LEARNING IS
Science
“Tell me and I forget. Teach me and I remember. Involve me and I learn.”Benjamin Franklin
Our thesis
Vergil’s Theory
Varga & Papp · 2026
We treat learning as one of the most consequential sciences there is. A platform built to teach the way the mind truly learns cannot rest on intuition. It has to answer to evidence: to how attention, memory, and understanding actually behave. So we ground Vergil in the most durable work the field has produced, the theories that have survived decades, and in some cases centuries, of scrutiny.
But we do not simply reprint what was published in the past. We take the most acclaimed and effective research ever conducted on human learning and recompose it, combining it, extending it, and testing every result against our own, until separate discoveries become a single, coherent instrument. Those studies are the building blocks of Vergil’s analytical engine: a system precise enough to glimpse the shape of a learner’s mind, and disciplined enough to know how certain it is.
We refine that engine without pause, keeping Vergil at the frontier of science-based learning. This is not a feature of the platform. It is its soul.
Item Response Theory
Lord & Rasch · 1960
Item Response Theory models the probability of a correct answer as a smooth function of a learner’s latent ability and an item’s own parameters: its difficulty, how sharply it separates strong learners from weak ones, and the chance of a lucky guess. Because every question is calibrated on the same underlying scale, Vergil can compare items that were never seen by the same people, and always serve the one that reveals the most about where a learner truly stands.
The DINA model
Junker & Sijtsma · 2001
The Deterministic-Input, Noisy-And-gate model connects each question to the precise set of skills it requires through a Q-matrix. To answer correctly you must have mastered every skill the item demands, with the “noisy” part forgiving the occasional slip or lucky guess around that rule. This lets Vergil move past a single score and report which specific competencies a learner has genuinely acquired, and which are still missing.
The G-DINA model
de la Torre · 2011
The Generalized DINA framework relaxes DINA’s strict all-or-nothing rule, letting the skills behind a question combine in flexible ways: some compensating for one another, others strictly required. It gathers a whole family of cognitive-diagnosis models under one estimator, so Vergil can fit the variant that best matches how skills genuinely interact within a domain and produce fine-grained mastery profiles across interdependent skills.
Bayesian statistics
Thomas Bayes · 1763
Bayesian inference treats every interaction as evidence. Rather than a single guess at what a learner knows, Vergil maintains a full probability distribution over their knowledge state and revises it with Bayes’ rule each time an answer arrives, sharpening confidence where signals agree, widening uncertainty where they conflict. The result is not just an estimate of mastery, but an honest measure of how sure that estimate is.
The forgetting curve
Hermann Ebbinghaus · 1885
In 1885 Hermann Ebbinghaus showed that memory decays exponentially: without reinforcement, most of what we learn slips away within days. Vergil fits each learner’s personal forgetting curve for every knowledge point and schedules review at the moment retention is about to fall: the spacing effect turned into a precise, individual timetable, so effort lands exactly where and when it does the most good.
