The trick: the LLM doesn't need to be right. It proposes proof steps in Lean, and the proof assistant mechanically checks each one. Wrong steps get rejected, right ones compose. AlphaProof and AlphaGeometry work this way: neural guesses, symbolic verification.
October 9, 2026 at 2:00 AM
The trick: the LLM doesn't need to be right. It proposes proof steps in Lean, and the proof assistant mechanically checks each one. Wrong steps get rejected, right ones compose. AlphaProof and AlphaGeometry work this way: neural guesses, symbolic verification.
Most research mathematicians must have realized that if they didn't adapt after "AlphaGo versus Lee Sedol" & "AlphaGeometry 2" that they were living on borrowed time.
Pure hubris to have thought otherwise, imho.
Pure hubris to have thought otherwise, imho.
October 7, 2026 at 2:41 AM
Most research mathematicians must have realized that if they didn't adapt after "AlphaGo versus Lee Sedol" & "AlphaGeometry 2" that they were living on borrowed time.
Pure hubris to have thought otherwise, imho.
Pure hubris to have thought otherwise, imho.
AI has fought over two 60-year-old traditions: symbolic (rules) and neural (pattern-matching). Neither won — the best systems use both. AlphaGeometry solved 25/30 Olympiad geometry problems this way.
sgopalanbtg.substack.com/p/explainer-...
#AI #Neurosymbolic
sgopalanbtg.substack.com/p/explainer-...
#AI #Neurosymbolic
Explainer: Neural vs. Symbolic AI — The Two Traditions Behind Everything
Sriram Gopalan's thoughts on AI
sgopalanbtg.substack.com
September 23, 2026 at 8:14 PM
AI has fought over two 60-year-old traditions: symbolic (rules) and neural (pattern-matching). Neither won — the best systems use both. AlphaGeometry solved 25/30 Olympiad geometry problems this way.
sgopalanbtg.substack.com/p/explainer-...
#AI #Neurosymbolic
sgopalanbtg.substack.com/p/explainer-...
#AI #Neurosymbolic
I have done enough work with secondary and some primary school students to know just how absurd the statement of a grad student being pretty close to a blank slate is :-)
But talking about facts, unless this one here is a blatant lie, how does it fit your model? deepmind.google/blog/ai-solv... 1/
But talking about facts, unless this one here is a blatant lie, how does it fit your model? deepmind.google/blog/ai-solv... 1/
AI achieves silver-medal standard solving International Mathematical Olympiad problems
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
deepmind.google
September 18, 2026 at 6:15 PM
I have done enough work with secondary and some primary school students to know just how absurd the statement of a grad student being pretty close to a blank slate is :-)
But talking about facts, unless this one here is a blatant lie, how does it fit your model? deepmind.google/blog/ai-solv... 1/
But talking about facts, unless this one here is a blatant lie, how does it fit your model? deepmind.google/blog/ai-solv... 1/
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
A new reinforcement-learning model tailored for topological quantum circuits synthesised a 14-qubit error-resilient state preparation protocol requiring 70% fewer quantum gates than the best human-de…
thewhole.day
September 3, 2026 at 10:13 AM
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
A new reinforcement-learning model tailored for topological quantum circuits synthesised a 14-qubit error-resilient state preparation protocol requiring 70% fewer quantum gates than the best human-de…
thewhole.day
September 2, 2026 at 7:17 PM
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
A new reinforcement-learning model tailored for topological quantum circuits synthesised a 14-qubit error-resilient state preparation protocol requiring 70% fewer quantum gates than the best human-de…
thewhole.day
September 2, 2026 at 6:56 PM
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
A new reinforcement-learning model tailored for topological quantum circuits synthesised a 14-qubit error-resilient state preparation protocol requiring 70% fewer quantum gates than the best human-de…
thewhole.day
September 2, 2026 at 6:48 PM
Google DeepMind’s AlphaGeometry-Quantum designs novel room-temperature quantum algorithm in seconds
https://thewhole.day/s/552/en/s02.html
https://thewhole.day/s/552/en/s02.html
Samuel Xiao, Judy Song, Rory Hu, Ziliang Zong: NL2AGBench: Benchmarking LLM Auto-Formalization for AlphaGeometry https://arxiv.org/abs/2608.28481 https://arxiv.org/pdf/2608.28481 https://arxiv.org/html/2608.28481
August 31, 2026 at 6:40 AM
Samuel Xiao, Judy Song, Rory Hu, Ziliang Zong: NL2AGBench: Benchmarking LLM Auto-Formalization for AlphaGeometry https://arxiv.org/abs/2608.28481 https://arxiv.org/pdf/2608.28481 https://arxiv.org/html/2608.28481
This is part of the problem on social media. "Sorry, but my LLM query was wrong, so all AI is trash" while ignoring the success of AlphaFold, AlphaGeometry, or FireSat. Look at non-LLM AI models. There are major breakthroughs occurring.
August 22, 2026 at 11:00 AM
This is part of the problem on social media. "Sorry, but my LLM query was wrong, so all AI is trash" while ignoring the success of AlphaFold, AlphaGeometry, or FireSat. Look at non-LLM AI models. There are major breakthroughs occurring.
Google diz que sua IA seria medalha de ouro na Olimpíada de Matemática
https://tecnoblog.net/noticias/google-diz-que-sua-ia-seria-medalha-de-ouro-na-olimpiada-de-matematica/?utm_source=flipboard&utm_medium=activitypub
Posted into Tecnologia @tecnologia-FlipboardBR
https://tecnoblog.net/noticias/google-diz-que-sua-ia-seria-medalha-de-ouro-na-olimpiada-de-matematica/?utm_source=flipboard&utm_medium=activitypub
Posted into Tecnologia @tecnologia-FlipboardBR
Google diz que sua IA seria medalha de ouro na Olimpíada de Matemática • Tecnoblog
AlphaGeometry 2 acerta 42 de 50 questões de geometria. Google DeepMind acredita que habilidades podem ser úteis para resolver problemas mais complexos.
tecnoblog.net
February 7, 2025 at 10:31 PM
Google diz que sua IA seria medalha de ouro na Olimpíada de Matemática
https://tecnoblog.net/noticias/google-diz-que-sua-ia-seria-medalha-de-ouro-na-olimpiada-de-matematica/?utm_source=flipboard&utm_medium=activitypub
Posted into Tecnologia @tecnologia-FlipboardBR
https://tecnoblog.net/noticias/google-diz-que-sua-ia-seria-medalha-de-ouro-na-olimpiada-de-matematica/?utm_source=flipboard&utm_medium=activitypub
Posted into Tecnologia @tecnologia-FlipboardBR
Clearly the search space of AlphaGeometry (last year's system) is very large. A great depth of domain knowledge has been brought into the formal language by many large collaborations (e.g. Lean). I assume DeepMind builds on it implicitly (synthetic data?).
leanprover-community.github.io
leanprover-community.github.io
Lean community
leanprover-community.github.io
September 7, 2025 at 8:41 PM
Clearly the search space of AlphaGeometry (last year's system) is very large. A great depth of domain knowledge has been brought into the formal language by many large collaborations (e.g. Lean). I assume DeepMind builds on it implicitly (synthetic data?).
leanprover-community.github.io
leanprover-community.github.io
Deepmind claims that its AI is superior to international mathematical Olympic gold medalists
The AI system developed by Google Deepmind, the leading AI research lab at Google, appears to outperform the average gold medalist when solving geometric problems in international mathematical…
The AI system developed by Google Deepmind, the leading AI research lab at Google, appears to outperform the average gold medalist when solving geometric problems in international mathematical…
Deepmind claims that its AI is superior to international mathematical Olympic gold medalists
The AI system developed by Google Deepmind, the leading AI research lab at Google, appears to outperform the average gold medalist when solving geometric problems in international mathematical competition. The system called Alphageometry2 is an improved version of the system, Alphageometry. Its deep attitude was released last January. in Newly published researchThe deep researchers behind Alphageometry2 claim that AI can solve 84% of all geometric problems over the past 25 years at the International Mathematics Olympiad (IMO), a mathematics contest for high school students.
memotrends.com
February 7, 2025 at 6:59 PM
Deepmind claims that its AI is superior to international mathematical Olympic gold medalists
The AI system developed by Google Deepmind, the leading AI research lab at Google, appears to outperform the average gold medalist when solving geometric problems in international mathematical…
The AI system developed by Google Deepmind, the leading AI research lab at Google, appears to outperform the average gold medalist when solving geometric problems in international mathematical…
Most of current LLM based deployments lack a post-generation validation mechanism. A good example of such system is Alpha Geometry, which use LLM to generate constructs, and a symbolic engine to validate.
deepmind.google/blog/alphage...
deepmind.google/blog/alphage...
AlphaGeometry: An Olympiad-level AI system for geometry
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics
deepmind.google
November 19, 2025 at 3:41 PM
Most of current LLM based deployments lack a post-generation validation mechanism. A good example of such system is Alpha Geometry, which use LLM to generate constructs, and a symbolic engine to validate.
deepmind.google/blog/alphage...
deepmind.google/blog/alphage...
2502.03544
Trinhら(2024)で紹介されたAlphaGeometryの大幅な改良版であるAlphaGeometry2を紹介する。AlphaGeometryは、オリンピックの幾何学問題を解く平均的な金メダリストを凌駕した。これを実現するために、まずオリジナルのAlphaGeometry言語を拡張し、物体の動きを含む難しい問題や、角度、比、距離の線形方程式を...
Trinhら(2024)で紹介されたAlphaGeometryの大幅な改良版であるAlphaGeometry2を紹介する。AlphaGeometryは、オリンピックの幾何学問題を解く平均的な金メダリストを凌駕した。これを実現するために、まずオリジナルのAlphaGeometry言語を拡張し、物体の動きを含む難しい問題や、角度、比、距離の線形方程式を...
February 8, 2025 at 12:21 AM
2502.03544
Trinhら(2024)で紹介されたAlphaGeometryの大幅な改良版であるAlphaGeometry2を紹介する。AlphaGeometryは、オリンピックの幾何学問題を解く平均的な金メダリストを凌駕した。これを実現するために、まずオリジナルのAlphaGeometry言語を拡張し、物体の動きを含む難しい問題や、角度、比、距離の線形方程式を...
Trinhら(2024)で紹介されたAlphaGeometryの大幅な改良版であるAlphaGeometry2を紹介する。AlphaGeometryは、オリンピックの幾何学問題を解く平均的な金メダリストを凌駕した。これを実現するために、まずオリジナルのAlphaGeometry言語を拡張し、物体の動きを含む難しい問題や、角度、比、距離の線形方程式を...
En maskin för matematikgåtor visar hur framtidens AI kan vara uppbyggd. F&F:s @landetannien.bsky.social har pratat med @moajohansson.bsky.social om bevismaskinen #Alphageometry
fof.se/artikel/spra...
fof.se/artikel/spra...
January 30, 2024 at 2:44 PM
En maskin för matematikgåtor visar hur framtidens AI kan vara uppbyggd. F&F:s @landetannien.bsky.social har pratat med @moajohansson.bsky.social om bevismaskinen #Alphageometry
fof.se/artikel/spra...
fof.se/artikel/spra...
AI systems seems to gradually become better in solving math problems. AlphaGeometry2 by Google DeepMind has solved 84% of 25 years of geometry problems from the International Mathematical Olympiads. A preprint is available.
Nature Briefing: www.nature.com/articles/d41...
Nature Briefing: www.nature.com/articles/d41...
DeepMind AI crushes tough maths problems on par with top human solvers
The company’s AlphaGeometry 2 reaches the level of gold-medal students in the International Mathematical Olympiad.
www.nature.com
February 11, 2025 at 6:24 PM
AI systems seems to gradually become better in solving math problems. AlphaGeometry2 by Google DeepMind has solved 84% of 25 years of geometry problems from the International Mathematical Olympiads. A preprint is available.
Nature Briefing: www.nature.com/articles/d41...
Nature Briefing: www.nature.com/articles/d41...
When large language models (generative AI) have been so poor at mathematics, this is a stunning step forward by Google DeepMind (tho an approach I've been advocating). Silver medal-level performance had it been at the International Mathematical Olympiad (with caveats) deepmind.google/discover/blo...
AI achieves silver-medal standard solving International Mathematical Olympiad problems
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
deepmind.google
July 27, 2024 at 12:05 PM
When large language models (generative AI) have been so poor at mathematics, this is a stunning step forward by Google DeepMind (tho an approach I've been advocating). Silver medal-level performance had it been at the International Mathematical Olympiad (with caveats) deepmind.google/discover/blo...
Davis and Marcus dive deep in AlphaGeometry 2, deflating hype but also pointing to some genuine positives.
garymarcus.substack.com/p/alphageome...
garymarcus.substack.com/p/alphageome...
AlphaGeometry2: Impressive accomplishment, but still a long path ahead
What GoogleDeepMind’s latest does and doesn’t show, and what we like about it
garymarcus.substack.com
February 17, 2025 at 5:27 PM
Davis and Marcus dive deep in AlphaGeometry 2, deflating hype but also pointing to some genuine positives.
garymarcus.substack.com/p/alphageome...
garymarcus.substack.com/p/alphageome...
At IMO 2024, AlphaGeometry and AlphaProof required experts to first translate problems from natural language into domain-specific languages, such as Lean, and vice-versa for the proofs.
July 21, 2025 at 10:23 PM
At IMO 2024, AlphaGeometry and AlphaProof required experts to first translate problems from natural language into domain-specific languages, such as Lean, and vice-versa for the proofs.
AlphaGeometryの内容を他分野に適用させる方法を考えるみたいなのはやりたい。なるべく混み合わず、手法は疎結合に。中期的な目標はここかな。
他分野、何があるかな。作図可能数みたいな、再帰的に具体例が構成されて、かつパターン認識しやすい対象がいいな。図形問題ってやっぱりとっつきやすいのか。
他分野、何があるかな。作図可能数みたいな、再帰的に具体例が構成されて、かつパターン認識しやすい対象がいいな。図形問題ってやっぱりとっつきやすいのか。
April 21, 2024 at 6:21 AM
AlphaGeometryの内容を他分野に適用させる方法を考えるみたいなのはやりたい。なるべく混み合わず、手法は疎結合に。中期的な目標はここかな。
他分野、何があるかな。作図可能数みたいな、再帰的に具体例が構成されて、かつパターン認識しやすい対象がいいな。図形問題ってやっぱりとっつきやすいのか。
他分野、何があるかな。作図可能数みたいな、再帰的に具体例が構成されて、かつパターン認識しやすい対象がいいな。図形問題ってやっぱりとっつきやすいのか。
具体例からLeanの定理を生成させたいなと思うんだけど、
1. 具体例の生成
2. 具体例からパターンを認識
3. パターンをLeanで形式化
の3つのハードルが存在し、局所的な分野での成功例はあれど、数学のどの分野にも普遍的に適用できるような方法は思い当たらず。AlphaGeometryやAlphaZeroのように局所的な解決の例から普遍的解決を探っていく方がいいかなあ。
DeepMindそういうところすげえなあ
1. 具体例の生成
2. 具体例からパターンを認識
3. パターンをLeanで形式化
の3つのハードルが存在し、局所的な分野での成功例はあれど、数学のどの分野にも普遍的に適用できるような方法は思い当たらず。AlphaGeometryやAlphaZeroのように局所的な解決の例から普遍的解決を探っていく方がいいかなあ。
DeepMindそういうところすげえなあ
April 21, 2024 at 6:12 AM
具体例からLeanの定理を生成させたいなと思うんだけど、
1. 具体例の生成
2. 具体例からパターンを認識
3. パターンをLeanで形式化
の3つのハードルが存在し、局所的な分野での成功例はあれど、数学のどの分野にも普遍的に適用できるような方法は思い当たらず。AlphaGeometryやAlphaZeroのように局所的な解決の例から普遍的解決を探っていく方がいいかなあ。
DeepMindそういうところすげえなあ
1. 具体例の生成
2. 具体例からパターンを認識
3. パターンをLeanで形式化
の3つのハードルが存在し、局所的な分野での成功例はあれど、数学のどの分野にも普遍的に適用できるような方法は思い当たらず。AlphaGeometryやAlphaZeroのように局所的な解決の例から普遍的解決を探っていく方がいいかなあ。
DeepMindそういうところすげえなあ
Les IA de Google ont battu la plupart des humains lors d’une compétition de mathématiques
Les IA de Google ont battu la plupart des humains lors d'une compétition de mathématiques
Google a réussi à placer ses IA AlphaGeometry 2 et AlphaProof à deux doigts de la médaille d'or des Olympiades Internationales de Mathématiques. Les deux programmes ont reçu une médaille d'argent et AlphaGeometry 2 a bluffé par l'élégance et la rapidité de sa solution. C'est un nouveau record pour une intelligence
www.numerama.com
July 25, 2024 at 6:03 PM
Les IA de Google ont battu la plupart des humains lors d’une compétition de mathématiques