Descartes
In order to seek truth, it is necessary once in the course of our life to doubt, as far as possible, of all things.
Who says what is true?
An AI system produces a mathematical result through inference. A computer algebra system computes one. They may agree, they may not. Who decides which is correct? On what basis? And what would “correct” mean when every source is fallible?
The invention of certainty
We can say for sure that 1 + 1 = 2. Mathematics is where humans invented certainty: a formal system of abstractions where “true” and “false” are defined and computable. Outside mathematics, assertions rely on concepts that only partially represent reality, so they remain debatable.
Two layers of uncertainty
AI and Computer Algebra Systems (CAS) sit on top of mathematical certainty, each introducing its own uncertainty. AI reasons about mathematics but carries training gaps, hallucinations, and plausible-but-wrong inferences. CAS computes but is subject to bugs, incomplete algorithms, and scope limitations. Neither layer is the mathematical bedrock; both are fallible machinery operating above it.
ExaktAI’s focus is on these two layers, questioning whether the AI-inferred result and the CAS’s computation converge and withstand scrutiny.
Three principles
ExaktAI’s validation architecture rests on three ideas, none of them new.
Popper
Since we can never know anything for sure, it is simply not worth searching for certainty; but it is well worth searching for truth; and we do this chiefly by searching for mistakes, so that we can correct them.*
Feynman
The first principle is that you must not fool yourself - and you are the easiest person to fool.
These three principles map directly to ExaktAI’s flow: question AI outputs → validate through convergence → report what could not be validated.
The real landscape
“The AI proposed it, the CAS computed it, and they agree” is the easy sentence. Behind it lies a landscape where no single validation is infallible.
AI and CAS disagree
The AI infers one result; the CAS computes a different one. The discrepancy is caught. AI-CAS agreement is what most people imagine when they think of validation.
CAS cannot verify
The AI reasons, but the CAS lacks the algorithm, or the problem falls outside its scope. The result may be correct, but no CAS evidence supports it.
No AI inference at all
The problem is outside training data. No AI system produces a meaningful answer.
CAS has a bug
Computer algebra systems can have bugs. Cross-checking with an independent source (AI, other CAS, or other method) makes the bug visible.
Cross-CAS verification
Two systems rarely implement the same algorithms, so one may not be able to compute what the other did. Decomposing the problem into finer steps to get around that multiplies the places where an error can enter.
Every validation method is partial and can fail. The point, then, is not whether any single check can be trusted, but that the composition of the appropriate independent checks can produce something significantly stronger than any one alone.
What validated means
ExaktAI runs independent validation procedures on the result the AI inferred, and reports one of three outcomes: the result passed every check performed; a check found that it does not hold, an independent computation having disagreed; or the checks could neither confirm nor refute it, which is not failure and leaves room for human review.
The validation is auditable. Every step is present in an executable document: a Maple document, a Mathematica notebook, or an ExaktAI Workspace document that you can inspect, re-run, and verify independently. The trust is in the evidence the executable document contains.
AI-mathematics: weeding out its unreliability
Neither AI nor CAS, alone or through an MCP tool, can guarantee mathematical correctness, or detect that an inferred result is wrong. What ExaktAI does is validate AI-mathematics results. Where an AI-inferred result is refuted by the ExaktAI validation procedures, the independently computed result using computer algebra is shown beside it, in a CAS document where you can reproduce the computation, and edit it as you see fit.
* Karl Popper, In Search of a Better World (from the 1982 Alpbach lecture “Knowledge and the Shaping of Reality”); quoted at The Marginalian. ↩