Evidence

Format Online paper / PDF

"LLM and reinforcement-learning systems can generate mathematical proofs whose correctness is established by an independent formal checker."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title Olympiad-level formal mathematical reasoning with reinforcement learning

Source authors Thomas Hubert; Rishi Mehta; Laurent Sartran; et al.

Source year 2025

Confidence high

Importance high

Format Web Page

"The tediousness and unintuitiveness of writing formal proofs helped keep proof assistants niche, an asymmetry AI could change."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title A shallow dive into formal verification

Source authors Vitalik Buterin

Source year 2026

Confidence high

Importance high

Format Online paper / PDF

"Writing machine-checkable proofs remains tedious and difficult for human programmers."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title What’s in a Proof? Analyzing Expert Proof-Writing Processes in F* and Verus

Source authors Rijul Jain; Shraddha Barke; Gabriel Ebner; Md Rakib Hossain Misu; Shan Lu; Sarah Fakhoury

Source year 2025

Confidence high

Importance high

Format Web Page

"An accepted formal proof establishes the stated theorem under its assumptions, not necessarily the theorem’s intended informal meaning."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title Validating a Lean Proof

Source authors Lean development team

Source year 2026

Confidence high

Importance high

Format Web Page

"A formal proof can be produced by a human, a search procedure, or an LLM, while a trusted checker independently verifies that it follows from the stated axioms and inference rules."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title Validating a Lean Proof

Source authors Lean development team

Source year 2026

Confidence high

Importance high

Format Online paper / PDF

"Proof assistants have existed for roughly 60 years."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER The Final Form of Software Development

Source title Characteristics of de Bruijn’s early proof checker Automath

Source authors Herman Geuvers; Rob Nederpelt

Source year 2022

Confidence high

Importance high

Format Online paper / PDF

"Terence Tao argues that training mathematicians requires human understanding, not merely the production of correct homework answers."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER Judging the Plausibility Machine

Source title Mathematics in the age of AI

Source authors Terence Tao

Source year 2026

Confidence high

Importance mid

Format Podcast / Spotify embed

"Terence Tao recommends using AI only to the extent that its outputs can be independently verified."

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER Judging the Plausibility Machine

Source title Can AI help us solve the hardest problems in Mathematics? Terry Tao - #535

Source authors Brian Keating; Terence Tao

Source year 2025

Confidence high

Importance high

Format Podcast / Spotify embed

"Terence Tao argues that students need substantially more training in how to validate information when AI can generate polished but unreliable answers."

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER Judging the Plausibility Machine

Source title Can AI help us solve the hardest problems in Mathematics? Terry Tao - #535

Source authors Brian Keating; Terence Tao

Source year 2025

Confidence high

Importance high

Format Online paper / PDF

"AI-generated unit tests can contain incorrect expected values and require human correction before they become reliable checks."

View Source

Location PART 3 - THE THIRD AXIS CHAPTER 15: DEPLOY NOW, PRAY LATER Judging the Plausibility Machine

Source title How students use generative AI for software testing: An observational study

Source authors Baris Ardic; Quentin Le Dilavrec; Andy Zaidman

Source year 2026

Confidence high

Importance high