He majored in Mathematical Engineering in 1958 from the University of Tokyo then graduated in 1963 from the Graduate School of the University of Tokyo.
His Master of Engineering in 1960 was entitled Topological and Information-Theoretical Foundation of Diakoptics and Codiakoptics. His Doctor of Engineering in 1963 was entitled Diakoptics of Information Spaces.
Shun’ichi Amari received several awards and is a visiting professor of various universities.
This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here’s how it works.
The equation owes its power to the way that it lets mathematicians quickly understand the frequency content of any kind of signal. It’s quite a feat. But don’t just take my word for it—in 1867, the physicist Lord Kelvin expressed his undying love for this fine piece of mathematics, too. He wrote, “Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.” And so it remains.
Math Will Tear Us Apart
Somehow, we all know how a warp drive works. You’re in your spaceship and you need to get to another star. So you press a button or flip a switch or pull a lever and your ship just goes fast. Like really fast. Faster than the speed of light. Fast enough that you can get to your next destination by the end of the next commercial break.
Warp drives are staples of science fiction. And in 1994, they became a part of science fact. That’s when Mexican physicist Miguel Alcubierre, who was inspired by Star Trek, decided to see if it was possible to build a warp drive. Not like actually build one with wrenches and pipes, but to see if it was even possible to be allowed to build a warp drive given our current knowledge of physics.
Physics is just a mathematical exploration of the natural universe, and the natural universe appears to play by certain rules. Certain actions are allowed, and other actions are not allowed. And the actions that are allowed have to proceed in a certain orderly fashion. Physics tries to capture all of those rules and express them in mathematical form. So Alcubierre wondered: does our knowledge of how nature works permit a warp drive or not?
Researchers will soon be able to study biological changes at scales and speeds not previously possible to significantly expand knowledge in areas such as disease progression and drug delivery.
Physicists at The University of Queensland have used “tweezers made from light” to measure activity within microscopic systems over timeframes as short as milliseconds. Professor Halina Rubinsztein-Dunlop from UQ’s School of Mathematics and Physics said the method could help biologists understand what was happening within single living cells.
“For example, they will be able to look at how a cell is dividing, how it responds to outside stimuli, or even how chemical reactions affect cell properties,” Professor Rubinsztein-Dunlop said.
Here Harkos et al. review the role of continuous models and discrete models in predicting and understanding therapy delivery and efficacy in solid tumours. They propose ways to integrate mechanistic and AI-based models to further improve patient outcomes.
I’m back, baby. I’ve been away traveling for podcasts and am excited to bring you new ones with Michael Levin, William Hahn, Robin Hanson, and Emily Riehl, coming up shortly. They’re already recorded. I’ve been recovering from a terrible flu but pushed through it to bring you today’s episode with Urs Schreiber. This one is quite mind-blowing. It’s quite hairy mathematics, something called higher category theory, and how using this math (which examines the structure of structure) allows one manner of finding \.
The symbols and mathematical operations used in the laws of physics follow a pattern that could reveal something fundamental about the universe
Can one single mathematical framework describe the motion of a fluid and the individual particles within it? This question, first asked in 1900, now has a solution that could help us understand the complex behaviour of the atmosphere and oceans.
Reinforcement learning (RL) has become central to advancing Large Language Models (LLMs), empowering them with improved reasoning capabilities necessary for complex tasks. However, the research community faces considerable challenges in reproducing state-of-the-art RL techniques due to incomplete disclosure of key training details by major industry players. This opacity has limited the progress of broader scientific efforts and collaborative research.
Researchers from ByteDance, Tsinghua University, and the University of Hong Kong recently introduced DAPO (Dynamic Sampling Policy Optimization), an open-source large-scale reinforcement learning system designed for enhancing the reasoning abilities of Large Language Models. The DAPO system seeks to bridge the gap in reproducibility by openly sharing all algorithmic details, training procedures, and datasets. Built upon the verl framework, DAPO includes training codes and a thoroughly prepared dataset called DAPO-Math-17K, specifically designed for mathematical reasoning tasks.
DAPO’s technical foundation includes four core innovations aimed at resolving key challenges in reinforcement learning. The first, “Clip-Higher,” addresses the issue of entropy collapse, a situation where models prematurely settle into limited exploration patterns. By carefully managing the clipping ratio in policy updates, this technique encourages greater diversity in model outputs. “Dynamic Sampling” counters inefficiencies in training by dynamically filtering samples based on their usefulness, thus ensuring a more consistent gradient signal. The “Token-level Policy Gradient Loss” offers a refined loss calculation method, emphasizing token-level rather than sample-level adjustments to better accommodate varying lengths of reasoning sequences. Lastly, “Overlong Reward Shaping” introduces a controlled penalty for excessively long responses, gently guiding models toward concise and efficient reasoning.
The collective motion of bacteria—from stable swirling patterns to chaotic turbulent flows—has intrigued scientists for decades. When a bacterial swarm is confined in small circular space, stable rotating vortices are formed. However, as the radius of this confined space increases, the organized swirling pattern breaks down into a turbulent state.
This transition from ordered to chaotic flow has remained a long-standing mystery. It represents a fundamental question not only in the study of bacterial behavior but also in classical fluid dynamics, where understanding the emergence of turbulence is crucial for both controlling and utilizing complex flows.
In a recent study published in Proceedings of the National Academy of Sciences on March 14, 2025, a research team led by Associate Professor Daiki Nishiguchi from the Institute of Science Tokyo, Japan, has revealed in detail how bacterial swarms transition from organized movement to chaotic flow. Combining large-scale experiments, computer modeling, and mathematical analysis, the team observed and explained previously unknown intermediate states that emerge between order and turbulence.
