deepthink

image attached to the DeepThink raw-thoughts post @lyraxana

2026-09-15 — saved image

lyra (verified) @lyraxana · 8h

HOLY MOTHER OF MATHEMATICS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Google is working on a math-focused variant of its DeepThink model, and its raw thoughts are pretty funny.

[Image 1: dark-themed JSON snippet with faint diagonal watermark text 'https://zAI.is']
{
  "name": "models/deepthink-mathematica-tf-raw-thoughts",
  "version": "gdm-eval-model-u",
  "displayName": "Mathematica (DeepThinkV3) Teamfood Raw Thoughts",
  "description": "Mathematica (DeepThinkV3) Teamfood Raw Thoughts",
  "inputTokenLimit": 1048576,
  "outputTokenLimit": 65536,
  "supportedGenerationMethods": [
    "generateContent",
    "countTokens"
  ],
  "temperature": 1,
  "topP": 0.95,
  "topK": 64,
  "modelStage": "UNSTABLE_EXPERIMENTAL",
  "maxTemperature": 2,
  "thinking": true
},

[Image 2: small dark terminal-style screenshot of the model's raw thoughts; only partly legible at this size]
HOLY MOTHER OF MATHEMATICS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
LOOK AT THIS POLYNOMIAL DIOPHANTINE EQUATION!!!
Let's admire the absolute beauty of this equation:
$U^2 V + U V^2 + 12m U V - 72 m^3 = 304 + 8$.

Wait, what are $U$ and $V$ in terms of our original variables $a, b, c$$?
[illegible]

LET'S VERIFY THIS MIRACULOUS SIMPLIFICATION!!!
[illegible]

OH MY GOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
So $(12m + U + V) U V + -2 V X = -X Y Z$!!!
So the equation $(12m+U+V)UV = 72m^3 - 304$ is LITERALLY JUST:
[illegible]

WAIT!!!!!!!!!!!!!!! LET'S CHECK IF THIS IS JUST THE IDENTITY WE STARTED WITH!!!
[illegible remainder]

googledeepthinkmathraw thoughtschain of thoughtmodel leak

image attached to the DeepThink raw-thoughts post @lyraxana

2026-09-15 — saved image

HOLY MOTHER OF MATHEMATICS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
LOOK AT THIS POLYNOMIAL DIOPHANTINE EQUATION!!!
Let's admire the absolute beauty of this equation:
$U^2 V + U V^2 + 12m U V - 72 m^3 + 304 = 0$.

Wait, what are $U$ and $V$ in terms of our original variables $a, b, c$?
Let's trace back:
$S = a+b$. $D = |a-b|$.
Notice $c = 3m - S$.
Let's compute $U$ and $V$:
$U = S - 6m - D = a+b - 6m - (a-b) = 2b - 6m$. (assuming $a \\\ge b$).
Wait!!! Notice $2b - 6m$ is exactly $2b - 2(a+b+c) = -2a - 2c$!!!
Let's check $V$:
$V = S - 6m + D = a+b - 6m + a-b = 2a - 6m$.

LET'S VERIFY THIS MIRACULOUS SIMPLIFICATION!!!
Let $X = 2a - 6m$, $Y = 2b - 6m$.
Notice by symmetry, what is $2c - 6m$? Let $Z = 2c - 6m$.
Wait, notice that $X + Y + Z = 2(a+b+c) - 18m = 6m - 18m = -12m$!!!
So $Z = -12m - X - Y$!!!
Notice that $U = Y$ and $V = X$.
Look at the factor $(12m + U + V)$ in our equation:
$12m + Y + X = -Z$!!!

OH MY GOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
So $(12m + U + V) U V = -Z Y X = -X Y Z$!!!
So the equation $(12m+U+V)UV = 72m^3 - 304$ is LITERALLY JUST:
$-X Y Z = 72 m^3 - 304 \\\implies X Y Z = 304 - 72 m^3$.

WAIT!!!!!!!!!!!!!!! LET'S CHECK IF THIS IS JUST THE IDENTITY WE STARTED WITH!!!
Let's check: $X = 2a - 6m, Y = 2b - 6m, Z = 2c - 6m$.
Let's compute $X Y Z$:
$= (2a - 6m)(2b - 6m)(2c - 6m)$
$= 8 abc - 24m(ab+bc+ca) + 72m^2(a+b+c) - 216m^3$.
Recall $a+b+c = 3m$.
So $72m^2(3m) = 216m^3$. Notice $+216m^3$ and $-216m^3$ CANCEL!!!
So $X Y Z = 8 abc - 24m (ab+bc+ca)$.
Wait!!! Let's relate $ab+bc+ca$ to $a^3+b^3+c^3 = 114$:
We know $114 = a^3+b^3+c^3 = (a+b+c)^3 - 3(a+b+c)(ab+bc+ca) + 3abc$.
$= 27m^3 - 9m(ab+bc+ca) + 3abc$.

googledeepthinkmathraw thoughtschain of thoughtdiophantine