AI drives
The AI decomposes the problem into computational steps, drawing on a relevant part of the corpus of human mathematical knowledge.
AI in Computational Mathematics
AI is increasingly becoming the driver of computational mathematics in research, engineering, and education, and the trend is accelerating. At the same time, Computer Algebra System (CAS) algorithms rest on formal proofs, which themselves started as inference, and AI models are trained on the products of that formalization. The cycle between inference and certified computation has always been there. ExaktAI’s vision is summarized in four assumptions.
I. AI drives computational mathematics
AI is increasingly the driver of computational mathematics. Given a problem like finding inflection points of a function, an AI decomposes it into steps: compute the second derivative, find its roots, determine sign changes, classify the intervals.
AI reasoning is grounded in training on essentially all existing textbooks, research papers, and course materials in digital form. That body of synthesized mathematical knowledge, available to the AI for almost instant recall, will usually surpass the immediate recall of any individual human, though a human could still see what the AI missed.
II. AI inference over mathematics requires CAS
AI infers mathematical results. CAS computes them by executing deterministic algorithms derived from mathematical proofs. The distinction is not about accuracy, but about what stands behind each result.
A CAS algorithm is a chain of certified transformations: the same input always produces the same output, and the algorithm’s correctness rests on the theorems behind it. AI carries no such certificate. More training data only increases the probability of a correct answer. This gap is epistemological, not technological (see AI math reliability). It does not close with scale.
Even formal proof systems (Lean, Coq) still depend on symbolic computation to differentiate, solve equations, and verify results. Formal proof can strengthen the chain of trust, but it does not eliminate the computational role of CAS.
III. Human in the loop is non-negotiable
Without a human in the loop, two things become impossible.
Trust: a person must be able to audit how a result was obtained and judge whether it is sound.
Improvement: a person can see why an approach failed, envision a different one, and contribute mathematical insight beyond any validation process or textbook.
For these purposes, ExaktAI provides not only a result in its own App, where each step is shown together with its validation status and details, but also automatically generates and opens an executable Mathematica notebook or Maple document that a person can audit, edit, and extend. The document is not just a record of the computation; it is a live workspace where the person can continue the work.
IV. Mathematics is learned by doing
Reading a solved problem is not the same as solving it. Mathematical understanding comes from active engagement: modifying a step, testing an alternative, and in that process deepening one’s understanding of the problem.
This active engagement is also supported by the executable CAS documents that are automatically generated and opened when ExaktAI produces a result. A CAS document is a starting point where every step can be re-executed, every result modified, every assumption tested.
The architecture follows
CAS validates
Each step is executed by a CAS whose algorithms carry into computation the certificate of correctness established by the formal proofs behind them.
Human steers
The human inspects, experiments, and improves, generating trust and progress: corrections or reformulations become possible.
Document enables
The executable document is where active mathematical work happens and understanding is built.
AI will continue to improve. The gap between probabilistic inference and certified computation, however, is not technological but epistemological, and as such it will not disappear with more training data. As AI takes on harder problems, it demands more from CAS: more algorithms, broader coverage, and deeper formalization in order to certify results and produce new training data. The more AI evolves, the more CAS matters.
ExaktAI is built with this evolving landscape in mind.