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"First, the problems were manually translated into formal mathematical language for our systems to understand. In the official competition, students submit answers in two sessions of 4.5 hours each. Our systems solved one problem within minutes and took up to three days to solve the others. AlphaProof solved two algebra problems and one number theory problem by determining the answer and proving it was correct. This included the hardest problem in the competition, solved by only five contestants at this year's IMO. AlphaGeometry 2 proved the geometry problem, while the two combinatorics problems remained unsolved."

"O'Neill recounts an exercise to improve service to homeless families in New York City, in which data-analysis was used to identify risk-factors for long-term homelessness. The problem, O'Neill describes, was that many of the factors in the existing data on homelessness were entangled with things like race (and its proxies, like ZIP codes, which map extensively to race in heavily segregated cities like New York). Using data that reflects racism in the system to train a machine-learning algorithm whose conclusions can't be readily understood runs the risk of embedding that racism in a new set of policies, these ones scrubbed clean of the appearance of bias with the application of objective-seeming mathematics. "

"MIT researcher's at CSAIL have developed a lane-changing algorithm for self-driving cars. the algorithm allows for aggressive lane changes much like the kind only real drivers would be capable of.   it works by computing 'buffer zones' around autonomous vehicles and reassessing them on the fly. MIT uses a mathematically efficient approach which calculates new buffer zones if the default buffer zones lead to performance that's far worse than a human's driver."

"The firm's software uses machine learning (ML), an advanced form of artificial intelligence, to detect patterns in user behaviour that could indicate attempts to cheat. Its technology can also automatically mark multiple-choice answers and mathematics exams. In addition, it checks each exam-sitter's identity using the webcam, to ensure that no-one else is sitting the test for them. The Better Examinations program also temporarily restricts access to the internet, or certain websites and applications on each person's computer. "

"or its latest update, which it released Wednesday, the COVID-19 Scenario Modeling Hub combined nine different mathematical models from different research groups to get an outlook for the pandemic for the next six months. "Any of us who have been following this closely, given what happened with delta, are going to be really cautious about too much optimism," says Justin Lessler at the University of North Carolina, who helps run the hub. "But I do think that the trajectory is towards improvement for most of the country," he says. The modelers developed four potential scenarios, taking into account whether or not childhood vaccinations take off and whether a more infectious new variant should emerge. "

"PhotoGuard works by altering select pixels in an image such that they will disrupt an AI's ability to understand what the image is. Those "perturbations," as the research team refers to them, are invisible to the human eye but easily readable by machines. The "encoder" attack method of introducing these artifacts targets the algorithmic model's latent representation of the target image - the complex mathematics that describes the position and color of every pixel in an image - essentially preventing the AI from understanding what it is looking at."

"To arrive at a recommended rent, the software deploys an algorithm - a set of mathematical rules - to analyze a trove of data RealPage gathers from clients, including private information on what nearby competitors charge. For tenants, the system upends the practice of negotiating with apartment building staff. RealPage discourages bargaining with renters and has even recommended that landlords in some cases accept a lower occupancy rate in order to raise rents and make more money. One of the algorithm's developers told ProPublica that leasing agents had "too much empathy" compared to computer generated pricing."

"But ChatGPT and similar programs are, by design, unlimited in what they can "learn" (which is to say, memorize); they are incapable of distinguishing the possible from the impossible. Unlike humans, for example, who are endowed with a universal grammar that limits the languages we can learn to those with a certain kind of almost mathematical elegance, these programs learn humanly possible and humanly impossible languages with equal facility. Whereas humans are limited in the kinds of explanations we can rationally conjecture, machine learning systems can learn both that the earth is flat and that the earth is round. They trade merely in probabilities that change over time."