If you're comparing online proof courses, pick the proof assistant before you pick a certificate. For a broad first experiment, start with Learning Lean 4 and Mathematics in Lean. Choose Programming Language Foundations in Agda if Agda's dependent-type workflow is your goal. For Coq, use the Software Foundations installation guide, while Isabelle learners should begin with the official Isabelle site.
These aren't all video MOOCs. Several are interactive books, exercise collections, or software guides. That distinction matters. Turns out, setup and version support can matter more than a badge.
Z3 and ACL2 need a separate comparison. The available source material here doesn't verify a current course, price, or support route for either, so they aren't ranked alongside these four paths.
Choose by goal
| Goal | Start here | Why it fits | Consumer check |
|---|---|---|---|
| General Lean 4 orientation | Learning Lean 4 | A Lean 4-focused resource list with links to exercises, theory, and programming material | Some older resources use Lean 3 |
| Mathematical proofs in Lean | Mathematics in Lean | Installation guidance, VS Code setup, and small theorem examples | Expect local software setup |
| More challenging Lean exercises | eXperimental Lean Lab | Lean 4 setup instructions and problems involving algebra, probability, graphs, and group theory | It is more specialized than a first lesson |
| Coq with a Software Foundations route | Coq installation instructions | Explains opam, Coq, and the VsCoq editor options | Installation can take 15-20 minutes |
| Agda and dependent types | PLFA Getting Started | Explains interactive holes, editor setup, and version requirements | Exact tool versions matter |
| Isabelle and Isabelle/HOL | Official Isabelle site | Provides application bundles, documentation, and hardware guidance | It is a distinct local toolchain |
This is a fit guide, not a league table. Your target language, computer, and tolerance for setup decide the value.
Lean resources: a practical first test
The Lean learning page is useful because it separates current Lean 4 material from older resources. It notes that some earlier items use Lean 3, so check the version before following a tutorial.
Mathematics in Lean gives the learning process more shape. Its introduction covers Lean 4, VS Code, basic assumptions, and small goals such as theorem easy : 2 + 2 = 4 :=. That is a useful first test. You can see whether the editor, notation, and feedback suit you before committing to a long course.
The eXperimental Lean Lab adds harder examples. Its exercises include linear transformations, Beatty sequences, expected edge counts in random graphs, and group theory. This makes it better for someone who has already completed a few basic proofs and wants mathematical practice.
Start with the smallest example. A working proof tells you more than a polished course description.
Coq: budget for the toolchain
Coq is a sensible choice if the material you want follows the Software Foundations tradition. The installation page associated with that material treats setup as part of the learning path, rather than assuming a browser will do everything.
The guide warns that installing through opam can take 15-20 minutes because OCaml, Coq, and related libraries may need to compile. It also distinguishes VsCoq 2 from the older VsCoq extension. Thing is, extension names age badly.
Check the current instructions before copying a command from an old video. Record which Coq version and editor extension you installed. That small note can save an afternoon when a lesson no longer matches your screen.
Agda: follow the version instructions
PLFA is closer to an interactive textbook than a conventional video course. It teaches programming language foundations through Agda, using editor-supported holes as part of the proof and programming workflow.
The Getting Started page explains how to configure Agda and its standard library. It also gives operating system instructions and tested version guidance for Agda, GHC, and related tools.
Use the listed versions first. Upgrading one component in the middle of an exercise can create avoidable errors, especially when the course expects a particular library layout.
Choose PLFA when the type theory and programming-language angle appeals to you. It may feel less convenient than a guided web tutorial, but the interactive editing model is the point.
Isabelle: plan for a local application
Isabelle follows a different route. The official site provides downloadable application bundles containing source, binary packages, and documentation, so you should think about software installation before comparing lessons.
The site lists Isabelle2025-2 with a January 2026 date. It also gives planning figures for different project sizes: 4 GB of memory and 2 CPU cores for small experiments, 8 GB and 4 cores for medium applications, 16 GB and 8 cores for large projects, and 64 GB and 16 cores for extra-large projects.
Those figures are planning guidance, not a reason to buy a new computer immediately. Start with a small example and see how your machine performs. Isabelle may suit you well if you want its application-based workflow and documentation rather than a lightweight browser lesson.
What controls a course purchase?
Use the provider's current page and checkout terms to verify price, billing frequency, cancellation, refunds, and certificate details. Use the proof assistant's documentation to verify compatibility. A star rating or forum comment answers neither question.
The source pages cited here don't establish the enrollment totals, completion rates, salary premiums, or fixed certificate prices claimed in many course roundups. Treat those figures as unverified unless the provider explains how they were calculated.
A public page may be readable without a purchase and still offer no graded assessment, certificate, instructor support, or refund promise. Check each item separately.
Before paying, check these five points:
- Version: Does the course name the Lean, Coq, Agda, or Isabelle version it uses?
- Hands-on work: Will you run checked proofs, or only watch demonstrations?
- Total price: Is access one-time, subscription-based, trial-based, or tied to another service?
- Credential terms: Who issues the certificate, what work earns it, and how long does access last?
- Exit route: What do the current terms say about cancellation, refunds, and access after a subscription ends?
Save the checkout page and confirmation email. Boring evidence is useful when course terms change.
The setup cost is part of the course
The learning paths described here are not purely browser-based. Lean's introductory material tells you to install Lean 4 and VS Code, then download the mathematics_in_lean repository. Coq uses a local installation and an editor extension. PLFA requires an Agda editing setup, while Isabelle uses application bundles.
That can be worthwhile. You get direct feedback from the proof assistant instead of relying on a video's result. It also means the real cost includes installation time, storage, memory, and troubleshooting.
If a course promises a completely effortless experience, compare that promise with the tool's own setup documentation first. The official instructions are the better test.
A sensible starting decision
Lean is a sensible first click for a general math-and-programming experiment. If the material you want is Software Foundations, begin with Coq instead.
PLFA is the focused option for Agda's hole-driven, dependent-type workflow. Isabelle deserves its own decision because its software, documentation, and hardware planning differ.
To be honest, you don't need a certificate to find out whether theorem proving suits you. Open one official starting page, note its version, and complete the first checked exercise before paying for anything.