AI is learning to speak the language of physics — and the results are getting surprisingly close to real scientific reasoning.
Just over a year ago, the best-performing AI model tested on a set of exam-style physics problems scored about 64%. A year later, a newer model reached 90% — including problems that required considerably more advanced reasoning.
But the more intriguing development is happening beyond exams.
Researchers are beginning to give AI access to scientific data and the fundamental principles of physics, then asking it to work backward from observations to discover what might be missing.
In one striking experiment, researchers trained an AI system called ALBERT on the building blocks of quantum field theory and gave it experimental data from the Large Electron–Positron Collider, along with only the physics knowledge that existed before 1990.
The AI was not told about the top quark — a particle that would only be discovered in 1995.
Yet in less than an hour, it inferred the top quark's mass and other properties from the older experimental data.
That doesn't mean AI has suddenly become a physicist.
These systems can still make mistakes, lack human physical intuition, and require researchers to check their reasoning. But something important is changing: AI is moving beyond simply *answering questions about science* toward helping researchers analyze data, construct mathematical models, explore theories, and identify patterns that humans might otherwise miss.
The emerging vision is not AI replacing physicists.
It is AI becoming a new kind of scientific collaborator — one capable of searching through enormous spaces of possible explanations at machine speed, while humans provide the intuition, judgment, and direction.
And if that trajectory continues, the next breakthrough in physics might not come from a machine that knows all the answers…
Tim Cook told employees he will miss the role of chief executive officer but has "enormous comfort" in the leadership of his replacement, John Ternus.
Cook said he is not leaving Apple, but is stepping away from a role that he has loved deeply, and will remain at peace with his decision.
As executive chairman, Cook will remain responsible for working with governments around the world, including those of the US and China.
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Apple Inc.’s Tim Cook told employees that he’ll miss the role of chief executive officer but has “enormous comfort” in the leadership of his replacement, John Ternus.
Cook made the comments in an email to all employees on Monday, his final day as CEO. Cook took over for Steve Jobs in August 2011, when he embarked on a record-breaking 15-year tenure that included the launch of the Apple Watch, AirPods, and major expansions to the iPhone, iPad and Mac lines.
“As you know, I am not leaving Apple. But I am stepping away from a role that I have loved deeply,” Cook said in his email. “I will miss this work in ways I can only begin to imagine, even as I remain completely at peace with my decision.”
Discussing Ternus, Cook said that “few people understand what it takes to build products that change the world the way John does and I could not be more excited for his leadership.”
In his new job as executive chairman, Cook will remain responsible for working with governments around the world, including those of the US and China.
Here is Cook’s final memo to all employees as CEO:
Team,
Today is my last day as CEO of Apple. This is a moment I always knew would come one day, and yet it is still hard to believe it has arrived and I am writing these words. I love this company and the team behind it, and I couldn’t let this day pass without sending a note to you to tell you how grateful I am for the outpouring of affection you’ve sent my way, for the way you’ve shown up each and every day, and most of all, for the privilege of a lifetime serving as your leader.
The truth is, whatever there is to say about my success, I know it is all because of you. You have brought out the best in me. In all my life, I have never seen or been with such an extraordinary team of people before, and every day I get to see more examples of that.
There is something truly special about Apple. I am most proud of what an annual report could never capture. This place is proof that culture triumphs over everything. We share a belief that what we build matters and that we have both the opportunity and the responsibility to leave the world better than we found it. That purpose is part of what makes this place extraordinary. Apple helps nurture it, but I believe it lived within each of you long before you arrived here. It is what brought you to this company and what continues to drive the work you do every day.
Together, we have created something far greater than any one of us could have imagined or accomplished alone. And that’s the secret to our success. We bring out the best in each other. We lift each other up. We have made it possible to leave our “dent in the universe,” as Steve once described it, because of who we are and what we believe, because of what we value and how we see the world. How fortunate we are. How fortunate I am.
As you know, I am not leaving Apple. But I am stepping away from a role that I have loved deeply. I will miss this work in ways I can only begin to imagine, even as I remain completely at peace with my decision. I will miss leading you and being with you for every step, even as I take enormous comfort in handing the helm to someone as brilliant and wonderful and capable as John. Few people understand what it takes to build products that change the world the way John does and I could not be more excited for his leadership.
I hope you know how much I appreciate you and what an honor it has been to be your CEO. Most of all, I hope you will continue to be proud to be part of this remarkable place we call Apple and always give it your very best. When we bring our whole selves to this work, with care for one another and for the people we serve, there is no limit to the profound difference we can make.
I look forward to seeing you in my new role at Apple Park and around the world.
With all I have and all I am, I am always.
Yours,
Tim
Mark Gurman is the managing editor of the consumer technology team for Bloomberg News and chief correspondent for Apple and consumer hardware companies.
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Cecile G. Tamura' post:
Steve Jobs pulled off one of the greatest “reality distortion field” recruiting moves in business history.
In 1998, he convinced Tim Cook to leave Compaq—a company then valued at more than $30 billion—and join Apple, which was worth roughly $3 billion and was widely seen as being close to collapse.
Cook was 37, successful at Compaq, and had no obvious reason to jump into a troubled company. But Jobs got him into one meeting.
And somehow, that was enough.
Cook later recalled that Jobs laid out his vision for Apple: while virtually everyone else in the PC industry was abandoning the consumer market for servers, storage, and enterprise customers, Jobs was going all-in on consumers.
Jobs also showed Cook an early glimpse of what would become the iMac.
Cook remembers thinking:
> “I always thought following the herd was a bad idea.”
Then came the decisive realization: he believed he could make a contribution—and that working with Jobs would be “the privilege of a lifetime.”
So he listened to his gut.
> “There was literally no one around me that was advising me to do it.”
In March 1998, Cook joined Apple as Senior Vice President of Worldwide Operations, reportedly on a $400,000 base salary plus a $500,000 signing bonus.
He was 37.
Apple was struggling.
Compaq was enormously more valuable.
And virtually everyone around him thought he was making a mistake.
The rest, of course, became history.
Cook would eventually become the person who succeeded Steve Jobs as Apple’s CEO—and preside over one of the most valuable companies the world has ever seen.
Sometimes the biggest career decisions don't make sense on paper.
Sometimes you see something other people don't.
And sometimes, the most important thing you can do is listen to your gut.
Sắt gọi Zalo video lúc đang đi cắt tóc nên tạm ngắt rồi Mr. Lợi gọi lại lúc 10h29, cuộc gọi kéo dài 30 phút.
Cập nhật:
Sắt, Quế dành thời gian lên thăm bà Liên, Tuân
Gặp chị Liên qua video: béo bệu, không khỏe, răng rụng hết, nói phều phào, nghe không rõ, nói trước quên sau. Nghe Yến kể lại thì vừa rồi ngã ngồi ở sân, tay bị sưng nghi là do chóng mặt. Bị đại tràng kinh niên, ăn uống khó tiêu, hay bị đau bụng.
Tuất ở Đà Nẵng
Toản ở Quảng Trị, quê vợ, có 2 đứa con
Tiến ở Trảng Bom - Đồng Nai. Vợ đầu ở Phú Hòa - Phú Thủy có 1 đứa con gái. Vợ 2 ở Đồng Tháp có 2 đứa con đã ly dị, mỗi người nuôi một đứa con. Vợ 3 ở Đồng Nai, chưa có con.
Tùng ở Biên Hòa, Đồng Nai? Nói chung ổn.
Yến: Kiếm béo, bụng phệ cao 1 mét 4, nặng 70 kg. Có đứa đầu sinh năm 1994 đang làm ở Hà Nội, hiện đã có người yêu tuổi Mùi (2003), người Ninh Bình. Dự kiến tháng 8 âm lịch năm nay (Bính Ngọ) gia đình nhà trai sẽ đi gặp gia đình nhà gái.
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Sắt ngày 1/9 sẽ họp lớp cấp 3 Lệ Thủy, coi bơi 2/9, bay vào SG 3/9
Phong (con Sắt - Quế) đã có 2 đứa: trai đầu gái sau, đứa đầu 14 tuổi
Thắng (con Sắt - Quế) có 1 đứa con trai đầu 4 tuổi, đang mang thai đứa 2, con gái, sinh vào tháng 10. Thắng có 4 ô ô tải, 1 xe con do Sắt đầu tư. Chăm chỉ làm ăn, vợ ở nhà nội trợ.
Is substantive AI use in math research increasing? Which subfields are most affected? What problems have been solved? Who is writing them—and which AI models are they using? An empirical study of 32,944 math arXiv submissions from Mar. 1–Aug. 20, 2026.
The AI Math "Gold Rush": A Reality Check
Lately, the mathematics world has been buzzing with a mix of excitement and anxiety over artificial intelligence. Some see AI as a powerful new tool for groundbreaking discoveries, while others worry it could undermine traditional research. But until now, this debate has been driven more by speculation than by hard data.
To find out what’s *actually* happening, researchers took a deep dive into the data, analyzing nearly 33,000 mathematics papers posted to the preprint server arXiv over a six-month period in 2026. They were looking for papers where authors explicitly admitted to using AI in meaningful, substantive ways.
What they found paints a picture of a genuine "gold rush" that is accelerating rapidly, but remains highly concentrated:
* A Meteoric Rise: AI adoption is exploding. In March, only about 1.4% of math papers disclosed meaningful AI use. By mid-August, that number had skyrocketed to over 14%.
* Winning the Lottery on Hard Problems: AI isn’t just being used for basic formatting or simple calculations. Researchers are actively applying it to genuine, unsolved mathematical mysteries. Strikingly, authors reported that they were able to fully resolve 71% of the open problems they tackled with AI, mostly by successfully proving new conjectures.
* A Concentrated Effort: This AI-driven research isn’t spread evenly. It is heavily clustered in specific branches of mathematics (like Combinatorics and Metric Geometry). Geographically, the United States and China dominate the field, accounting for roughly two-thirds of this research.
* Big Tech’s Footprint: The tools powering this shift are also concentrated, with OpenAI’s systems being the most frequently used, followed by Anthropic.
The integration of AI into mathematical research is no longer just a hypothetical future—it is happening right now, and at a breathtaking pace. However, the "gold rush" is still in its early, uneven stages. As these tools become more powerful and widespread, the mathematical community will need to navigate both the thrilling new opportunities for discovery and the valid concerns about how this technology will reshape the future of the field.
1. Donald E. Knuth. Claude’s cycles, 2026. Stanford Computer Science Department.
AI Overview
Donald E. Knuthpublished a short paper titled "Claude's Cycles" in early 2026 after Anthropic's Claude Opus 4.6 AI model successfully solved an open graph theory and combinatorics problem he had been working on for weeks. [1, 2]
What is the Paper About?
The Problem: Knuth was wrestling with a directed Hamiltonian cycle decomposition challenge for a future volume of The Art of Computer Programming involving a m × m × m grid graph where vertices must be split into three separate cycles. [1, 2, 3]
The AI's Role: Collaborator Philip Stappers guided Claude Opus 4.6 through 31 systematic explorations over the course of about an hour until the AI produced a working concrete construction and Python program for odd values of m. [1]
The Proof: Knuth analyzed the AI's output, understood the underlying logic, wrote the formal mathematical proof himself, and generalized it to 760 valid structural solutions. [1, 2]
Significance
The Reaction: Knuth famously opened his paper with the words "Shock! Shock!" and noted that the experience forced him to revise his skepticism toward generative AI.
Collaboration Milestone: It stands as a landmark human-AI collaboration verified by one of the founding pioneers of computer science. [1, 2, 3, 4]
2. Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood. Remarks on the disproof of the unit distance conjecture, 2026.
AI Overview
The paper titled "Remarks on the disproof of the unit distance conjecture" is an influential 19-page mathematical expository note published on arXiv on May 20, 2026. [1]
Co-authored by a prestigious panel of nine mathematicians—Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood—it serves as the definitive human-verified translation and commentary on OpenAI's autonomous disproof of Paul Erdős's 80-year-old unit distance conjecture. [1, 2]
Core Purpose of the Paper
Human Verification: The authors thoroughly reviewed and verified a 125-page computational counterexample generated by an internal OpenAI reasoning model (utilizing contributions from OpenAI researchers like Boris Alexeev and Lijie Chen). [1, 2]
Simplification & Digestion: The 19-page document provides a "human-digested," simplified, and generalized version of the highly technical AI proof. [1, 2]
Contextual Analysis: It maps the AI's unexpected techniques to existing human mathematical theories. [1]
The Mathematical Breakthrough
Paul Erdős's 1946 conjecture stated that the maximum number of pairs exactly one unit apart in a set of \(n\) points in a Euclidean plane grew near-linearly, at \(n^{1+o(1)}\), optimized by a square grid configuration. [1, 2]
The paper confirms that the AI successfully disproved this by proving:
Polynomial Bound: There exists an absolute constant \(\delta > 0\) such that the number of unit distances is at least \(n^{1+\delta }\) for infinitely many \(n\). [1, 2]
Shift in Field: Instead of traditional geometric or graph-theoretic approaches, the proof uniquely utilizes algebraic number theory. It constructs configurations using infinite class field towers, Minkowski lattices, and Golod–Shafarevich theory. [1, 2, 3]
Historical Precedents: The paper highlights that the underlying logic draws on deep arithmetic concepts that can retrospectively be attributed to Ellenberg–Venkatesh, Golod–Shafarevich, and Hajir–Maire–Ramakrishna. [1]
3. Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, and Lauren Williams. First proof second batch, 2026.
AI Overview
First Proof Second Batch (arXiv:2606.18119) is a June 2026 research report and project release by mathematicians Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, and Lauren Williams that tests frontier artificial intelligence models on original, unpublished research-level mathematics problems. [1, 2, 3]
Project Overview
The Editors: Mohammed Abouzaid (Stanford), Nikhil Srivastava (UC Berkeley), Rachel Ward (UT Austin), and Lauren Williams (Harvard). [1, 2]
The Goal: Assess whether leading AI systems can perform genuine mathematical reasoning rather than just pattern-matching against previously solved problems on the internet. [1, 2, 3]
The Method: The project used a set of 10 original, unpublished research problems from the authors' own work so the answers could not be found in the AI training data. [1, 2]
Findings: The initiative helps benchmark how well current AI systems handle advanced mathematical deduction and highlights the ongoing gap between automated calculation and conceptual mathematical framing. [1, 2]
4. Levent Alpöge and Claude Fable 5. A counterexample to the jacobian conjecture in dimension three, 2026. Announced July 2026.
AI Overview
In July 2026, mathematician Levent Alpöge used Anthropic's Claude Fable 5 to find a simple polynomial map that disproves the 87-year-old Jacobian Conjecture in three dimensions and higher. [1, 2, 3]
What is the Jacobian Conjecture?
First proposed in 1939 by mathematician Ott-Heinrich Keller.
It stated that if a polynomial function has a constant, non-zero Jacobian determinant, it must have a reverse function (be invertible).
Stephen Smale later named it one of the major math problems for the 21st century. [1, 2, 3, 4]
The Counterexample
Levent Alpöge found a function in three dimensions (\(C^{3}\)).
The function has a constant Jacobian determinant of \(-2\).
It fails to be one-to-one (injective) because it maps three different input points to the same output point.
Because it is not injective, it cannot be reversed, proving the conjecture false. [1, 2, 3, 4, 5, 6]
Why This Matters
It disproves the conjecture for every dimension greater than two.
The original two-dimensional case remains an open problem.
Other mathematicians quickly verified the short formula.
It marks a major milestone for using AI tools to solve pure mathematics problems. [1, 2, 3, 4, 5, 6]
5. OpenAI. Ten advances in mathematics and theoretical computer science, 2026.
AI Overview
On August 1, 2026, OpenAI published ten major breakthroughs in mathematics and theoretical computer science achieved by an internal AI prototype named Astra. [1, 2, 3]
Key Details of the Project
The AI Model: An unreleased version of OpenAI's model codenamed Astra did the core reasoning.
The Cost: The compute time cost roughly $2,000 at standard API rates.
The Output: A massive document containing ten distinct chapters or papers spanning nearly 250 pages.
Verification: Every single proof was translated into a machine-checkable Lean 4 formal proof to verify every logical step. [1, 2, 3, 4, 5, 6]
Fields and Problems Solved
The solved problems had been stuck or open for at least ten years. They cover several core areas: [1, 2]
Group Theory: Construction of non-sofic groups.
Operator Algebras: A disproof of Connes's rigidity conjecture.
Extremal Combinatorics: Solutions tackling specific Erdős problems (146, 180, and 183).
Other Fields: High-dimensional geometry (sphere packing), coding theory, arithmetic circuit complexity, quantum complexity, and lattice cryptography. [1, 2, 3, 4]
Current Status
Peer Review: The formal human peer review process is still underway.
Attribution: OpenAI openly stated that the AI generated the math arguments, while humans helped prepare manuscripts and check the framing.
Public Access: You can view the full documents and technical details through the OpenAI Research portal. [1, 2, 3]
6. Claude. More than two thirds of the zeros of the riemann zeta function are simple and on the critical line, 2026. Anthropic.
AI Overview
In August 2026, an unreleased research version of Claude developed by Anthropic made a major breakthrough in number theory by discovering and writing a paper titled "More than two thirds of the zeros of the Riemann zeta function are simple and on the critical line". [1, 2]
The paper was published on arXiv (authored by Claude, with verification and responsibility taken by Anthropic mathematicians Levent Alpöge and Ralph Furman). [1]
Key Takeaways of the Breakthrough
The Record Leap: Claude unconditionally proved that at least 67.25% (more than two thirds) of the non-trivial zeros of the Riemann zeta function are simple and lie on the critical line. [1, 2]
Previous Human Record: This shattered a mathematical bottleneck that had stood since 2020, raising the known lower bound from 41.6% to 67.25%. [1, 2]
Distinct Zeros: The proof also established that at least 83.62% (five sixths) of all non-trivial zeros are distinct. [1]
How it was Done: Running inside Claude Code, the model conducted an autonomous research cycle involving 60 subagents, 2,400 shell commands, and 31 million output tokens. It synthesized complex, previously separate lines of math literature and successfully formalized its proof in Lean 4. [1, 2, 3]
Status of the Riemann Hypothesis: This does not solve the Riemann Hypothesis itself (which requires 100% of non-trivial zeros to be on the critical line), but it represents the largest single advancement on this specific numerical bound in decades. [1, 2]
An independent evaluation conducted by former Google engineer Deedy Das tested 7 state-of-the-art LLMs on the IMO 2026 problems, while other independent sets or corporate disclosures highlighted varying counts of participating or evaluated models. [1, 2]
Key Details on AI Evaluation at IMO 2026
Independent Runs: Deedy Das ran an evaluation featuring 7 frontier models in his GitHub benchmark, with multiple models achieving a perfect 42/42 score. [1, 2]
Top Performers: Models such as Claude Fable 5, GPT-5.6 Sol, and Kimi K3 achieved perfect scores in independent or self-administered harnesses. [1, 2, 3]
Official Status: AI models did not officially participate in real-time alongside human contestants; instead, they were tested offline after the human exam concluded using independent evaluation harnesses. [1, 2, 3]
Corporate Entries: Specific companies like Huawei (with "Celia") and Xiaohongshu (with "dots-note-3.0") also submitted independent runs for official grading after the human competition. [1, 2]
