Will Artificial Intelligence Bring a Golden Age or a Dark Age to Science?
Large language models can now build mathematical proofs and help researchers discover new connections across scientific literature. However, the evidence comes from early observations and developer announcements without complete transparency or full human comprehension.
In short: Large language models can now build mathematical proofs and help researchers discover new connections across scientific literature. However, the evidence comes from early observations and developer announcements without complete transparency or full human comprehension.
Artificial intelligence can now solve complex mathematical puzzles, but when computers understand the math better than we do, what happens to human science?
What happened, in plain words
Artificial intelligence tools known as large language models have shown a striking ability to create mathematical proofs, such as a finite-time blow-up solution to the Navier-Stokes equations and a proposed proof of the quasi-Riemann Hypothesis. Francesco Maggi wrote a guest post on Terence Tao's UCLA blog examining how these tools could lead to either a golden age of scientific acceleration or a dark age where human understanding fades. The post explores how these systems excel at combining existing ideas at a scale humans cannot match, yet struggle to translate their computer-checked proofs into readable natural language. It also stresses that the future depends on human choices, leadership, and how these technologies are integrated into research ecosystems.
Key points
- Powerful mathematical tools: Large language models have generated notable proofs, including work related to the Navier-Stokes equations and the quasi-Riemann Hypothesis. These successes show that artificial intelligence can serve as a real research tool.
- The translation barrier: When computers write proofs in a language checkers can verify, the resulting code can be hundreds of thousands of lines long. The machine-generated translations into regular language often become messy and extremely difficult for humans to read.
- Recombining existing knowledge: Theory and practice show that these models excel at recombining current intellectual structures and finding hidden links across vast scientific literature. This happens at a scale that individual human researchers cannot reach.
- Two possible futures: Society faces a choice between a golden age that empowers new scientists and preserves open collaboration, or a dark age where human scientific activity weakens and knowledge becomes alien to human understanding.
Terms explained
- Large language model — A type of artificial intelligence built to process and generate human-like text by finding patterns in massive amounts of data. Example: An advanced computer program that can write essays, answer questions, or draft computer code by predicting what words usually come next.
- Proof — A logical argument that demonstrates beyond any doubt that a mathematical statement is true. Example: Showing every step of arithmetic to prove why adding two even numbers always results in an even number.
- Lean — A specialized software assistant that checks whether a formal mathematical argument follows all the rules of logic. Example: A strict digital teacher that reviews a geometry proof line by line to make sure every single claim is properly justified.
- Mathematization — The creative process of inventing new mathematical language to make sense of the real world. Example: Developing an entirely new system of measurement to describe how objects fall or how heat travels through space.
Critical analysis
What is encouraging. The commentary offers a thoughtful, balanced perspective from an active field, avoiding blind hype while acknowledging genuine technological breakthroughs. It rightly highlights that the social impact of new tools depends on human choices and institutional leadership rather than inevitable destiny.
What deserves caution:
- Unclear commercial details. Commercial developers are not transparent about how their models work. Without knowing the internal details, outsiders cannot fully judge how these systems succeed or fail.
- Vague performance disclosures. Company announcements often use vague language and aggregated data when reporting success rates. It remains hard to study why certain complex problems were solved while others were left out.
- Early stage observations. The capabilities of these models are still being explored and remain incompletely understood. Treating early technological tricks as proof of deep intelligence or consciousness goes beyond the available evidence.
Bottom line: While artificial intelligence is becoming a powerful research assistant, losing human understanding of mathematics would risk the very meaning of scientific discovery.
What we still don't know
The source does not provide complete data on all the problems tested by developers, nor does it fully explain why models struggle with natural language translation. The long-term social and scientific outcomes remain completely unknown and depend entirely on future human decisions.
Based on reporting from Terence Tao (UCLA). This is an independent explainer, written in our own words with AI assistance; Terence Tao (UCLA) has not reviewed or endorsed it. Read the original for the full details.