The 23rd of June 2023 marks 30 years since Andrew Wiles delivered his first proof of Fermat’s Last Theorem, right here at INI. In this article, podcast and video interview, we celebrate this tremendous milestone for one of mathematics’ most compelling stories.
Category: mathematics
Mind May Be Older Than the Brain | Michael Levin on Life and Intelligence
Michael Levin is a developmental and synthetic biologist at Tufts University whose work sits at the intersection of biology, bioelectricity, artificial life, regenerative medicine, synthetic biology, computer science, cognitive science, and philosophy of mind. He is known for his research on how cells communicate, make decisions, build bodies, repair tissues, and form collective intelligence through bioelectric signals. His work on Xenobots and Anthrobots has opened new questions about living robots, synthetic life forms, biological machines, morphogenesis, basal cognition, cellular intelligence, regeneration, cancer, aging, and the nature of mind beyond the brain.
In this conversation, Michael Levin and I explore whether mind and intelligence are binary or exist on a continuum, why cognition may be much older than brains, and how systems from cells to humans can pursue goals in different ways. We discuss the TAME framework, the spectrum of persuadability, cognitive light cones, bioelectricity, gap junctions, multicellular intelligence, Xenobots, Anthrobots, kinematic self-replication, neural wound healing, emergence, physicalism, mathematics, Platonic space, algorithms, bubble sort, Turing machines, evolution, human creativity, artificial intelligence, regenerative medicine, and the future of biology. This episode is for anyone interested in philosophy, consciousness, mind, intelligence, synthetic biology, developmental biology, AI, complex systems, evolution, and the deeper question of what it means for matter to become alive, intelligent, or aware.
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Michael’s website: https://drmichaellevin.org/
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/ masud.gaziyev Support the work: https://buymeacoffee.com/philosophy.e… Get new episodes, guest announcements, reading notes, and ideas worth thinking about. Subscribe here: https://philosophyeveryday.beehiiv.com/ Chapters: 00:00 Mind Beyond the Brain 01:19 Is Mind Older Than the Brain? 04:06 Why Intelligence Is Not All-or-Nothing 06:58 How to Interact With Different Kinds of Minds 09:54 From Single Cells to Collective Intelligence 13:17 How Cells Build Bigger Goals 16:05 Life Recreated — Xenobots and Anthrobots 18:54 Where Do New Behaviours Come From? 21:57 Synthetic Life and the Limits of Evolution 35:01 What Happens When Biology Is Freed? 43:00 Why Biology Eventually Leads to Mathematics 46:07 Is “Emergence” Just a Fancy Word for Surprise? 53:11 Platonic Space: A Strange New Map of Reality 01:03:21 What We Received from Platonic Space 01:11:24 Human Evolution, Technology, and the Patterns Behind Progress 01:16:43 Regeneration, Cancer, and Aging.
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Massimo (@Rainmaker1973) on X
Scientists have identified a reversal of the long-standing Flynn effect—the roughly 200-year trend of rising average intelligence (measured via IQ and cognitive tests) across generations. For the first time in modern recorded history, Generation Z (born roughly 1997–2012) shows lower performance than previous generations in key cognitive domains, including attention, memory, literacy, numeracy, executive function, problem-solving, and general IQ—despite spending more years in formal education than ever before. Neuroscientist and educator Dr. Jared Cooney Horvath, PhD, MEd, testified before the U.S. Senate Committee on Commerce, Science, and Transportation on January 15, 2026, highlighting this shift. In his written testimony, he stated that cognitive development in children across much of the developed world has stalled or reversed over the past two decades, with declines evident in international assessments (e.g., PISA, TIMSS) and other large-scale data starting around the mid-2000s and accelerating post-2010. Horvath attributes the primary driver not to reduced schooling, but to the widespread integration of digital screens and educational technology (EdTech) in classrooms. He argues that human brains evolved for deep, focused learning through face-to-face interaction and sustained attention, not fragmented skimming or constant task-switching encouraged by devices. Key points from his testimony include: — Teens now spend over half their waking hours on screens, with significant portions in school involving computers or tablets—often leading to off-task behavior and shallower processing. — Evidence from meta-analyses and national/international studies shows a consistent pattern: higher classroom screen exposure correlates with weaker outcomes in reading, math, science, and higher-order reasoning. — Digital tools may aid narrow, repetitive skill practice in controlled settings, but in core academic contexts, they tend to reduce depth of understanding, retention, and critical thinking. Horvath describes this as a “structural mismatch” between human cognition and how digital platforms are designed (to capture and fragment attention), warning that unchecked EdTech adoption risks long-term harm to workforce skills, innovation, and societal reasoning. [Horvath, J. C. (2026). Written testimony before the U.S. Senate Committee on Commerce, Science, and Transportation. U.S. Senate]
Specific cognitive abilities are highly heritable independent of general intelligence
A massive new meta-analysis reveals that individual cognitive abilities, like reading and math, rely on inherited DNA just as much as overall intelligence, suggesting people possess heavily customized genetic cognitive profiles independent of general smarts.
New AI math tool could sharpen image editing, drug discovery and simulations
Clarkson University researchers have developed a new mathematical tool that could make artificial intelligence systems more accurate, controllable and useful across applications ranging from image editing to drug discovery.
Clarkson University postdoctoral researcher Zander Blasingame and Chen Liu, professor of electrical and computer engineering, created a new family of numerical solvers called Rex that improves how generative AI models move between random noise and meaningful data. Their work, “Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers,” will be presented this summer at the International Conference on Machine Learning (ICML 2026), and an earlier version of the paper is available on the arXiv preprint server.
Diffusion and flow-matching models are the foundation of many modern generative AI systems, including image generators, molecular design tools and scientific simulators. They work by gradually transforming random noise into useful outputs. While that process is effective for creating new content, many important applications require running it in reverse. Existing methods often introduce errors that make it difficult to accurately recover the original information.
Corrected microbial family tree offers statistically sound model for how earliest life forms evolved
In this era of Big Data, the prevailing wisdom is that more information leads to better answers. However, a new Canadian study shows that in the hunt for life’s ancient ancestors, more data can actually lead to less truth. Published in the Proceedings of the National Academy of Sciences, the research by UdeM associate professor of computer science Miklós Csűrös reveals that standard methods for reconstructing the genomes of ancient microbes are being overwhelmed by an explosion of information.
This paradox causes current models to “hallucinate” evolutionary events—specifically, an implausibly high number of horizontal gene transfers—that are actually just statistical ghosts, the study shows.
In it, Csűrös identifies a crisis point in evolutionary biology: As researchers try to reconcile thousands of gene sequences across the entire tree of life, the actual evolutionary signal begins to vanish, replaced by mathematical noise.
How do flocking birds and schools of fish move? New research offers crystal-clear answer
Flocking birds and schools of fish are a familiar sight. While previous research has uncovered the broad dynamics driving these movements, their underlying intricacies remain a mystery. Now a study by a team of New York University mathematicians offers new insights into these phenomena. It reveals that flocks and schools behave in ways similar to a soft crystalline material, with individual birds and fish serving as “atoms” that are evenly spaced in a lattice-like formation.
The findings, reported in the journal Physical Review Fluids, offer detailed insights into the hydrodynamic and aerodynamic interactions crucial in aerospace and automotive engineering, robotics and energy harvesting.
“Our findings offer a new way to understand how animal collectives coordinate movement and respond to their environment,” says Christiana Mavroyiakoumou, a researcher at NYU’s Courant Institute School of Mathematics, Computing, and Data Science at the time of the study and now a fellow at Oxford University’s Mathematical Institute. “More specifically, lines of birds or fish behave like an elastic material with regularly spaced individuals held together by flexible, or spring-like, bonds—akin to soft crystalline substances in which atoms are arranged in an orderly, repeating pattern.”
How Divergence and Curl Were Discovered
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This video is about how Divergence and Curl, along with the theory of Vector Analysis was discovered.
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Image Credits:
https://commons.wikimedia.org/wiki/Fi…, https://creativecommons.org/licenses/.… Approaching a Black Hole: NASA’s Scientific Visualization Studio — Caltech-IPAC/Robert Hurt, Caltech-IPAC/Keith Miller, NASA/JPL/Chelsea Gohd, Global Science and Technology, Inc./Ella Kaplan, NASA/GSFC/Mark SubbaRao Many more images that are public domain from wikimedia commons _____ Sources: Vector, A Surprising Story of Space, Time, and Mathematical Transformation by Robyn Arianrhod A History of Vector Analysis by Michael J. Crose Maxwell’s Treatise on Electricity and Magnetism + A Dynamical Theory of the Electromagnetic Field Great videos by Kathy Loves Physics: • Quaternions are Amazing and so is William…,
• How Maxwell’s Equations (and Quaternions)… _____ Corrections: 15:12 — on screen it should read “born in Scotland 1831″ instead of 1931 _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski This video was sponsored by Surfshark.
https://commons.wikimedia.org/wiki/Fi…, https://creativecommons.org/licenses/.…
Approaching a Black Hole: NASA’s Scientific Visualization Studio — Caltech-IPAC/Robert Hurt, Caltech-IPAC/Keith Miller, NASA/JPL/Chelsea Gohd, Global Science and Technology, Inc./Ella Kaplan, NASA/GSFC/Mark SubbaRao.
Many more images that are public domain from wikimedia commons.