diff --git a/math.test.ts b/math.test.ts
new file mode 100644
index 0000000..3f4ec32
--- /dev/null
+++ b/math.test.ts
@@ -0,0 +1,368 @@
+import {clamp, Vec2, AffineTransform, Rect} from './math'
+import * as jsc from 'jsverify'
+
+test('clamp', () => {
+  jsc.assertForall(jsc.number, jsc.number, jsc.number, (a, b, c) => {
+    const result = clamp(a, b, c)
+    if (a < b) return result == b
+    if (a > c) return result == c
+    return result == a
+  })
+})
+
+// Change this to jsc.integer to debug failures more easily
+let numericType = jsc.number
+
+const arbitraryVec2 = jsc
+  .record({x: jsc.integer, y: numericType})
+  .smap(v => new Vec2(v.x, v.y), v => v)
+
+const positiveVec2 = jsc.suchthat(arbitraryVec2, v => v.x > 0 && v.y > 0)
+
+const arbitraryTransform = jsc
+  .record({
+    m00: numericType,
+    m01: numericType,
+    m02: numericType,
+    m10: numericType,
+    m11: numericType,
+    m12: numericType,
+  })
+  .smap(t => new AffineTransform(t.m00, t.m01, t.m02, t.m10, t.m11, t.m12), t => t)
+
+const invertibleTransform = jsc.suchthat(arbitraryTransform, t => t.det() != 0)
+
+const simpleTransform = jsc.suchthat(
+  jsc
+    .record({scale: arbitraryVec2, translation: arbitraryVec2})
+    .smap(
+      t => AffineTransform.withScale(t.scale).withTranslation(t.translation),
+      t => ({scale: t.getScale(), translation: t.getTranslation()}),
+    ),
+  t => t.det() != 0,
+)
+
+const arbitraryRect = jsc
+  .record({origin: arbitraryVec2, size: positiveVec2})
+  .smap(r => new Rect(r.origin, r.size), r => r)
+
+describe('Vec2', () => {
+  test('constructor', () => {
+    jsc.assertForall(jsc.number, jsc.number, (a, b) => {
+      const v = new Vec2(a, b)
+      return v.x == a && v.y == b
+    })
+  })
+
+  test('withX', () => {
+    jsc.assertForall(arbitraryVec2, jsc.number, (v, n) => {
+      return v.withX(n).x === n
+    })
+  })
+
+  test('withY', () => {
+    jsc.assertForall(arbitraryVec2, jsc.number, (v, n) => {
+      return v.withY(n).y === n
+    })
+  })
+
+  test('plus', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      const sum = v1.plus(v2)
+      return sum.x === v1.x + v2.x && sum.y === v1.y + v2.y
+    })
+  })
+
+  test('minus', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      const diff = v1.minus(v2)
+      return diff.x === v1.x - v2.x && diff.y === v1.y - v2.y
+    })
+  })
+
+  test('times', () => {
+    jsc.assertForall(arbitraryVec2, jsc.number, (v1, s) => {
+      const prod = v1.times(s)
+      return prod.x === v1.x * s && prod.y === v1.y * s
+    })
+  })
+
+  test('timesPointwise', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      const prod = v1.timesPointwise(v2)
+      return prod.x === v1.x * v2.x && prod.y === v1.y * v2.y
+    })
+  })
+
+  test('dividedByPointwise', () => {
+    jsc.assertForall(
+      arbitraryVec2,
+      jsc.suchthat(arbitraryVec2, v => v.x !== 0 && v.y !== 0),
+      (v1, v2) => {
+        const div = v1.dividedByPointwise(v2)
+        return div.x === v1.x / v2.x && div.y === v1.y / v2.y
+      },
+    )
+  })
+
+  test('dot', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return v1.dot(v2) === v1.x * v2.x + v1.y * v2.y
+    })
+  })
+
+  test('equals', () => {
+    jsc.assertForall(jsc.number, jsc.number, (a, b) => {
+      return new Vec2(a, b).equals(new Vec2(a, b))
+    })
+
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (a, b) => {
+      return a.equals(b) === (a.x === b.x && a.y === b.y)
+    })
+  })
+
+  test('length2', () => {
+    jsc.assertForall(arbitraryVec2, v => {
+      return v.length2() === v.x * v.x + v.y * v.y
+    })
+  })
+
+  test('length', () => {
+    jsc.assertForall(arbitraryVec2, v => {
+      return v.length() === Math.sqrt(v.x * v.x + v.y * v.y)
+    })
+  })
+
+  test('abs', () => {
+    jsc.assertForall(arbitraryVec2, v => {
+      const q = v.abs()
+      return q.x === Math.abs(v.x) && q.y === Math.abs(v.y)
+    })
+  })
+
+  test('min', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      const min = Vec2.min(v1, v2)
+      return min.x === Math.min(v1.x, v2.x) && min.y === Math.min(v1.y, v2.y)
+    })
+  })
+
+  test('max', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      const max = Vec2.max(v1, v2)
+      return max.x === Math.max(v1.x, v2.x) && max.y === Math.max(v1.y, v2.y)
+    })
+  })
+
+  test('flatten', () => {
+    jsc.assertForall(arbitraryVec2, v1 => {
+      const flat = v1.flatten()
+      return flat[0] == v1.x && flat[1] == v1.y
+    })
+  })
+})
+
+describe('Rect', () => {
+  test('isEmpty', () => {
+    jsc.assertForall(arbitraryVec2, jsc.number, (v, n) => {
+      return new Rect(v, new Vec2(0, n)).isEmpty()
+    })
+    jsc.assertForall(arbitraryVec2, jsc.number, (v, n) => {
+      return new Rect(v, new Vec2(n, 0)).isEmpty()
+    })
+    jsc.assertForall(arbitraryVec2, v => {
+      return !new Rect(v, Vec2.unit).isEmpty()
+    })
+  })
+
+  test('width', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).width() == v2.x
+    })
+  })
+  test('height', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).height() == v2.y
+    })
+  })
+  test('left', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).left() == v1.x
+    })
+  })
+  test('top', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).top() == v1.y
+    })
+  })
+  test('right', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).right() == v1.x + v2.x
+    })
+  })
+  test('bottom', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).bottom() == v1.y + v2.y
+    })
+  })
+  test('topLeft', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).topLeft().equals(v1)
+    })
+  })
+  test('topRight', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).topRight().equals(v1.plus(v2.withY(0)))
+    })
+  })
+  test('bottomLeft', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).bottomLeft().equals(v1.plus(v2.withX(0)))
+    })
+  })
+  test('bottomRight', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return new Rect(v1, v2).bottomRight().equals(v1.plus(v2))
+    })
+  })
+
+  test('withOrigin', () => {
+    jsc.assertForall(arbitraryRect, arbitraryVec2, (r, v) => {
+      return r.withOrigin(v).origin.equals(v)
+    })
+  })
+  test('withSize', () => {
+    jsc.assertForall(arbitraryRect, arbitraryVec2, (r, v) => {
+      return r.withSize(v).size.equals(v)
+    })
+  })
+
+  test('closestPointTo', () => {
+    jsc.assertForall(arbitraryRect, arbitraryVec2, (r, v) => {
+      const p = r.closestPointTo(v)
+      return p.x >= r.left() && p.x <= r.right() && p.y >= r.top() && p.y <= r.bottom()
+    })
+  })
+
+  test('hasIntersectionWith', () => {
+    jsc.assertForall(arbitraryRect, arbitraryRect, (r1, r2) => {
+      return r1.hasIntersectionWith(r2) === !r1.intersectWith(r2).isEmpty()
+    })
+  })
+
+  test('intersectWith', () => {
+    jsc.assertForall(arbitraryRect, arbitraryRect, (r1, r2) => {
+      const inter = r1.intersectWith(r2)
+      return inter.isEmpty() || (r1.hasIntersectionWith(inter) && r2.hasIntersectionWith(inter))
+    })
+  })
+})
+
+describe('AffineTransform', () => {
+  test('inverted', () => {
+    expect(new AffineTransform(0, 0, 0, 0, 0, 0).inverted()).toBe(null)
+
+    jsc.assertForall(invertibleTransform, t => {
+      return t
+        .inverted()!
+        .inverted()!
+        .approxEquals(t)
+    })
+  })
+
+  test('translation', () => {
+    jsc.assertForall(arbitraryTransform, arbitraryVec2, (t, v1) => {
+      return t
+        .withTranslation(v1)
+        .getTranslation()
+        .equals(v1)
+    })
+
+    jsc.assertForall(arbitraryTransform, arbitraryVec2, (t, v1) => {
+      const initialTranslation = t.getTranslation()
+      return t
+        .translatedBy(v1)
+        .getTranslation()
+        .approxEquals(initialTranslation.plus(v1))
+    })
+  })
+
+  test('scale', () => {
+    jsc.assertForall(arbitraryTransform, arbitraryVec2, (t, v1) => {
+      return t
+        .withScale(v1)
+        .getScale()
+        .equals(v1)
+    })
+  })
+
+  test('transformVector', () => {
+    // Vector transformation are translation-invariant
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return AffineTransform.withTranslation(v1)
+        .transformVector(v2)
+        .approxEquals(v2)
+    })
+
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return AffineTransform.withScale(v1)
+        .transformVector(v2)
+        .approxEquals(v2.timesPointwise(v1))
+    })
+  })
+
+  test('inverseTransformVector', () => {
+    jsc.assertForall(invertibleTransform, arbitraryVec2, (t, v) => {
+      return t.inverseTransformVector(t.transformVector(v))!.approxEquals(v)
+    })
+  })
+
+  test('transformPosition', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return AffineTransform.withTranslation(v1)
+        .transformPosition(v2)
+        .approxEquals(v2.plus(v1))
+    })
+
+    jsc.assertForall(arbitraryVec2, arbitraryVec2, (v1, v2) => {
+      return AffineTransform.withScale(v1)
+        .transformPosition(v2)
+        .approxEquals(v2.timesPointwise(v1))
+    })
+  })
+
+  test('inverseTransformPosition', () => {
+    jsc.assertForall(invertibleTransform, arbitraryVec2, (t, v) => {
+      return t.inverseTransformPosition(t.transformPosition(v))!.approxEquals(v)
+    })
+  })
+
+  test('transformRect', () => {
+    jsc.assertForall(arbitraryVec2, arbitraryRect, (v, r) => {
+      return AffineTransform.withTranslation(v)
+        .transformRect(r)
+        .equals(r.withOrigin(r.origin.plus(v)))
+    })
+
+    jsc.assertForall(arbitraryVec2, arbitraryRect, (v, r) => {
+      const t = AffineTransform.withScale(v)
+      const rt = t.transformRect(r)
+      return Math.abs(rt.area() - r.area() * Math.abs(t.det())) < 1e-6
+    })
+  })
+
+  test('inverseTransformRect', () => {
+    jsc.assertForall(simpleTransform, arbitraryRect, (t, r) => {
+      return t.inverseTransformRect(t.transformRect(r))!.approxEquals(r)
+    })
+  })
+
+  test('times', () => {
+    jsc.assertForall(invertibleTransform, invertibleTransform, (t1, t2) => {
+      return t1
+        .times(t2)
+        .times(t2.inverted()!)
+        .approxEquals(t1)
+    })
+  })
+})
diff --git a/math.ts b/math.ts
index 63fb9d9..bf8d417 100644
--- a/math.ts
+++ b/math.ts
@@ -34,6 +34,10 @@ export class Vec2 {
   equals(other: Vec2) {
     return this.x === other.x && this.y === other.y
   }
+  approxEquals(other: Vec2, epsilon = 1e-9) {
+    return Math.abs(this.x - other.x) < epsilon && Math.abs(this.y - other.y) < epsilon
+  }
+
   length2() {
     return this.dot(this)
   }
@@ -130,6 +134,17 @@ export class AffineTransform {
     )
   }
 
+  approxEquals(other: AffineTransform, epsilon = 1e-9) {
+    return (
+      Math.abs(this.m00 - other.m00) < epsilon &&
+      Math.abs(this.m01 - other.m01) < epsilon &&
+      Math.abs(this.m02 - other.m02) < epsilon &&
+      Math.abs(this.m10 - other.m10) < epsilon &&
+      Math.abs(this.m11 - other.m11) < epsilon &&
+      Math.abs(this.m12 - other.m12) < epsilon
+    )
+  }
+
   timesScalar(s: number) {
     const {m00, m01, m02, m10, m11, m12} = this
     return new AffineTransform(s * m00, s * m01, s * m02, s * m10, s * m11, s * m12)
@@ -313,6 +328,14 @@ export class Rect {
     return this.origin.equals(other.origin) && this.size.equals(other.size)
   }
 
+  approxEquals(other: Rect) {
+    return this.origin.approxEquals(other.origin) && this.size.approxEquals(other.size)
+  }
+
+  area() {
+    return this.size.x * this.size.y
+  }
+
   static empty = new Rect(Vec2.zero, Vec2.zero)
   static unit = new Rect(Vec2.zero, Vec2.unit)
   static NDC = new Rect(new Vec2(-1, -1), new Vec2(2, 2))
diff --git a/package-lock.json b/package-lock.json
index 447a3fd..8820e68 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -6395,6 +6395,18 @@
         "verror": "1.10.0"
       }
     },
+    "jsverify": {
+      "version": "0.8.3",
+      "resolved": "https://registry.npmjs.org/jsverify/-/jsverify-0.8.3.tgz",
+      "integrity": "sha1-AukXjhkktar5WcAjmvhO1cbQc4w=",
+      "dev": true,
+      "requires": {
+        "lazy-seq": "1.0.0",
+        "rc4": "0.1.5",
+        "trampa": "1.0.0",
+        "typify-parser": "1.1.0"
+      }
+    },
     "kind-of": {
       "version": "3.2.2",
       "resolved": "https://registry.npmjs.org/kind-of/-/kind-of-3.2.2.tgz",
@@ -6411,6 +6423,12 @@
       "dev": true,
       "optional": true
     },
+    "lazy-seq": {
+      "version": "1.0.0",
+      "resolved": "https://registry.npmjs.org/lazy-seq/-/lazy-seq-1.0.0.tgz",
+      "integrity": "sha1-iAy4qrJWAmOC4C9T7AiWgqdMW2o=",
+      "dev": true
+    },
     "lcid": {
       "version": "1.0.0",
       "resolved": "https://registry.npmjs.org/lcid/-/lcid-1.0.0.tgz",
@@ -9994,6 +10012,12 @@
       "integrity": "sha1-9JvmtIeJTdxA3MlKMi9hEJLgDV4=",
       "dev": true
     },
+    "rc4": {
+      "version": "0.1.5",
+      "resolved": "https://registry.npmjs.org/rc4/-/rc4-0.1.5.tgz",
+      "integrity": "sha1-CMbgSgFo9utiHCKrbLEVG9n0pk0=",
+      "dev": true
+    },
     "read-pkg": {
       "version": "1.1.0",
       "resolved": "https://registry.npmjs.org/read-pkg/-/read-pkg-1.1.0.tgz",
@@ -11942,6 +11966,12 @@
         }
       }
     },
+    "trampa": {
+      "version": "1.0.0",
+      "resolved": "https://registry.npmjs.org/trampa/-/trampa-1.0.0.tgz",
+      "integrity": "sha1-Ukc0esM0gH+mwAAERMuRtjmECtU=",
+      "dev": true
+    },
     "trim-right": {
       "version": "1.0.1",
       "resolved": "https://registry.npmjs.org/trim-right/-/trim-right-1.0.1.tgz",
@@ -12319,6 +12349,12 @@
         "semver": "5.5.0"
       }
     },
+    "typify-parser": {
+      "version": "1.1.0",
+      "resolved": "https://registry.npmjs.org/typify-parser/-/typify-parser-1.1.0.tgz",
+      "integrity": "sha1-rHO/pfJTQ0aOLQ8zRsYRe8A9PJk=",
+      "dev": true
+    },
     "uglify-es": {
       "version": "3.2.2",
       "resolved": "https://registry.npmjs.org/uglify-es/-/uglify-es-3.2.2.tgz",
diff --git a/package.json b/package.json
index 160bfb8..2a211f0 100644
--- a/package.json
+++ b/package.json
@@ -24,6 +24,7 @@
     "eslint": "^4.19.1",
     "eslint-plugin-prettier": "^2.6.0",
     "jest": "^23.0.1",
+    "jsverify": "^0.8.3",
     "pako": "1.0.6",
     "parcel-bundler": "1.7.0",
     "preact": "8.2.7",