AI Hustle Podcast: "AI's Math Breakthroughs: New Paradigms & Problem Solving"

Hosts: Jaeden Schafer & Jamie McCauley
Date: January 17, 2026

Episode Overview

In this episode, Jaeden Schafer explores how AI is driving groundbreaking advances in mathematical problem-solving. The discussion moves beyond the hype, focusing on real-world achievements—such as AI inventing new math methods, solving previously unsolved problems, and reshaping how research is verified. Listeners are treated to stories of AI's recent victories in math competitions, the evolving relationship between human intuition and AI reasoning, and how these developments may impact not just math, but other fields like engineering and medicine.

Key Discussion Points & Insights

1. AI as an Inventor of New Math Methods

Timestamp: 00:45 – 03:40

• Mo Gawdat's Keynote Example:
  AI went beyond code optimization for matrix multiplication—historically unchanged for 56 years—and invented a “completely new way of doing math,” leading to a 26% performance boost and saving hundreds of millions in cost and energy at Google.

  “He said that recently … he told AI to improve itself … instead it invented a completely new way of doing math.” (01:04)

• Implications:
  AI is not just replicating human approaches but originating new paradigms, creating methods even experts haven’t considered.

2. AI’s Rapid Advances in Solving Math Problems

Timestamp: 04:00 – 09:00

• Recent Breakthroughs & Benchmarks:

  • GPT-5 Pro solved the “Yu Samurutsu’s 554th problem”—a feat no model had previously achieved.
  • AI achieved a perfect 120/120 score in the notoriously difficult Pootman competition, outperforming all human participants (“The median was zero … Huge milestone in AI.”). (05:08)
  • Neil Simani’s experiment:
    Simani, testing OpenAI’s latest model, pasted an unsolved math problem into ChatGPT. It generated a solution in 15 minutes, verified as correct by Harmonic, an automated math solution checker.

• Process Insight:
  ChatGPT’s “chain of thought” drew from a variety of mathematicians’ work and handled references creatively—not just mimicking, but synthesizing and improving upon ideas.

  “It pulled out a bunch of well known ideas from mathematicians … and then what absolutely blew my mind, it went and it found an old math overflow post from 2013 … and then instead of copying … it took a completely different approach and … produced a much more complete answer.” (07:15)

3. The Collaborative Nature of AI-Driven Discovery

Timestamp: 09:00 – 11:30

• Human Guidance is Key:
  AI needs direction—a human must “point it in a direction” for problem-solving, at least for now.

• Erdős Problems as a Benchmark:
  Since Christmas, 15 long-open problems from the famous Erdős list were solved; in 11 cases, published solutions cited AI tools.

  “11 out of 15 of those Erdős problems that got solved since Christmas were using AI tools.” (10:32)

• Role of AI Tools:
  Often AI assists rather than wholly replaces the mathematician, e.g., finding relevant past research or helping check logical arguments.

4. Experts’ Perspectives and the Limits of AI

Timestamp: 11:30 – 12:30

• Terence Tao’s View:
  One of the world’s top mathematicians, Tao recognizes that AI can produce “meaningfully new ideas on their own” but also strengthens human work by highlighting relevant research.

  “Tao … says that 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.” (11:45)

• AI’s Strengths:
  Especially skilled at systematically attacking overlooked or less-famous problems, since it doesn’t get bored or tired.

5. Progress in Verifying Mathematical Arguments

Timestamp: 12:30 – 13:15

• Checkable Proofs:
  New software lets researchers formalize difficult proofs so they’re machine-verifiable—a process sped up further by AI systems.

• Quote:

  “The most important signal is not how many problems actually get solved, but who's willing to use the tools.” — Tutor Archimec, founder of Harmonic (13:02)
  “These are people whose careers depend on being careful and credible. So when they say they rely on AI tools, that says a lot.” (13:10)

6. Broader Implications for Research & Innovation

Timestamp: 13:15 – 13:46

• The abilities that let AI reason through tough math are also applicable to fields like engineering, economics, medicine, and the sciences.
• As validation gets faster and models grow more capable, research timelines across disciplines could shrink dramatically.
• The host expresses personal enthusiasm for how this is already changing software engineering and predicts it will “dramatically speed up research and innovation.”

Notable Quotes & Memorable Moments

• On AI’s Inventiveness:

  “AI is definitely getting better at math … but beyond just getting better at solving math or … the way we might solve it, it’s creating new ways to solve math and coming up with completely new methods when it thinks that our methods are flawed.” (02:13)

• On Human-AI Collaboration:

  “AI isn’t out just there in a vacuum. It’s not just running around solving all the math problems of the world. Like, you have to point it in a direction …” (09:25)

• On Why AI is Particularly Good at Overlooked Problems:

  “AI systems can work really, like, methodically. They can search through thousands of possibilities. … it’s also because they don’t get bored.” (12:13)

• On Wider Impact:

  “The advancements being made in AI and math isn’t just exciting for math, but for so many other areas that are going to benefit … so many different areas are going to improve, including software engineering, which personally is getting me really excited this week.” (13:24)

Segment Timestamps

| Topic | Timestamp | |---------------------------------------------------------------|-----------------| | Mo Gawdat’s AI invents new math method at Google | 00:45 – 03:40 | | AI’s recent math breakthroughs (GTP-5 Pro, Pootman, Simani) | 04:00 – 09:00 | | Human guidance, Erdős problems, AI-assisted discovery | 09:00 – 11:30 | | Terence Tao’s perspective and AI’s limits/strengths | 11:30 – 12:30 | | Formal verification, Harmonic, expert adoption | 12:30 – 13:15 | | Cross-disciplinary implications, host reflections | 13:15 – 13:46 |

Summary & Takeaways

• AI is moving from replicator to originator—creating new math methods and solving long-standing problems, often in collaboration with human guidance.
• Verification tools like Harmonic make it easier to trust and build upon AI-generated solutions—gaining acceptance among top researchers.
• The most profound impact may come in fields beyond math, as AI’s reasoning and verification capacities turbocharge innovation in other sciences and industries.
• While a fully independent “AI mathematician” is still far off, the tools are already indispensable to serious research, and their role will only grow.