A few days ago, I exchanged some e-mails with a fellow volunteer Maxima developer. That exchange reminded me of a pet project of mine, something I’ve been contemplating for quite some time: a computer algebra system, one significantly less ambitious than a frontier-class system like Mathematica, Maple or, I dare include it in that list, Maxima, but one that runs in the browser, with no server-side code and nothing to install on the user’s computer either.
This time around, I decided to test my idea with Claude Opus 5.5, their latest and greatest model. I outlined my ambition in a couple of paragraphs. The result was less than overwhelming: After some 20 minutes, Claude ran out of “thinking” tokens, and returned nothing other than 128,000 tokens wasted.
Never mind, I figured, let’s try it again, with a slightly refined prompt to ensure that Claude doesn’t embark on a project bigger than itself. And that, well, worked. Claude presented a plan and then, following my instructions and my replies to its questions, began to proceed with the implementation one step at a time.
In this past, this is usually where things got derailed. Sometimes, the model got too ambitious and ran into token limits. Sometimes, the model’s code was incoherent, self-contradictory. Sometimes, the initial code was working, more-or-less, but additions did not.
But not this time. Claude kept churning out sensible code and, most notably, starting at the very first stage, included a testsuite. So even though we had no usable system yet, the testsuite was an assurance that the code we’re building is doing what it was supposed to do.
Notice that I am not using Claude as an “agent”. I did not give it carte blanche in a folder of its own, to build code, download libraries, mess around. No. Claude was talking to me. It was then I who decided if the code Claude presented was good enough or not, it was I who incorporated it into the code base. Claude, accordingly, provided helpful, detailed explanations at each stage. The important point is that the role I retained was that of a senior programmer who may delegate subtasks to junior programmers, but retains overall control of the project at a technical level.
And Claude delivered beyond expectations. Soon, I found myself hooked. One module after another, which I added, tested, tried. A rather nice-looking application was beginning to take shape. And there was both breadth and depth: the application was already acquiring features more sophisticated than I ever dared to plan for, while at the same time Claude never forgot to deal with the mundane, such as appropriate visual representation via MathJax or a growing collection of sections in interactive help.
About halfway through the project we got to basic calculus. I was beginning to wonder: When will Claude falter? When will useful code give way to AI hallucinations, code referencing non-existent language features or capabilities? But none of that happened. Claude robustly, methodically implemented basic calculus, one subroutine at a time.
Again, I stress, Claude had no free reign. We were proceeding step by step, I took the code Claude wrote, integrated it into the application, scrutinized it when I had to, looked for testsuite failures, even corrected the trivial ones.
Once we got past linear algebra and multivariate equations, I decided to get really greedy. I asked Claude, can we do ODEs and PDEs? Because even a half-decent differential equation solver makes a world of a difference when it comes to the usability of a CAS. Claude accordingly revised our plan, and then did the grunt work.
Claude remained enthusiastic throughout, but I began to notice that its responses felt… a little less coherent. Nothing big, no real mistakes, just subtle things like harder-to-understand explanations or instructions on where to place a code patch. No wonder: we were by now around 700,000 input tokens per conversational turn, rapidly approaching Claude’s 1 million token limit. (I also noticed the increasing frequency at which I received notifications from Anthropic about additional credit card charges. But, I digress.)
Claude was still eager to proceed with more ambitious additions but I asked it for something else: something genuinely useful in a CAS, a broader class of special functions like hypergeometric functions or Lambert’s W function. Claude delivered.
So roughly 36 hours after I sent my first prompt to Claude, I was in possession of a full-featured, rich, eminently capable browser-based computer algebra application. One that can also be installed on an Android device as an offline computer algebra tool.
This has been an amazing experience. Was it “vibe coding”? I don’t think so. I was not just playing the dumb user, asking the agentic AI to deliver a solution. I was a senior partner with an incredibly capable, knowledgeable junior assistant, but I retained intellectual ownership of the result, indeed I can confidently edit, and fix/expand the code myself when I have to, since I understand what it does.
End result: 26,412 code lines in 163 files, at the cost of 31,006,699 input tokens and 3,048,131 output tokens, consumed over the course of less than two days. And WebCAS — the name picked by Claude — is already my favorite computer algebra application, one that will likely receive regular updates frmo me in the future.
