Origin: It Started with a "Fact"
AlgeBrain was born not in a classroom, but in a conversation about the impossible. It began with a challenge I posed: "Tell me three strange science facts." As I dissected the facts with an AI thought partner, I found I couldn't be stumped. This led to a pivot—from trivia to the open problems of physics.
We realized that many "unsolvable" problems in physics don't necessarily require a Ph.D. to crack; they require a mind capable of unique conceptual leaps. This line of thinking led us to the P vs. NP problem.
The Perpetual Consistency Framework
This birthed the Perpetual Consistency Framework (PCF). This theory proposes that the laws of physics are effectively the "decompression algorithms" of reality. They are the rules that unpack the source code of the universe into the physical world we see. And what is the language of that source code? Algebra.
That is why AlgeBrain exists. It is not just a math game. It is a "Gym" designed to train your mind to see the underlying source code of reality. By stripping away the arithmetic and focusing purely on the balancing of equations, we are training the brain to recognize the fundamental symmetry that governs everything from simple scales to quantum mechanics.
Strategy Guide: The Curriculum
Stuck on a level? Here is the official breakdown of the logic engines.
Level 2: The Basics (Linear Equations)
The foundation. Solve simple linear equations in the form ax + b = c.
- Example: 3x + 5 = 17
- Step 1:
-5→ 3x = 12 (Remove the constant) - Step 2:
/3→ x = 4 (Isolate x)
Level 3: The Juggling Act
Variables appear on both sides. Group your terms first.
- Example: 5x + 2 = 3x + 12
- Step 1:
-3x→ 2x + 2 = 12 (Group x terms) - Step 2:
-2→ 2x = 10 (Remove constant) - Step 3:
/2→ x = 5 (Solve)
Level 4: The Distributor
Parentheses appear. You must distribute the multiplier or divide it away.
- Example: 5(x+2) = 40
- Step 1:
dist→ 5x + 10 = 40 (Distribute the 5) - Step 2:
-10→ 5x = 30 - Step 3:
/5→ x = 6
Level 5: The Quadratic Curve
Introduction to curves. Isolate x² and use the sqrt command.
- Example: 3x² = 27
- Step 1:
/3→ x² = 9 (Isolate squared term) - Step 2:
sqrt→ x = 3 (Apply Square Root)
Level 7: Fraction Action
Dealing with division. Multiply the whole equation to clear the denominator.
- Example: x/4 + 3 = 8
- Step 1:
-3→ x/4 = 5 (Isolate fraction) - Step 2:
*4→ x = 20 (Multiply to clear division)
Level 8-10: Systems & Substitution
Multi-variable algebra. You are provided the value of y and must solve for x.
- Example: 4x + 3y = 26 (Given y=2)
- Step 1:
-3y→ 4x = 20 (Subtracting 3y, which is 6, from 26) - Step 2:
/4→ x = 5 (Solve)
Level 13: The Thunderdome
"Two equations enter, one value leaves." You must substitute the expression for y into the main equation.
- Example: 3x + 2y = 29 (Given y = x + 2)
- Step 1:
sub→ 3x + 2x + 4 = 29 (Substitutes y) - Step 2:
-4→ 5x = 25 - Step 3:
/5→ x = 5
Level 14-15: The Negative Traps
Advanced substitution. You must distribute a negative multiplier (sometimes an invisible -1), which flips internal signs.
- Example: 4x - 3y = 18 (Given y = 2x - 10)
- Step 1:
sub→ 4x - 6x + 30 = 18 (Note: -3 * -10 = +30) - Step 2:
-30→ -2x = -12 - Step 3:
/-2→ x = 6
Level 16: Literal Equations (Abstract Mode)
No numbers, only logic. You must treat letters like numbers to isolate x. This is the essential skill for Physics.
- Example: ax + b = c (Solve for x)
- Step 1:
-b→ ax = c - b (Move constant) - Step 2:
/a→ x = (c - b) / a (Divide by coefficient)
Level 17: Inequalities (The Sign Flip)
The rules of equality change. If you multiply or divide by a negative number, the direction of the inequality must flip.
- Example: -2x + 4 > 14
- Step 1:
-4→ -2x > 10 - Step 2:
/-2→ x < -5 (FLIP! > becomes <)
