For gifted and advanced math learners

AI math tutoring for gifted and advanced students.

Pythago sees each written step and listens to the learner explain it. A small slip gets a focused prompt. A secure idea opens a deeper question. The tutor follows the thought as far as it can go.

Start learning See how feedback works

Begin with their current mathematics or a new question.

Depth you can see

Follow the thought further.

Written work reveals the depth, gaps, and questions inside each attempt. Pythago uses those signals to choose a step that matches what the learner understands.

They work it on-screen.
The learner writes, draws, and explains on the shared canvas with a stylus, touch, or mouse.
Pythago sees the attempt.
It responds to the step that changed the result—a conceptual gap, an incorrect operation, or a small calculation slip.
The learner keeps the problem.
The tutor gives a focused question or hint, then waits for a correction and checks the idea on fresh work.

Shared math canvas

Solving a linear equation

Feedback in progress

Learner work

$3(2x-1)=21$

$6x-1=21$

$6x=22$

Pythago

You distributed the 3 to 2x. Check the −1 inside the parentheses: what does 3 × −1 become?

Now try the next step.

If this sounds familiar

Find the edge of their understanding.

Gifted learners may move quickly through a procedure, want the proof behind it, and still have one missing idea that deserves careful attention. Visible work helps separate all three.

A right answer can be too little information.

Pythago can ask for the derivation, counterexample, or harder application that reveals whether an idea is actually secure.

Their real question is often one level deeper.

The work on the canvas gives the tutor somewhere concrete to begin before following the learner into the why behind the method.

One small slip can reveal the next useful question.

Pythago can isolate one fragile idea or calculation slip and keep the rest of the course moving at the learner’s pace.

How it works

Follow the work to the edge of what they understand.

The learner’s explanation, written work, and goal shape the next question.

01
Give them a real mathematical task.
Choose a Pythago lesson, upload current class material, or build a rigorous bridge toward what they want to learn next.
02
They make the thinking visible.
The learner writes, draws, and explains on the shared canvas. The tutor follows the reasoning inside each attempt.
03
Pythago follows the idea to its edge.
It gives a focused hint, checks the correction, and goes deeper when the work shows they are ready.

One learner. One coherent path forward.

Give Pythago the context a fixed curriculum misses, then choose whether the next lesson begins with their current class or a more ambitious destination.

Example learner profile

Maya Chen

Mastery approach

What Pythago should know

Maya is a rising 10th grader who completed Precalculus. She moves quickly through symbolic procedures and wants to derive calculus rules from first principles.

Learning goal

Begin Calculus through limits and derive important rules from first principles. Require Maya to explain each connection before moving forward.

Bring your own material

Upload files or folders

precalculus-syllabus.pdf
Current course
limits-and-continuity.pdf
Textbook chapter
function-behavior-review.pdf
Recent work

Research

Web and YouTube

Build a rigorous bridge from Precalculus function behavior to the first ideas in Calculus.

Dialogue with Assistant

Build a rigorous bridge from Precalculus function behavior to the first ideas in Calculus.

I can prepare one lesson for today, or a sequence that follows the outline.

Web sources saved · Course references saved

How can I help you today?

Prepared for the learner

One lesson

From Average Change to a Limit

Connect average rate of change to what happens as an interval shrinks.

A sequence over time

Precalculus to Calculus Foundations

Limits, derivatives from first principles, and applications that preserve conceptual depth.

What progress looks like

Reasoning leaves a trail.

After every lesson, the learner and parent can return to the whiteboard, conversation, demonstrated understanding, remaining gaps, and next question.

See the reasoning.

The board and transcript preserve what Maya could explain, how she corrected the work, and where the idea led next.

Sessions

Session 1 · Review ready

Deriving the Power Rule

Calculus Foundations · Lesson 1

Whiteboard replay

Whiteboard from the learner’s session.

Why the derivative of x² is 2x

Start with average change

$\frac{(x+h)^2-x^2}{h}$

Simplify

$\frac{2xh+h^2}{h}=2x+h$

Let the interval shrink

$h \to 0 \Rightarrow 2x+h \to 2x$

The derivative is the limiting rate of change as the interval shrinks to zero.

81 updatesProgress saved

Transcript

Conversation from Maya’s session.

Maya

I know the power rule, but I never understood where the 2x came from.

Tutor

Let’s derive the rule from first principles. What does $(x+h)^2$ expand to?

Maya

$x^2+2xh+h^2$. Then the $x^2$ terms cancel and I can divide by $h$.

Tutor

Exactly. Now explain what happens to $2x+h$ as the interval $h$ approaches zero.

See what changes next.

The review separates secure understanding from the idea that still needs another context.

Sessions

Session 1 · Review ready

Deriving the Power Rule

Calculus Foundations · Lesson 1

Review

Review generated after the session.

Session Report

What we worked on

Deriving the power rule for $x^2$ from the difference quotient and explaining each connection.

What changed

Connected average rate of change to the derivative at a point.
Expanded and simplified the difference quotient without prompting.

Evidence from today

Explained why the two $x^2$ terms cancel.
Described in their own words why $2x+h$ approaches $2x$ as $h$ approaches zero.

Still developing

Extending the same reasoning from $x^2$ to $x^3$ .

Next time

Use the binomial expansion to derive the power rule for another exponent.

Practice it again before you forget it.

After every four lessons, Pythago builds a mixed review. Strong ideas return beside the ones that still need work.

Lesson 01Learn
Lesson 02Build
Lesson 03Apply
Lesson 04Extend
Generated next
Spiral review
A mixed review of the last four lessons.

Scope and fit

Built for mathematical depth.

Follow a complete course, begin at the learner’s current edge, or build a bridge to a more ambitious destination.

Pre-AlgebraAlgebra IGeometryAlgebra IIPrecalculusCalculus ABAP Calculus BCAP Statistics / College StatisticsLinear AlgebraMultivariable Calculus

A strong fit

Working anywhere from Pre-Algebra through advanced college-level mathematics
Learns quickly but still wants to understand why the method works
Can explain ideas aloud and work through mathematics on a shared whiteboard
Needs flexible one-to-one depth that grows with each attempt

A different need

CogAT, NNAT, OLSAT, or gifted-program admissions test preparation
Live group classes, peer clubs, or a gifted-school community
An accredited course provider that awards school credit
Answer-supply software or automated homework completion

Built for family oversight

Live tutoring. Visible family controls.

The learner gets room to think aloud. The family keeps a reviewable record and clear privacy choices.

Voice stays live.

Pythago discards microphone audio after transcription.

The learning record stays inspectable.

Families can return to the transcript, uploaded sources, learner profile, and whiteboard work—and delete the session or account.

Learner work stays theirs.

Model training for other users excludes identifiable tutoring messages, transcripts, recordings, files, and canvas content.

Read the Privacy Policy

Questions gifted families ask first.

The learner’s current mathematics, reasoning, and goal determine where Pythago begins.

Does a learner need a formal gifted identification?+

Formal identification is unnecessary. Pythago responds to demonstrated readiness, pace, and reasoning. This page is for families whose learner needs more mathematical depth than their current path provides.

What math levels does Pythago cover?+

Pythago includes complete paths from Pre-Algebra through AP Calculus BC, AP Statistics / College Statistics, Linear Algebra, and Multivariable Calculus. A learner can follow a course, enter at their current edge, or work from material supplied by their family.

What age is Pythago for?+

Mathematical readiness guides placement. Pythago is designed for learners ready to work anywhere from Pre-Algebra through advanced college-level mathematics who can explain ideas aloud and use a shared whiteboard. A learner under 13 uses a parent-managed account.

Will Pythago simply push them ahead faster?+

Moving forward depends on evidence from the learner’s explanation and work. Pythago can accelerate through secure ideas, stop at a hidden gap, and revisit fragile concepts in later spiral reviews.

Can they use material from school or another curriculum?+

Yes. Upload a syllabus, chapter, problem set, notes, or a folder of course material. Pythago uses it with the learner profile to prepare one lesson or a connected sequence.

What can a parent review after a lesson?+

Each session preserves the whiteboard activity, conversation, corrections, demonstrated understanding, remaining gaps, and recommended next step. Parents can see the reasoning behind progress.

Is the tutor a live person?+

Pythago is an AI tutor. The learner speaks with it and works on a shared whiteboard. Qualified professionals and institutions remain the right source for formal evaluation, clinical accommodations, and school credit.

How does Pythago handle a learner’s voice and work?+

Pythago discards live microphone audio after transcription. Learning records are saved for family review. Model training for other users excludes identifiable learner content.