US in a qualifier for the USA Math Olympiad (AIME), and exceeds human PhD-level accuracy on…

We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.

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.

Continue reading “The FBI spent decades tracking mathematician Paul Erdős, only to conclude that the guy was just really into math” »

By tapping into a decades-old mathematical principle, researchers are hoping that Kolmogorov-Arnold networks will facilitate scientific discovery.

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.