Breakthroughs, discoveries, and DIY tips sent every weekday. Using advanced imaging techniques, an international research team has reconstructed an ancient extinct fish's heart, brain, and fins from an intricately detailed, fingernail-sized fossil fragment. But cartoon lookalikes aside, the creature may help rewrite one of the earliest chapters in animal evolution. Its details are described in a study published on August 6 in Nature. Earth's first fish arrived about half a billion years ago, but not anywhere near the ocean's surface.

When David Fajgenbaum was a twenty-five-year-old medical student, at the University of Pennsylvania, he started to feel so tired that he could barely stand. Fajgenbaum, a former college quarterback, could still bench-press three hundred and seventy-five pounds; he was known for doing pullups on a tree near his workplace. But now he was desperately ill. The lymph nodes in his groin and neck swelled. Small red dots--blood moles--emerged on his chest, and he woke up soaked in sweat. One day, at the hospital where he was doing his rotation, he stumbled down the hall into the emergency room, and doctors told him that his liver, bone marrow, and kidneys were failing. Fluid had leaked out of his blood vessels, into his abdomen and around his heart; bleeding in his retina temporarily blinded him in his left eye.

Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have Q-factorial terminal singularities. Q-Fano varieties are of fundamental importance in geometry as they are "atomic pieces" of more complex shapes - the process of breaking a shape into simpler pieces in this sense is called the Minimal Model Programme. Despite their importance, the classification of Q-Fano varieties remains unknown. In this paper we demonstrate that machine learning can be used to understand this classification. We focus on 8-dimensional positively-curved algebraic varieties that have toric symmetry and Picard rank 2, and develop a neural network classifier that predicts with 95% accuracy whether or not such an algebraic variety is Q-Fano. We use this to give a first sketch of the landscape of Q-Fanos in dimension 8. How the neural network is able to detect Q-Fano varieties with such accuracy remains mysterious, and hints at some deep mathematical theory waiting to be uncovered. Furthermore, when visualised using the quantum period, an invariant that has played an important role in recent theoretical developments, we observe that the classification as revealed by ML appears to fall within a bounded region, and is stratified by the Fano index. This suggests that it may be possible to state and prove conjectures on completeness in the future. Inspired by the ML analysis, we formulate and prove a new global combinatorial criterion for a positively curved toric variety of Picard rank 2 to have terminal singularities. Together with the first sketch of the landscape of Q-Fanos in higher dimensions, this gives new evidence that machine learning can be an essential tool in developing mathematical conjectures and accelerating theoretical discovery.

Mathematicians attempting to build a "periodic table" of shapes have turned to artificial intelligence for help – but say they don't understand how it works or whether it can be 100 per cent reliable. Tom Coates at Imperial College London and his colleagues are working to classify shapes known as Fano varieties, which are so simple that they can't be broken down into smaller components.

Fano varieties are basic building blocks in geometry - they are `atomic pieces' of mathematical shapes. Recent progress in the classification of Fano varieties involves analysing an invariant called the quantum period. This is a sequence of integers which gives a numerical fingerprint for a Fano variety. It is conjectured that a Fano variety is uniquely determined by its quantum period. If this is true, one should be able to recover geometric properties of a Fano variety directly from its quantum period. We apply machine learning to the question: does the quantum period of X know the dimension of X? Note that there is as yet no theoretical understanding of this. We show that a simple feed-forward neural network can determine the dimension of X with 98% accuracy. Building on this, we establish rigorous asymptotics for the quantum periods of a class of Fano varieties. These asymptotics determine the dimension of X from its quantum period. Our results demonstrate that machine learning can pick out structure from complex mathematical data in situations where we lack theoretical understanding. They also give positive evidence for the conjecture that the quantum period of a Fano variety determines that variety.

To get her start in Hollywood, Chivonne Michelle studied acting at New York University. But what helped her break into the industry and gave her the key training she needed was working on set as a background actor. Today, the rise of artificial intelligence (AI) technology threatens to put those "entry level and working class" Hollywood jobs at risk, Michelle and other striking actors say. AI is threatening jobs across many sectors, from doctors and lawyers to data scientists and journalists. But Hollywood actors and writers, currently united in their first "double strike" in more than 60 years, are fighting back in an unprecedented way, vowing to protect every worker in their industry, from the extras to the stars, from being replaced by new technologies.

America's credibility among its adversaries has dwindled under President Biden, with some experts arguing a line can be drawn from the disastrous U.S. withdrawal from Afghanistan to more recent events such as the Chinese spy balloon and the downing of a U.S. drone by Russian forces. "I think the Biden administration's disastrous withdrawal from Afghanistan was a key catalyst for multiple trends that have undermined U.S. influence and deterrence," James Phillips, the senior research fellow for foreign policy at the Heritage Foundation, told Fox News Digital. "U.S. allies were shocked by the naive assumptions behind the withdrawal, the speed with which Washington abandoned longtime allies, and the incompetence of the policymakers that supervised the withdrawal." Phillips argues that it was not just American allies who took note of the administration's hastily executed exit from Afghanistan, but also adversaries such as China and Russia, who no longer fear U.S. deterrence. "U.S. adversaries perceived the withdrawal from Afghanistan as a manifestation of U.S. weakness and a desire to rapidly exit the Middle East," Phillips said.

Mark Minevich is the principle founder of Going Global Ventures and venture partner of GVA Capital in Silicon Valley. While the public is becoming aware of the possibilities of artificial intelligence, I've been evangelizing, researching and working with it for years. As a fellow of the U.S. Council on Competitiveness, a senior advisor to the United Nations Office for Project Services, and a member of both the World Artificial Intelligence Organization and B20, I've been researching AI (and sharing what I learn) for years. Although AI buzz typically surrounds statements from famous minds like Stephen Hawking or Elon Musk – both of whom rightfully worry about granting sentience to machines that control our way of life -- there are plenty of worthy conversations being had on the subject. AI also represents cybersecurity's next evolution, both as a threat and a solution.

Students code software at desktops, while others assemble odd machines with wires and multi-colored boxes. Earning a spot at this elite university isn't easy; UC-Berkeley accepted a mere 14.8 percent of applicants for the class of 2020. So this young crew will likely be tomorrow's tech leaders and pioneers. Despite all the promise, it appears that BRETT is struggling. BRETT is a robot, and he – or she, or it – is attempting to place a small wooden block into a small hole. Again and again, BRETT swings his arm over the opening, attempts to place the block, but fumbles. Just can't make it fit. However, as robots go, BRETT has a huge advantage: he can learn. Every time BRETT swings his arm and fails, he calculates what went wrong. In essence he's doing what we humans do: he's failing, and in response he's deciding how to improve the next effort. I stand watching for about 15 minutes, and finally BRETT succeeds – a lengthy period given the simple task. But the astounding point is that the robot really did learn.

Students code software at desktops, while others assemble odd machines with wires and multi-colored boxes. Earning a spot at this elite university isn't easy; UC-Berkeley accepted a mere 14.8 percent of applicants for the class of 2020. So this young crew will likely be tomorrow's tech leaders and pioneers. Despite all the promise, it appears that BRETT is struggling. BRETT is a robot, and he – or she, or it – is attempting to place a small wooden block into a small hole. Again and again, BRETT swings his arm over the opening, attempts to place the block, but fumbles. Just can't make it fit. However, as robots go, BRETT has a huge advantage: he can learn. Every time BRETT swings his arm and fails, he calculates what went wrong. In essence he's doing what we humans do: he's failing, and in response he's deciding how to improve the next effort. I stand watching for about 15 minutes, and finally BRETT succeeds – a lengthy period given the simple task. But the astounding point is that the robot really did learn.