Flattening adoption rate = the second derivative is negative
Starting to flatten = the third derivative is negative
I don't think anyone cares what the third derivative of something is when the first derivative could easily change by a macroscopic amount overnight.
Adoption rate is not derivative of Adoption. Rate of change is. Adoption rate is the percentage of uptake (there, same order with Adoption itself). It being flattening means first derivative is getting close to 0.
I agree, I think I misunderstood their wording.
In which case it's at least funny, but maybe subtract one from all my derivatives.. Which kills my point also. Dang.
It maps pretty cleanly to the well understood derivatives of a position vector. Position (user count), velocity (first derivative, change in user count over time), acceleration (second derivative, speeding up or flattening of the velocity), and jerk (third derivative, change in acceleration such as the shift between from acceleration to deceleration)
It really is a beautiful title.
It is not velocity, it is not change. Have you read the graphs? What do you think 12% in Aug and Sep for 250+ Employee companies mean, that another 12% of companies adopted AI or is it a flat "12% of the companies have adopted in Aug, and it did not change in Sep"
> Have you read the graphs?
Yes. The title specifically is beautiful. The charts aren't nearly as interesting, though probably a bit more than a meta discussion on whether certain time intervals align with one interpretation of the author's intent or another.
The function log(x) also has derivative that goes closer and closer to 0.
However lim x->inf log(x) is still inf.
Is it your assertion that an 'infinite' percentage! of the businesses will use AI on a long enough time scale?
If you need everything to be math, at least have the courtesy to use the https://en.wikipedia.org/wiki/Logistic_function and not unbounded logarithmic curves when referring to on our very finite world.
I don’t understand, how can adoption rate change overnight if its derivative is negative? Trying to draw a parallel to get intuition, if adoption is distance, adoption rate speed, and the derivative of adoption rate is acceleration, then if I was pedal to the floor but then release the pedal and start braking, I’ll not lose the distance gained (adoption) but my acceleration will flatten then get negative and my speed (adoption rate) will ultimately get to 0 right? Seems pretty significant for an industry built on 2030 projections.
One announcement from a company or government can suddenly change the derivative discontinuously.
Derivatives irl do not follow the rules of calculus that you learn in class because they don't have to be continuous. (you could quibble that if you zoom in enough it can be regarded as continuous.. But you don't gain anything from doing that, it really does behave discontinuous)
Not sure what kinda calculus you took at least here in the states it's very standard to learn about such functions in class, and yes there is a difference between discontinuous and the slope being really large (though finite) for a brief period of time
You rarely study delta and step functions in an introductory calculus class. In this case the first derivative would be a step function, in the sense that over any finite interval it appears to be discontinuous. Since you can only sample a function in reality there's no distinguishing the discontinuous version from its smooth approximation.
I think it might be answering long-term questions about direct chat use of AIs. Of course as AI goes through its macroscopic changes the amount it gets used for each person will increase, however some will continue to avoid using AI directly, just like I don't fully use GPS navigation but I benefit from it whether I like it or not when others are transporting me or delivering things to me.
While there's an extreme amount of hype around AI, it seems there's an equal amount of demand for signs that it's a bubble or it's slowing down.
Well, that’s only because it exhibits all the signs of a bubble. It’s not exactly a grand conspiracy.
You could use that logic to dismiss any analysis of any trajectory ever.
Perfectly excusable post that says absolutely nothing about anything.
Yeah, what a jerk.
> Adoption = number of users
> Adoption rate = first derivative
If you mean with respect to time, wrong. The denonimator in adoption rate that makes it a “rate” is the number of existing businesses, not time. It is adoption scaled to the universe of businesses, not the rate of change of adoption over time.
The adoption rate is the rate of adoption over time.
One could try to make an argument that "adoption rate" should mean change in adoption over time, but the meaning as used in this article is unambiguously not that. It's just percentages, not time derivatives, as clearly shown by the vertical axis labels.
There's another axis on the charts.
Normally, the adoption rate of something is the percentage ratio of adopters to non-adopters.
Looking at the graphs in the linked article, a more accurate title would probably be "AI adoption has stagnated" - which a lot of people are going to care about.
Corporate AI adoption looks to be hitting a plateau, and adoption in large companies is even shrinking. The only market still showing growth is companies with fewer than 5 employees - and even there it's only linear growth.
Considering our economy is pumping billions into the AI industry, that's pretty bad news. If the industry isn't rapidly growing, why are they building all those data centers? Are they just setting money on fire in a desperate attempt to keep their share price from plummeting?
Not really. In this context adoption might be number of users. But adoption rate is a fraction of users that adopted this to all users.
Hm that's true. Both seem plausible in English. I didn't look closely enough to figure out which they meant.
I think what is happening is that people are realizing AI is not just plug and play. It can do amazing things but needs engineering around it.
I think what will happen is in parallel more products will be built that address the engineering challenges and the models will keep getting better. I don't know though if that will lead to another hockey stick or just slow and steady.
They show two different surveys that are supposed to show the same underlying truth but differ by a factor of 3x? For the Ramp survey: why the sudden jump from 30% to 50% in March? For the Census one: How could it possibly be that only 12% of companies with more than 250 people „adopted“ (whatever that means) AI? It would be interesting if it were true but these charts don’t make any sense at all to me
The least volatile dataset, employee count 1-4 businesses, is steadily climbing in adoption. I feel like as long as the smallest businesses (so the most agile, non-enterprise software ones) increase in adoption, other sizes will follow.
Not to be lost, but the first chart is actually a 3-month moving average. Surprised they buried that in the notes and didn't simply include it in the chart title. "Note: Data is six-survey moving average. The survey is conducted bi-weekly. Sources: US Census Bureau, Macrobond, Apollo Chief Economist"
Given the charts, that’s a ridiculous claim. Just compare early 2024 in the first chart, for example.
It’s way too early to decide whether it’s flattening out.
Three consecutive months of decline starts to look more like a trend. Unless you think there's a transient issue causing the decline, something fundamental has changed
Especially interesting is the adoption by the smallest companies. This means people find it still increasingly useful at the grassroot level where things are actually done.
At larger companies adoption will probably stop at the level where managers will start to be threatened.
But what does that grassroot adoption look like in practice? Is that a developer spending $250/month on Claude, or is it a local corner shop using it once a month to replace their clip art flyer with AI slop, and the example contract they previously found via Google with some legalese gobbledygook ChatGPT hallucinated?
Giving AI away for free to people who don't give a rat's ass about the quality of its output isn't very difficult. But that's not exactly going to pay your datacenter bill...
From the chart, the percentage of companies using AI has been going down over the past couple of months
That's a massive deal because the AI companies today are valued on the assumption that they'll 10x their revenue over the next couple of years. If their revenue growth starts to slow down, their valuations will change to reflect that
If I was openAI or whatever I would be investing in circular partnerships with claude or whatever, claim agentic use should be considered the same as real users, then have each other's LLM systems use each other and finally achieve infinite, uncapped user growth
No no, we just need to put even more money in.
Without weighing in on the accuracy of this claim, this would be an expected part of the maturity cycle.
Compare to databases. You could probably have plotted a chart of database adoption rates in the '90s as small companies started running e.g. Lotus Notes, FoxPro and SQL server everywhere to build in-house CRMs and back-office apps. Those companies still operate those functions, but now most small businesses do not run databases themselves. Why manage SQL Server when you can just pay for Salesforce and Notion with predictable monthly spend?
(All of this is more complex, but analogous at larger companies.)
My take is the big rise in AI adoption, if it arrives, will similarly be embedded inside application functions.
People push back against comments like these. But, as you suggest, the win isn't about individual developers potentially increasing their productivity by some inflated amount. It's about baking more prediction and automation into more tools that people who aren't developers use. Which is probably part of where the general meme of lack of interest in entry level programmers come from.
I'm more interested in what the implications are for the economy and what this next AI winter looks like.
What happens to all the debt? Was all this just for chatbots that are finally barely good enough for satnav and image gen that does slightly better photoshop that the layperson can use?
Adoption = number of users
Adoption rate = first derivative
Flattening adoption rate = the second derivative is negative
Starting to flatten = the third derivative is negative
I don't think anyone cares what the third derivative of something is when the first derivative could easily change by a macroscopic amount overnight.
Adoption rate is not derivative of Adoption. Rate of change is. Adoption rate is the percentage of uptake (there, same order with Adoption itself). It being flattening means first derivative is getting close to 0.
I agree, I think I misunderstood their wording.
In which case it's at least funny, but maybe subtract one from all my derivatives.. Which kills my point also. Dang.
It maps pretty cleanly to the well understood derivatives of a position vector. Position (user count), velocity (first derivative, change in user count over time), acceleration (second derivative, speeding up or flattening of the velocity), and jerk (third derivative, change in acceleration such as the shift between from acceleration to deceleration)
It really is a beautiful title.
It is not velocity, it is not change. Have you read the graphs? What do you think 12% in Aug and Sep for 250+ Employee companies mean, that another 12% of companies adopted AI or is it a flat "12% of the companies have adopted in Aug, and it did not change in Sep"
> Have you read the graphs?
Yes. The title specifically is beautiful. The charts aren't nearly as interesting, though probably a bit more than a meta discussion on whether certain time intervals align with one interpretation of the author's intent or another.
The function log(x) also has derivative that goes closer and closer to 0.
However lim x->inf log(x) is still inf.
Is it your assertion that an 'infinite' percentage! of the businesses will use AI on a long enough time scale?
If you need everything to be math, at least have the courtesy to use the https://en.wikipedia.org/wiki/Logistic_function and not unbounded logarithmic curves when referring to on our very finite world.
I don’t understand, how can adoption rate change overnight if its derivative is negative? Trying to draw a parallel to get intuition, if adoption is distance, adoption rate speed, and the derivative of adoption rate is acceleration, then if I was pedal to the floor but then release the pedal and start braking, I’ll not lose the distance gained (adoption) but my acceleration will flatten then get negative and my speed (adoption rate) will ultimately get to 0 right? Seems pretty significant for an industry built on 2030 projections.
One announcement from a company or government can suddenly change the derivative discontinuously.
Derivatives irl do not follow the rules of calculus that you learn in class because they don't have to be continuous. (you could quibble that if you zoom in enough it can be regarded as continuous.. But you don't gain anything from doing that, it really does behave discontinuous)
Not sure what kinda calculus you took at least here in the states it's very standard to learn about such functions in class, and yes there is a difference between discontinuous and the slope being really large (though finite) for a brief period of time
You rarely study delta and step functions in an introductory calculus class. In this case the first derivative would be a step function, in the sense that over any finite interval it appears to be discontinuous. Since you can only sample a function in reality there's no distinguishing the discontinuous version from its smooth approximation.
I think it might be answering long-term questions about direct chat use of AIs. Of course as AI goes through its macroscopic changes the amount it gets used for each person will increase, however some will continue to avoid using AI directly, just like I don't fully use GPS navigation but I benefit from it whether I like it or not when others are transporting me or delivering things to me.
While there's an extreme amount of hype around AI, it seems there's an equal amount of demand for signs that it's a bubble or it's slowing down.
Well, that’s only because it exhibits all the signs of a bubble. It’s not exactly a grand conspiracy.
You could use that logic to dismiss any analysis of any trajectory ever.
Perfectly excusable post that says absolutely nothing about anything.
Yeah, what a jerk.
> Adoption = number of users
> Adoption rate = first derivative
If you mean with respect to time, wrong. The denonimator in adoption rate that makes it a “rate” is the number of existing businesses, not time. It is adoption scaled to the universe of businesses, not the rate of change of adoption over time.
The adoption rate is the rate of adoption over time.
One could try to make an argument that "adoption rate" should mean change in adoption over time, but the meaning as used in this article is unambiguously not that. It's just percentages, not time derivatives, as clearly shown by the vertical axis labels.
There's another axis on the charts.
Normally, the adoption rate of something is the percentage ratio of adopters to non-adopters.
Looking at the graphs in the linked article, a more accurate title would probably be "AI adoption has stagnated" - which a lot of people are going to care about.
Corporate AI adoption looks to be hitting a plateau, and adoption in large companies is even shrinking. The only market still showing growth is companies with fewer than 5 employees - and even there it's only linear growth.
Considering our economy is pumping billions into the AI industry, that's pretty bad news. If the industry isn't rapidly growing, why are they building all those data centers? Are they just setting money on fire in a desperate attempt to keep their share price from plummeting?
Not really. In this context adoption might be number of users. But adoption rate is a fraction of users that adopted this to all users.
Hm that's true. Both seem plausible in English. I didn't look closely enough to figure out which they meant.
I think what is happening is that people are realizing AI is not just plug and play. It can do amazing things but needs engineering around it.
I think what will happen is in parallel more products will be built that address the engineering challenges and the models will keep getting better. I don't know though if that will lead to another hockey stick or just slow and steady.
They show two different surveys that are supposed to show the same underlying truth but differ by a factor of 3x? For the Ramp survey: why the sudden jump from 30% to 50% in March? For the Census one: How could it possibly be that only 12% of companies with more than 250 people „adopted“ (whatever that means) AI? It would be interesting if it were true but these charts don’t make any sense at all to me
The least volatile dataset, employee count 1-4 businesses, is steadily climbing in adoption. I feel like as long as the smallest businesses (so the most agile, non-enterprise software ones) increase in adoption, other sizes will follow.
Not to be lost, but the first chart is actually a 3-month moving average. Surprised they buried that in the notes and didn't simply include it in the chart title. "Note: Data is six-survey moving average. The survey is conducted bi-weekly. Sources: US Census Bureau, Macrobond, Apollo Chief Economist"
Apollo published a similar chart in September 2025: https://www.apolloacademy.com/ai-adoption-rate-trending-down... - their headline for that one was "AI Adoption Rate Trending Down for Large Companies".
I had fun with that one getting GPT-5 and ChatGPT Code Interpreter to recreate it from a screenshot of the chart and some uploaded census data: https://simonwillison.net/2025/Sep/9/apollo-ai-adoption/
Then I repeated the same experiment with Claude Sonnet 4.5 after Anthropic released their own code interpreter style tool later on that same day: https://simonwillison.net/2025/Sep/9/claude-code-interpreter...
Given the charts, that’s a ridiculous claim. Just compare early 2024 in the first chart, for example.
It’s way too early to decide whether it’s flattening out.
Three consecutive months of decline starts to look more like a trend. Unless you think there's a transient issue causing the decline, something fundamental has changed
Especially interesting is the adoption by the smallest companies. This means people find it still increasingly useful at the grassroot level where things are actually done.
At larger companies adoption will probably stop at the level where managers will start to be threatened.
But what does that grassroot adoption look like in practice? Is that a developer spending $250/month on Claude, or is it a local corner shop using it once a month to replace their clip art flyer with AI slop, and the example contract they previously found via Google with some legalese gobbledygook ChatGPT hallucinated?
Giving AI away for free to people who don't give a rat's ass about the quality of its output isn't very difficult. But that's not exactly going to pay your datacenter bill...
From the chart, the percentage of companies using AI has been going down over the past couple of months
That's a massive deal because the AI companies today are valued on the assumption that they'll 10x their revenue over the next couple of years. If their revenue growth starts to slow down, their valuations will change to reflect that
If I was openAI or whatever I would be investing in circular partnerships with claude or whatever, claim agentic use should be considered the same as real users, then have each other's LLM systems use each other and finally achieve infinite, uncapped user growth
No no, we just need to put even more money in.
Without weighing in on the accuracy of this claim, this would be an expected part of the maturity cycle.
Compare to databases. You could probably have plotted a chart of database adoption rates in the '90s as small companies started running e.g. Lotus Notes, FoxPro and SQL server everywhere to build in-house CRMs and back-office apps. Those companies still operate those functions, but now most small businesses do not run databases themselves. Why manage SQL Server when you can just pay for Salesforce and Notion with predictable monthly spend?
(All of this is more complex, but analogous at larger companies.)
My take is the big rise in AI adoption, if it arrives, will similarly be embedded inside application functions.
People push back against comments like these. But, as you suggest, the win isn't about individual developers potentially increasing their productivity by some inflated amount. It's about baking more prediction and automation into more tools that people who aren't developers use. Which is probably part of where the general meme of lack of interest in entry level programmers come from.
I'm more interested in what the implications are for the economy and what this next AI winter looks like.
What happens to all the debt? Was all this just for chatbots that are finally barely good enough for satnav and image gen that does slightly better photoshop that the layperson can use?
so no expot. growth? who would have guess?
/s