Claude Fable 5 has disproven the Jacobian conjecture, a significant milestone occurring just days after China's Kimi AI emerged as a major driver in bitcoin market movements.
By Shaurya Malwa|Edited by Aoyon Ashraf Jul 21, 2026, 4:19 p.m. 2 min readMake preferred on ShareShare this articleCopy linkX (Twitter)LinkedInFacebookEmailMake preferred on Claude Fable 5 has resolved an 87-year-old math problem, significantly affecting bitcoin. (Getty Images)SummaryShow- Claude Fable 5, an AI model from Anthropic, has successfully disproven the Jacobian conjecture, a renowned mathematical problem that has remained unsolved since 1939.
- The AI generated a tangible counterexample that mathematicians verified manually within a day, demonstrating that a specific type of mathematical “machine” can meet standard checks yet still lack reversibility.
- This breakthrough highlights the rapid evolution of AI technology, which is shifting speculative investments and interest away from cryptocurrencies toward computing advancements, chips, and model development.
An innovative artificial intelligence model has resolved a longstanding mathematical conjecture that had remained unanswered for 87 years, and its solution could be verified by anyone within a day.
Levent Alpöge, a number theorist at Anthropic and a former Harvard fellow, announced the finding on X on Sunday night, attributing the achievement to the Claude Fable 5 model.
The Jacobian conjecture, which has been unresolved since 1939, is listed among the significant unsolved problems of the century by mathematician Stephen Smale.
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
— levent (@__alpoge__) July 20, 2026
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3,…
The ability of AI to produce original mathematical results of this complexity is a significant development that is influencing markets, including cryptocurrencies. Bitcoin has recently been trading based on narratives surrounding artificial intelligence, aligning more closely with chip manufacturers and memory stocks than any intrinsic catalysts.
Last Friday, the cryptocurrency experienced a sharp decline when the Chinese lab Moonshot AI unveiled a model that unsettled the semiconductor sector, though it rebounded this week as those stocks recovered.
This connection is direct, as bitcoin miners, who are its largest holders, have transformed into operators of AI data centers, their fortunes now linked to the demand for computational resources.
However, the broader trend is more straightforward: speculative investment is increasingly directed towards AI, diverting capital that once flowed into crypto towards computing technology, semiconductors, and model developers, with every advancement in these areas enhancing their appeal.
Each breakthrough like Fable's resolution of the Jacobian conjecture reinforces the rationale for investing in AI, presenting a challenging dilemma for cryptocurrency investors: why hold a token that merely tracks the AI cycle when one can invest directly in the technology itself?
The rapid advancement of AI capabilities is drawing more risk appetite from the market, leaving crypto and other sectors at a disadvantage.
Understanding the Jacobian Conjecture
Imagine a machine that receives two numbers and outputs two new numbers using only addition and multiplication. The original question posed in 1939 was whether this machine could always be reversed: given the output, could one reliably deduce the original two numbers?
Mathematicians had a method to verify if a machine appeared reversible. The Jacobian conjecture posited that if a machine passed this verification, it should always be reversible.
Visual representation explaining why the 87-year-old Jacobian conjecture is incorrect. (Shaurya Malwa/CoinDesk)For 87 years, no one managed to prove its validity, nor could anyone construct a machine that contradicted the assertion.
The AI successfully created a machine that meets the verification criteria but is still irreversible, as it produces the same output from three different inputs. If three inputs yield a single output, one cannot trace back to the original inputs. One counterexample suffices to invalidate the rule indefinitely.
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TRON Network - Q2 2026
TRON Network - Q2 2026
In Q2; TRON's stablecoin dominance increased to 28.7%, USDT supply on TRON reached an all-time high of $89B, generating $89M in protocol fees (second only to Hyperliquid), TRX rose by 3%, and institutional engagement deepened.
By CoinDesk Research3 hours agoCommissioned byTronIn Q2; TRON's stablecoin dominance rose to 28.7%, USDT supply on TRON hit $89B ATH, $89M in protocol fees (2nd to Hyperliquid), TRX +3%, and deepening institutional & agentic reach.
Why it matters:
In Q2; TRON's stablecoin dominance rose to 28.7%, USDT supply on TRON hit $89B ATH, $89M in protocol fees (2nd to Hyperliquid), TRX +3%, and deepening institutional & agentic reach.
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