The complete map

The course in eight formulas

Each formula comes from a lesson; here they are simply gathered so you can see the thread.

1. A model and its error (lesson 3). A line predicts $\hat y = wx + b$, and the loss is the average of the squared errors: $L = \frac{1}{n}\sum_i (y_i - \hat y_i)^2$.
2. Gradient descent (lesson 4): $w \leftarrow w - \eta \, \frac{\partial L}{\partial w}$.
3. The neuron (lesson 5): $y = f(w_1x_1 + w_2x_2 + b)$, with $f$ an activation (step, sigmoid, ReLU).
4. Backpropagation (lesson 8): the chain rule, $\frac{\partial L}{\partial w} = \frac{\partial L}{\partial y}\,\frac{\partial y}{\partial z}\,\frac{\partial z}{\partial w}$, applied from the output back to the input.
5. Next piece and attention (lessons 19 and 21): $p_i = \frac{e^{z_i/T}}{\sum_j e^{z_j/T}}$ and $\text{softmax}\!\left(QK^\top/\sqrt{d}\right)V$.
6. Scale (lessons 24 and 25): training compute $C \approx 6ND$ (parameters times tokens) and memory $\approx$ parameters × bytes per parameter.
7. The cost of an answer (lesson 26): input × its price + output × its price.
8. Using it with judgment (lessons 32, 34, and 35): a chain of $n$ steps, each going right with probability $p$, succeeds end to end with $p^n$; a score’s margin shrinks like $1/\sqrt{n}$ cases; risk is $R = P \times I$.

The ten questions, and what counts as a good answer

#	Question	Lessons	Good answer	Red flag
1	Why AI and not written rules?	1	The rule is hard to write, there are examples with answers, and errors are tolerable	“Because everyone is using AI”
2	What data trained it, with what permission?	1, 23	Documented sources, licenses, and knowledge cutoff	“It’s confidential,” full stop
3	How often is it right on my unseen cases?	10, 34	A figure measured on your unseen cases, with its margin	Only a public benchmark or a demo
4	How does it fail, and how will I notice?	33	A measured error rate, types of error, and how they are checked	“It doesn’t make mistakes”
5	Where does what it says come from?	23, 31	It cites sources you can check and states its knowledge cutoff	Unsourced answers about your data or recent events
6	What does each full task cost?	20, 26, 30	A breakdown in input and output tokens per type of task	A “per user” price with no volume or tokens
7	Where does my data go?	30, 35	Where it is stored, for how long, and whether it is used for training, in the contract	“It’s safe,” with no contract
8	What can it do alone, and who approves?	32, 35	Minimal permissions, a log of every action, and human approval before anything irreversible	Full access “so it can be useful”
9	Does it work equally well for everyone?	34, 35	Error measured by group of people	Only the average
10	Who answers for it when it fails?	33, 35	An owner with a name, an incident log, and a way to correct things	“It’s the model’s fault”

The timeline, with its sources

McCulloch and Pitts (1943), the all-or-nothing neuron; Rosenblatt (1958), the perceptron; Samuel (1959), checkers that learns; Minsky and Papert (1969), Perceptrons; Rumelhart, Hinton, and Williams (1986), backpropagation; Hochreiter and Schmidhuber (1997), LSTM; Krizhevsky, Sutskever, and Hinton (2012), AlexNet; Mikolov and colleagues (2013), word2vec; Goodfellow and colleagues (2014), GANs; Vaswani and colleagues (2017), the transformer; Brown and colleagues (2020), GPT-3; Stability AI (August 22, 2022), Stable Diffusion; OpenAI (November 30, 2022), ChatGPT; OpenAI (September 12, 2024), o1; Anthropic (November 25, 2024), MCP. Each date was verified in the lesson that tells it. The choice of milestones is this course’s: there are many others (Bahdanau and colleagues’ attention in 2014, ResNet in 2015, Ho and colleagues’ diffusion in 2020, RAG in 2020, CLIP in 2021).

In code

import math

# 1) lessons 3 and 4: fit y = w·x with gradient descent
xs, ys = [1, 2, 3, 4], [2.1, 3.9, 6.2, 7.8]
w, eta = 0.0, 0.01
for step in range(200):
    grad = sum(2 * (w * x - y) * x for x, y in zip(xs, ys)) / len(xs)
    w -= eta * grad
print(round(w, 3))

# 2) lesson 19: from scores to probabilities with softmax
def softmax(z, T=1.0):
    e = [math.exp(v / T) for v in z]
    s = sum(e)
    return [round(v / s, 3) for v in e]
print(softmax([2.0, 1.0, 0.1]))

# 3) lesson 32: ten steps that each go right 95% of the time
print(round(0.95 ** 10, 3))

# 4) this lesson: how the timeline’s milestones are spread out
milestones = [1943, 1958, 1959, 1969, 1986, 1997, 2012, 2013, 2014, 2017, 2020, 2022, 2024]
before = [a for a in milestones if a < 2012]
print(2012 - 1943, len(before), 2026 - 2012, len(milestones) - len(before))

Output:

1.99
[0.659, 0.242, 0.099]
0.599
69 6 14 7

What comes next

There is no lesson thirty-eight. What follows is up to you: come back to the map when something isn’t clear, read an original source, and test whatever you use with your own cases.