01 · Exact first
Preserve the mathematics before approximating it.
Symbolic structure, assumptions and derivation stay visible so numerical methods extend the result instead of replacing it.
∫₀∞ x²e⁻ˣ dx = Γ(3) = 2
Exact form · assumptions retained
MathSphere Laboratory · scientific computation
Mathematics,
made visible.
Solve, explore and understand mathematics through exact computation, clear visualization and living scientific scenes.
∇ · F = 0
eiπ + 1 = 0
∫ab f(x) dx
ds² = dx² + dy² + dz²
d/dx sin x = cos x
Solve
Exact symbolic work, numerical methods and transparent assumptions.
Visualize
Large 2D, 3D and animated scientific output as a primary result.
Preserve
Keep the result structured, reproducible and ready for the Project.
The product
A laboratory built around the mathematical result.
The interface stays quiet until the mathematics needs depth. Enter the problem once, then move naturally from exact form to numerical verification, geometry, interpretation and export.
Fig 01 · Integral StudioLocal compute
Primary visualization
Surface interpretation
Exact result
Γ(3) = 2
The symbolic form stays primary; numerical evaluation remains a verification layer.
Interpretation
The integral maps directly to the gamma function. Assumptions, method and result remain available for later use.
ExactSaved to Project
Workflow
One problem. Every useful layer.
The hierarchy is deliberate: problem first, visualization second, result third. Advanced detail appears only when it helps the work.
01
Problem
Enter the mathematical question once, with assumptions and bounds kept explicit.
02
Visualize
Make geometry visible before the result is reduced to a number or expression.
03
Solve
Prefer exact forms, then use numerical methods to verify or extend them.
04
Interpret
Keep derivation, diagnostics and meaning beside the primary result.
05
Save
Preserve the scientific object so Notebook and Writer can continue the work.
Depth without noise
Serious mathematical work without an interface that fights you.
02 · Visual by default
The graph is part of the answer.
Plots and surfaces are large enough to inspect. Visual output is not reduced to a thumbnail beneath the calculation.
03 · Focused studios
Choose the mathematical instrument, not a generic dashboard.
Each studio keeps the same hierarchy while exposing domain-specific controls only where they matter.
01Integral StudioSymbolic, numerical and geometric integration.02Differential StudioDerivatives, Jacobians, Hessians and differential systems.03Matrix StudioLinear algebra, transformations and spectral structure.04Probability StudioDistributions, inference and simulation.05Series & Limit StudioLimits, sequences and convergence.
One research trail
The result should survive the handoff.
Math is one instrument in the larger Project. Save a result once, reason about it in Notebook, then use the same scientific object in Writer.
Math
Solve, visualize and save the scientific result.
Notebook
Keep reasoning and observations attached to the evidence.
Writer
Turn the result into a publication without rebuilding context.
Mathematics should be something you can see.
Open a focused laboratory and move from problem to exact result, visualization and reusable scientific output.
Open Laboratory