Podcast Summary: Jaeden’s Take on AI Math

The Jaeden Schafer Podcast | January 15, 2026

Episode Overview

Jaeden Schafer takes listeners on a journey through the rapidly evolving landscape of AI in mathematics. The episode explores stories and real-world breakthroughs where AI is not just solving math problems, but pioneering entirely new mathematical techniques—sometimes solving problems that have stumped humans for decades. Schafer offers an accessible, no-hype analysis, reflecting on why these advances matter and how they signal broader transformations in research, science, and innovation.

Key Discussion Points & Insights

1. AI Innovating in Math, Not Just Automating

• Mo Gawdat’s Example:
  • Former Google X executive, Mo Gawdat, described an AI that, when prompted to optimize itself, did not simply fine-tune existing software.
  • Instead, the AI invented a completely new matrix multiplication method, outperforming the decades-old standard and resulting in a 26% performance increase and saving "hundreds of millions of dollars in cost and energy use for Google."
    • (Jaeden Schafer, 00:43)
  • Key Point: AI now corrects and improves on human mathematical methods, establishing new benchmarks in efficiency.

2. AI’s Emerging Competence in High-Level Math Problems

• Recent Breakthroughs:
  • Jaeden references a social media post by Bartosz Nasrecki where GPT5Pro solved the challenging "Yu Semrutsu’s 554th problem" in only 15 minutes, without any internet search, displaying deep understanding of abstract algebra.
    • (Jaeden Schafer, 03:08)
  • In competitive math: Axiom’s AI Pro Prover in Lear aced the prestigious Pootman competition—with a perfect 120/120 score, whereas the highest human score was 90 and the median was zero.
    • (Jaeden Schafer, 04:00)

3. Solving Unsolved Math Problems

• Case Study: Neil Soni and Erdos Problems
  • Software engineer Neil Soni tested OpenAI’s latest model on tough, unsolved math questions compiled by the mathematician Paul Erdos.
  • The AI generated a solution to a particularly complex problem in 15 minutes; its answer passed rigorous checking via “Harmonic,” a tool for verifying math proofs.
  • Neil Soni’s quote:

    "I wanted to get a sense of where AI systems can actually solve open math problems and when they still get stuck."

    • (Jaeden Schafer relays, 07:46)
  • Implication: AI is now able to solve problems previously believed to be out of reach without human guidance.

4. AI’s Reasoning and Research Abilities

• How AI Solves Problems:
  • AI models exhibit reasoning by:
    • Collating knowledge from multiple renowned mathematicians (e.g., leveraging concepts like Bertrand’s postulate, the Star of David theorem, and Paul Erdos’s works).
    • Mining old academic discussions and adapting relevant ideas to tackle new problems.
  • Impressed reflection:

    "Its reasoning was so good, like it was going and doing research, finding old posts, finding solutions to similar problems, adapting them to this problem, and writing more complete versions of it, which was incredible."

    • (Jaeden Schafer, 10:25)

5. Collaboration Required: Human Direction Still Needed

• AI isn’t yet fully independent:
  • It still requires humans to “point it in a direction.”
  • Progress comes from directing AI at specific challenge sets (e.g., the Erdos list), not from it operating autonomously without guidance.

6. Quantifiable Impact of AI-Assisted Math

• Recent Stats:
  • Since Christmas, 15 math problems from the Erdos list have moved from “open” to “solved”; in 11 of these cases, published solutions explicitly acknowledged the use of AI tools in the process.
    • (Jaeden Schafer, 14:13)
  • This is evidence of meaningful progress and adoption within serious math circles.

7. Expert Perspectives: Mathematicians on AI’s Role

• Terence Tao:

  • Acknowledges that AI systems are, in some cases, producing “meaningfully new ideas” on their own, while also supporting humans by uncovering past research.
    • (Jaeden Schafer, 16:37)
  • Nuance: AI mathematicians fully supplanting humans are a long way off, but “these tools are already making a huge difference.”
    • (Jaeden Schafer paraphrasing Tao)

• AI especially apt at overlooked or tedious problems:

  "They can search through thousands of possibilities... they don't get bored."

  • (Jaeden Schafer, referencing Tao, 19:22)

8. Enabling Faster & More Reliable Proof Verification

• Formal Verification Tools:

  • New software allows for precise, automated checking of mathematical proofs (previously written in messy natural language).
  • Harmonic is highlighted as a popular tool among mathematicians for validation.

• Founder’s Insight (Tudor Arkemic, Harmonic):

  "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."

  • (Jaeden Schafer quoting Arkemic, 21:08)

9. Broader Implications for Other Fields

• AI’s math-focused advancements can "dramatically speed up research and innovation" in other complex domains such as engineering, economics, medicine, and science, as verifying and exploring new ideas becomes easier and faster.

• Personal excitement from Jaeden:

  "The reasoning capability of these models improving means that so many different areas are going to improve, including software engineering, which personally is getting me really excited this week."

  • (Jaeden Schafer, 23:45)

Notable Quotes & Memorable Moments

• On AI Innovating Math:

  "[The AI] invented a completely new way of doing math... resulting in a 26% performance boost and the removal of hundreds of millions of dollars in cost and energy use for Google."
  — Jaeden Schafer relaying Mo Gawdat’s keynote (01:02)

• On AI's Research Process:

  "It wasn't just copying how a Harvard mathematician solved that problem, it took a completely different approach and ended up producing a much more complete answer."
  — Jaeden Schafer (12:48)

• Mathematician Usage as a Signal:

  "What matters is that serious math and computer science professors are actually using them... when they say they rely on AI tools, that says a lot."
  — Tudor Arkemic, Harmonic (quoted by Jaeden Schafer, 21:08)

• AI Beyond Just Math:

  "Advancements being made in AI and math isn't just exciting for math, but for so many other areas that are going to benefit."
  — Jaeden Schafer (23:08)

Timestamps for Key Segments

• 00:43 – Matrix multiplication breakthrough at Google via AI
• 03:08 – GPT5Pro solves "Yu Semrutsu’s 554th problem"
• 04:00 – AI achieves perfect score in top math competition
• 07:46 – Neil Soni tests OpenAI model on Erdos list problems
• 10:25 – How the AI reasons and researches solutions
• 14:13 – 15 Erdos problems solved by AI since Christmas
• 16:37 – Terence Tao’s perspective on AI-generated math ideas
• 19:22 – AI and the tedium of large search spaces
• 21:08 – Professor adoption: credibility signal from Harmonic
• 23:08 – Implications for wider fields and Jaeden’s outlook

Overall Tone & Conclusion

Jaeden Schafer maintains an optimistic, grounded tone throughout the episode, emphasizing excitement without hype and focusing on tangible milestones and expert perspectives. He repeatedly underscores that while AI’s accomplishments in mathematics are stunning, the real transformative power is in how these advances spill over into other domains, catalyzing faster, more robust progress across science and industry.

For listeners wanting a snapshot of how AI is quietly—yet rapidly—reshaping the way humanity approaches and verifies math problems, this episode is a must-listen.