It may not seem like it, but the millennia-old academic discipline of mathematics has been undergoing a productivity revolution during the last thirty years.
That revolution is being enabled by the adoption of several new technologies, each of which is following a S-shaped logistic growth curve model. Mike Roberts of Strategic Tool Kits describes the pattern of how technological advancements increase performance over time:
The S curve is a strategic concept that describes how the old ways mature and are superseded by new ways.
In the early days of new technology, it takes a long time to improve performance. People are working out the technology, and the applications, ironing out the flaws, and building the ecosystem. Slowly over time, performance accelerates.
After a certain time, the rate of improvement hits a peak and then starts to slow down. Easy wins have all been made and the learning curve has been fully ridden for continuous improvement. Some of the fundamental barriers of the technology are reached. Eventually, the improvement tapers off and a plateau with this technology is reached. This is the “S” shaped curve.
When a new productivity-enhancing technology comes along after the older technology reaches its mature phase, the process repeats with performance building on its old plateau and rising to new heights.
For mathematicians, the two great technological improvements of the twenty-first century have been the widespread adoption of the arXiv database for publishing preprint papers to more quickly communicate their discoveries and the more recent development of Artificial Intelligence (AI) systems paired with proof assistant systems like Lean that are helping automate large portions of their work.
ArXiv provides data on the number of new papers that are uploaded to its preprint paper database each month. The following chart reveals its data for math papers, not counting cross listings from other categories of academic papers, from January 1992 through July 2026:
The data shows adoption of the arXiv database for communicating advancements in maths went through the full S-curve advancement cycle, reaching a fully mature phase by the early 2020s with output holding fairly level for several years. But after ChatGPT (3.5) was launched at the end of November 2022, the Large Language Model (LLM) technology facilitiated a steady increase in the productive output of mathematicians for the first time in years. By making it possible to automate a portion of writing academic papers, the number of papers published to arXiv each month began to rise in a steady, linear trend.
But soon after OpenAI's o3-mini LLM-based reasoning model was released on 31 January 2025, the rate of output for publishing new papers to arXiv exploded in what appears to be the exponential growth phase of the S-shaped logistic growth pattern. The new cost efficient o3-mini reasoning model was specifically developed to automate analytical tasks in Science, Technology, Engineering, and Mathematics fields and also coding.
For mathematics, the new AI technologies make rapid advancements possible by drawing on the body of published work, like the thousands of math preprint papers documented in the arXiv database and other resources that catalogued large numbers of unresolved conjectures in digital-friendly formats, to test new possible ways of testing those conjectures. When promising proofs or disproofs of the conjectures are identified, the technology automates their verification using the proof assistant software technology that has also come into its own during this period. Using proof assistants also has the benefit of coding any new successful proofs into their proof libraries, which can then be mixed and matched as needed to test other conjectures.
When that's done, the remaining step for the mathematicians orchestrating what's effectively become a massive, automated collaboration exercise is to write up a new preprint paper and publish it to the arXiv database.
Mathematics isn't the only field experiencing a boom in preprint papers. Economics has likewise seen the number of papers published each month almost double since ChatGPT 3.5's public release. Unlike math however, economists don't have the equivalent of maths' proof assistants to verify their findings, which raises questions about the quality and validity of the flood of new papers in the field.
References
arXiv. Math Submissions. [Online Database]. Accessed 8 August 2026.
arXiv. Monthly Submissions. [Online Article and CSV Data]. Accessed 8 August 2026.
Ecology.net. Logistic Growth. [Online Article]. 15 December 2025.
Pablo Groisman. Math papers uploaded to arXiv per month, January 1992 to July 2026. [Online Article]. 3 August 2026. [Our article was inspired by Pablo's chart!]
Mike Roberts. S Curve – What is it? [Online Article]. 13 July 2024.
ScriptByAI. OpenAI & ChatGPT Timeline: GPT Release Dates to GPT-5.6 (2026). [Online Database]. Accessed 20 August 2026.
Image credit: S Curve Concept in Science by Oliver Tacke on Wikiversity. Creative Commons CC BY-SA 3.0 Attribution-ShareAlike 3.0 Unported Deed. 17 July 2012.
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