this post was submitted on 29 Aug 2025
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tbf all good programmers are good at math. Not classic arithmetic necessarily, but at the very least applied calculus. It's a crime how many people used a mathematical discipline every day, but don't think they're "good at math" because of how lazer focused the world is on algebra, geometry and trig as being all that "math" is.
Serious question; how does Calculus apply to programming? I’ve never understood.
PID control is the classic example, but at a far enough abstraction any looping algorithm can be argued to be an implementation of the concepts underpinning calculus. If you're ever doing any statistical analysis or anything in game design having to do with motion, those are both calculus too. Data science is pure calculus, ground up and injected into your eyeballs, and any string manipulation or Regex is going to be built on lambda calculus (though a very correct argument can be made that literally all computer science is built of lambda calculus so that might be cheating to include it)
Lambda calculus has no relation to calculus calculus, though.
Lol, I like that. I mean, there's more calculus-y things, but it's kind of unusual in that you can't really interpret the non-calculus aspects of a neural net.
I wanna fight your math teachers. No seriously, what did they tell you calculus is if it's got nothing in common with lambda calculus?
Is there some connection I've just been missing? It's a pretty straight rewriting system, it seems Newton wouldn't have had much use for it.
Lot's of things get called "calculus". Originally, calculus calculus was "the infinitesimal calculus" IIRC.
I think the issue here might be the overloading of terms - lambda calculus is both the system of notation and the common name for the conceptual underpinnings of computational theory. While there is little to no similarity between the abstracted study of change over a domain and a notational system, the idea of function composition or continuous function theory (or even just computation as a concept) are all closely related with basic concepts from "calculus calculus" like limit theory and integral progression.
edit: clarity
I'm pretty sure the term was coined in the interwar era, so it's kind of interesting if people are just calling the concept of functions "lambda calculus" now. Obviously they're much older than that.
What? Nobody's doing that, it's just a distinct area of mathematics - I'm pretty confused where you got that idea from at all.
So, I took it from these parts together:
I'm still not seeing the connection otherwise.
Okay, meta question here: What would a 'connection' that you're willing to accept actually look like? Those I've already presented are what I would call pretty explicit connections between the two fields (and fragmenting this into an explanation of how lambda calculus relies and expands on functional mechanics is going to be a loooong diversion). It's starting to feel like you're pretty entrenched in your initial position, and are just looking for an internet debate.
I wouldn't say entrenched, because I think this is honestly the first time I've seen the two come up together outside of their shared name. I was surprised, but then again sometimes reality is surprising.
Both have function composition, and expressions which contain free variables in multiple places. At the time, that was just a shorthand for what they were trying to express about slight changes. A bit later, formal analysis was axiomised, and is full of infinite things like Cauchy sequences and general topology. In the 20th century, substitution of a composed function into free variables becomes an object of study of it's own, and found to be able to produce full complexity without anything else being added, being Turing equivalent.
All the infinite and continuous stuff that makes calculus work, at least as it's considered abstractly, doesn't really translate into a discrete system. You can numerically approximate it, and I guess you could even use lambda calculus-like functional language to do that, but I'm not mad that never came up in my math courses, like in your original comment.
If there's nothing more to add to that, I am sorry for wasting your time.
Graphics programming is the most obvious one and it uses it plenty, but really any application that can be modeled as a series of discrete changes will mostly likely be using calculus.
Time series data is the most common form of this, where derivatives are the rate of change from one time step to the next and integrals are summing the changes across a range of time.
But it can even be more abstract than that. For example, there's a recent-ish paper on applying signal processing techniques (which use calculus themselves, btw) to databases for the purposes of achieving efficient incremental view maintenance: https://arxiv.org/abs/2203.16684
The idea is that a database is a sequence of transactions that apply a set of changes to said database. Integrating gets you the current state of the database by applying all of the changes.
that can't be right. maybe they meant lambda calculus? programmers are definitely good at applied logic, graph theory, certain kinds of discrete math etc. but you're not whipping out integrals to write a backend.
Any function that relies on change over a domain is reliant on concepts that are fundementally calculus. Control systems, statistical analysis, data science, absolutely everything in networking that doesn't involve calling people on the phone to convince them to give you their password, that is all calculus.
Many things that work with time series data use calculus all the time. Both derivatives and integrals are very useful in that context: derivatives being the rate of change at some particular time step, and integrals being the sum of the changes across a range of time steps.
There's a pretty wide range of applications.
Lotta infinite sums in loops
Computers are just big calculators so to program them you need calculus.
A senior firmware engineer said to the group that we just have to integrate the acceleration of an IMU to get velocity. I said “plus a constant.” I was fired for it.
That sounds like it might be a gift in disguise.