The AI Podcast: Math's New Era

Episode Date: January 15, 2026
Host: The AI Podcast
Theme: How AI is not just solving mathematical problems but revolutionizing how math is done, with tangible impacts on research, verification, and intellectual discovery.

Episode Overview

This episode dives deep into the burgeoning capabilities of modern AI in mathematics. The host unpacks recent breakthroughs where AI doesn't just replicate human solutions but invents new mathematical methods, solves previously unsolved problems, and acts as both a creative and collaborative tool in the field. Drawing on recent stories, competitions, expert opinions, and verification technologies, the episode explores what this means for the future of math and beyond.

Key Discussion Points & Insights

1. AI Creating New Ways of Doing Math

• AI as an Inventor, Not Just a Problem Solver

  • The episode opens with a story about Mo Gada, former Google X executive, who highlighted how AI discovered a new matrix multiplication method that outperformed the decades-old human approach.
  • “When he told AI to improve itself, the AI realized that their matrix multiplication method was flawed. It invented a completely new way… resulting in a 26% performance boost and the removal of hundreds of millions of dollars in cost and energy use for Google.” (03:00–03:40)

• AI Moving Beyond Optimization

  • AI doesn't merely improve existing solutions but can invent novel approaches.
  • The host calls this "fascinating" and notes it signals AI's leap from mimicry to creativity.
  • “It’s creating new ways to solve math and coming up with completely new methods when it thinks that our methods are flawed.” (03:40–03:55)

2. State of AI and Math Today

• Recent Breakthroughs in Problem-Solving
  • Citing mathematician Bartosz Nasrecki, the host notes that GPT-5 Pro solved Yu Semrutsu's 554th problem—a first for an AI model, requiring “elementary abstract algebra reasoning.” (04:40–05:10)
  • AI tools are now achieving perfect scores in elite math competitions like the Putnam, which is known for its difficulty.
  • “AI just achieved a perfect score on the hardest math competition in the world. The Putman has 12 problems… the highest score last year was 90, the median was 0. Axiom’s AI Pro Prover in Lear scored 120 out of 120.” (05:30–06:00)

3. Solving Previously Unsolved Problems

• Anecdote From Neil Szymani (Software Engineer)
  • Szymani used OpenAI’s latest model to attempt an unsolved problem (from a famous list by mathematician Paul Erdős). Within 15 minutes, ChatGPT generated a solution—a first.
  • The reasoning was intricate: The AI combined information from known formulas and even referenced a previous Harvard mathematician’s approach, adapting and extending it.
  • “It found an old math overflow post from 2013… but instead of copying the solution… it took a completely different approach and ended up producing a much more complete answer.” (07:10–08:20)

4. Verification and Human Collaboration

• Human/AI Collaboration on Open Problems

  • Of 15 previously open Erdős problems solved since Christmas, 11 explicitly involved AI tools in their solutions.
  • “Whether… an AI model 100% solving the problem, or a human… using AI tools to help them, 11 out of 15… that got solved since Christmas were using AI tools.” (09:40–10:00)

• Role of Mathematicians

  • Mathematicians like Terence Tao acknowledge that while AI often builds on human research, it also introduces genuinely novel approaches or helps find relevant prior research to build upon.
  • “In a whole bunch of different cases, AI systems produce meaningfully new ideas on their own. But in other areas, they helped by finding relevant past research that humans could build on.” (10:15–10:40)

• Will AI Replace Mathematicians?

  • Not soon, according to Tao: “Fully independent mathematicians are still a long way off... but these tools are already making a huge difference.” (11:00–11:15)
  • AI is especially good at tackling overlooked problems due to its tirelessness and ability to methodically check thousands of possibilities.

5. Accelerating Research and Verification

• Automated Proof Checking

  • Advancements in software and AI allow translation of proofs from natural language to precise, verifiable formats—making it easier to confirm results and accelerate research cycles.
  • This shift speeds up the process of building upon verified knowledge.

• Notable Quote by Tutor Archimec (Founder of Harmonic)

  • “The most important signal is not how many problems actually get solved, but who’s willing to use the tools... When serious math and computer science professors say they rely on AI tools, that says a lot.” (12:40–13:00)

6. Broader Implications Beyond Math

• The advancements in reasoning and verification are already beginning to impact fields like engineering, economics, medicine, and software development.

• “Progress in a lot of those fields is often slow because problems are really complex, they’re hard to verify. So as the AI systems get better at exploring ideas and checking work and connecting past knowledge, they are going to dramatically speed up research and innovation.” (13:20–13:45)

Memorable Quotes & Moments

• "It’s creating new ways to solve math and coming up with completely new methods when it thinks that our methods are flawed." — Host (03:55)
• "AI just achieved a perfect score on the hardest math competition in the world... Axiom’s AI Pro Prover in Lear scored 120 out of 120." — Host quoting DD (05:50)
• “It took a completely different approach and ended up producing a much more complete answer to the question.” — Host, discussing ChatGPT’s problem-solving (08:20)
• “Fully independent mathematicians are still a long way off... but these tools are already making a huge difference.” — Host citing Terence Tao (11:10)
• “What matters is that serious math and computer science professors are actually using them. These are people whose careers depend on being careful and credible. So when they say they rely on AI tools, that says a lot.” — Tutor Archimec (13:00)

Timestamps of Important Segments

• [03:00] Mo Gada’s AI matrix multiplication breakthrough
• [04:40] GPT-5 Pro solves Yu Semrutsu's 554th problem
• [05:30] AI perfect score in Putnam math competition
• [06:50] OpenAI model solves previously unsolved math problem
• [08:20] AI’s new reasoning methods and knowledge synthesis
• [10:00] AI-human collaboration on Erdős problems
• [11:00] Terence Tao on the limitations and promise of AI in mathematics
• [12:40] Tutor Archimec on the adoption of AI by academic professionals
• [13:20] Implications for broader scientific and engineering fields

Tone and Style

The host’s language is engaged, enthusiastic, and clearly directed at both enthusiasts and professionals. He contextualizes technical achievements using accessible examples, expresses awe at AI's creativity, and emphasizes both the collaboration and the limitations of current models.

Summary

This episode convincingly shows that AI’s new era in mathematics is not just about automation, but the emergence of genuine innovation—solving old problems, devising new math, expediting verification, and amplifying human research. With testimony from both AI practitioners and world-class mathematicians, and with several remarkable recent milestones, the episode captures a field at the threshold of transformation and suggests cascading impacts for research and science more broadly.