The long view
Every product on this radar rests on maths written decades before the hardware existed to run it. Trace three lineages — AI, quantum computing and robotics — who wrote which formula, and what it powers today, then switch to the forward view.
1943 — 1959
Before there was a chip fast enough to matter, the maths was already written: artificial neurons, information theory, the learning rule and the question of whether a machine could think.
Warren McCulloch & Walter Pitts · University of Chicago
The first mathematical model of a neuron: weighted inputs summed against a threshold. Every artificial neuron since is a descendant of this one line of algebra.
y = 1 if Σ wᵢxᵢ ≥ θ, else 0
Threshold logic unit
Claude Shannon · Bell Labs
Information theory defined entropy — the amount of surprise in a message. Language models are trained by minimising exactly this quantity, token after token.
H(X) = −Σ p(x) log p(x)
Shannon entropy — the ancestor of cross-entropy loss
W. Grey Walter · Burden Neurological Institute, Bristol
Two analogue 'tortoises' with a light sensor, a touch sensor and two valves produced startlingly lifelike behaviour — the first demonstration that autonomy can emerge from very little computation.
Donald Hebb · McGill University
A biological account of how synapses strengthen with correlated activity. It gave machine learning its central idea: adjust the weight, not the wiring.
Δwᵢⱼ = η · xᵢ · xⱼ
Alan Turing · University of Manchester
Turing replaced 'can machines think?' with an operational game of imitation, and predicted learning machines trained like children rather than programmed like clocks.
John McCarthy, Marvin Minsky, Nathaniel Rochester, Claude Shannon · Dartmouth College
The proposal that coined 'artificial intelligence' and set the agenda: language, abstraction, self-improvement. It budgeted two months for problems still open seventy years later.
Frank Rosenblatt · Cornell Aeronautical Laboratory
Hardware that adjusted potentiometers until it classified images correctly. The learning rule below is gradient descent's direct ancestor.
wᵢ ← wᵢ + η(t − y)xᵢ
Perceptron update rule
1960 — 1985
Logic, search and expert systems dominated. Two funding winters followed over-promised results — the discipline learned that reasoning by hand-written rules does not scale.
George Devol & Joseph Engelberger · General Motors, Ewing Township
A 4,000-pound programmable arm stacking die-cast parts. It created the industrial robotics industry and the economics — payback in labour hours — that humanoid vendors still pitch today.
Lotfi Zadeh · UC Berkeley
Membership as a degree between 0 and 1 rather than a hard yes/no. Berkeley’s answer to the brittleness of symbolic logic, and the ancestor of every soft, probabilistic decision boundary.
μ_A: X → [0, 1]
Graded membership instead of {0,1}
Joseph Weizenbaum · MIT
200 lines of pattern matching convinced people they were being understood. Weizenbaum spent the rest of his life warning about what he had discovered: the 'ELIZA effect'.
Marvin Minsky & Seymour Papert · MIT
Proved a single-layer perceptron cannot learn XOR. Correct maths, catastrophic reception: neural network funding collapsed for over a decade.
Nils Nilsson, Charles Rosen et al. · SRI International
The first robot to reason about its own actions. Shakey's planner produced STRIPS and the A* search algorithm — both still running inside logistics and game engines.
f(n) = g(n) + h(n)
A* — cost so far plus admissible heuristic
Seppo Linnainmaa · University of Helsinki
The efficient chain rule for nested functions — published fifteen years before anyone applied it to neural networks. It is the literal engine inside PyTorch and JAX.
∂L/∂wᵢ = Σ (∂L/∂zⱼ)(∂zⱼ/∂wᵢ)
John McDermott, Edward Shortliffe et al. · CMU / Stanford
Rule engines that encoded specialists' knowledge and saved DEC millions a year. They also proved that hand-written rules rot — the maintenance cost triggered the second winter.
David Patterson & David Ditzel · UC Berkeley
Berkeley RISC argued that a small, regular instruction set beats a complex one once you let the compiler do the work. Arm, Apple silicon and every AI accelerator front-end inherit this argument.
CPU time = instructions × CPI × clock period
The iron law RISC optimises by driving CPI toward 1
Richard Feynman · Caltech / MIT keynote
Nature isn't classical, so simulating it on a classical machine costs exponentially. Feynman's answer — build the simulator out of quantum mechanics itself — is the founding argument for the whole field.
Computer Systems Research Group (Bill Joy et al.) · UC Berkeley
Berkeley Unix gave the world the socket API and a free TCP/IP stack. The permissive BSD licence and that networking code are why cloud training clusters talk to each other at all.
David Deutsch · University of Oxford
Formalised the quantum Turing machine and the idea of quantum parallelism — a register in superposition evaluates a function on every input at once, even if reading the answer out is the hard part.
|ψ⟩ = Σₓ αₓ|x⟩, Σ|αₓ|² = 1
Superposition of computational basis states
John Clarke, Michel Devoret & John Martinis · UC Berkeley
Berkeley experiments showed an entire electrical circuit can behave as a single quantum object with discrete energy levels. That result — awarded the 2025 Nobel Prize in Physics — is the physical basis of superconducting qubits.
E_J cos φ + (Q²/2C) → discrete levels |0⟩, |1⟩
The Josephson circuit as an artificial atom
1986 — 2005
Backpropagation made deep-ish networks trainable, convolutional nets read handwriting, LSTMs held memory, and statistical methods quietly took over speech and search.
David Rumelhart, Geoffrey Hinton & Ronald Williams · UC San Diego / CMU
The paper that made multi-layer networks trainable and hidden layers meaningful. Everything from GPT-5 to Midjourney is still trained this way.
θ ← θ − η ∇θ L(θ)
Gradient descent over a differentiable loss
Rodney Brooks · MIT AI Lab
Argued robots should react to the world rather than model it, layering simple competences instead of planning over a symbolic map. The split between reactive control and deliberative planning dates from here.
David Patterson, Garth Gibson & Randy Katz · UC Berkeley
Cheap commodity disks in an array beat one expensive drive on cost, throughput and reliability. The same reasoning later justified commodity GPU clusters over big iron.
MTTF_array ≈ MTTF_disk² / (N × (G−1) × MTTR)
Redundancy converts many unreliable parts into one reliable whole
Yann LeCun et al. · Bell Labs
Weight sharing and local receptive fields turned vision into a tractable learning problem. By the mid-90s LeNet was reading a large share of US bank cheques.
(f * g)(t) = Σ f(τ)g(t − τ)
Discrete convolution
Ethan Bernstein & Umesh Vazirani · UC Berkeley
Defined the universal quantum Turing machine and the class BQP, plus the first oracle separation hinting at super-polynomial speedup. Shor’s algorithm arrived a year later, building directly on it.
BPP ⊆ BQP ⊆ PSPACE
Where quantum power sits in the complexity zoo
Peter Shor · Bell Labs
Turned an abstract curiosity into a national-security concern: a large enough quantum computer breaks RSA and elliptic-curve cryptography. It is the reason post-quantum migration has a deadline.
O((log N)² (log log N)) vs classical sub-exponential
Period finding via the quantum Fourier transform
Peter Shor, then Calderbank, Steane & Kitaev
Qubits decohere in microseconds, which looked fatal. Encoding one logical qubit across nine physical ones proved errors can be corrected without measuring the state — the result the entire hardware industry is still chasing.
Stuart Russell & Peter Norvig · UC Berkeley
The rational-agent framing — an agent maximising expected utility over a perceived environment — became the shared vocabulary of the field, and the textbook of nearly every AI course since.
a* = argmax_a Σ P(s′|s,a) U(s′)
The rational agent that today’s ‘agents’ are named after
Lov Grover · Bell Labs
Unstructured search in √N steps instead of N. Modest next to Shor, but it applies to optimisation, and it set the honest expectation that most quantum speed-ups are polynomial, not magic.
O(√N) queries
Amplitude amplification
Sepp Hochreiter & Jürgen Schmidhuber · TU Munich / IDSIA
Gated memory cells solved the vanishing gradient and gave sequence models an attention span. LSTMs powered Google Translate and Siri until transformers arrived.
cₜ = fₜ ⊙ cₜ₋₁ + iₜ ⊙ c̃ₜ
Gated cell state update
IBM (Feng-hsiung Hsu, Murray Campbell et al.)
Brute-force search on custom silicon — 200 million positions per second. Not learning, but the first mainstream proof that specialised hardware changes what is possible.
Larry Page & Sergey Brin · Stanford
An eigenvector over the web's link graph. It funded the data centres, the talent and the ad revenue that later paid for deep learning research.
PR(p) = (1−d)/N + d Σ PR(q)/L(q)
2006 — 2016
GPUs plus a huge labelled dataset plus old algorithms produced a step change. Vision, speech and translation fell in under five years.
Sebastian Thrun & the Stanford Racing Team
212 km of desert, no driver. Probabilistic robotics — particle filters and learned terrain classification — beat hand-written rules, and the team went on to seed Google's self-driving programme.
NVIDIA (Ian Buck et al.)
Made graphics silicon programmable for ordinary maths. Without CUDA, the matrix multiplications behind modern models would still be running on CPUs.
Fei-Fei Li, Jia Deng et al. · Princeton / Stanford
The insight that data, not just algorithms, was the bottleneck. Crowd-sourced labelling at a scale nobody had attempted created the benchmark that started the boom.
Matei Zaharia, Ion Stoica & the AMPLab · UC Berkeley
Resilient distributed datasets kept working sets in memory across a cluster, making iterative jobs orders of magnitude faster. Most large training corpora are still cleaned and deduplicated with it.
Krste Asanović, Andrew Waterman, Yunsup Lee & David Patterson · UC Berkeley
A free, extensible ISA started as a Berkeley summer project. Custom vector and matrix extensions now sit inside AI accelerators, storage controllers and Chinese domestic silicon.
Alex Krizhevsky, Ilya Sutskever & Geoffrey Hinton · University of Toronto
A convolutional net trained on two consumer GPUs cut the ImageNet error rate by ten points overnight. Old algorithm, new hardware, big data — the recipe still in use.
ReLU: f(x) = max(0, x)
Cheap non-linearity that made depth trainable
Tomáš Mikolov et al. · Google
Words became vectors where direction carried meaning: king − man + woman ≈ queen. Every embedding, vector database and RAG pipeline descends from this.
sim(a,b) = (a·b)/(‖a‖‖b‖)
Cosine similarity over embeddings
Ian Goodfellow et al. · Université de Montréal
Two networks in a minimax game — one forges, one detects. GANs made synthetic media plausible years before diffusion made it easy.
min_G max_D 𝔼[log D(x)] + 𝔼[log(1 − D(G(z)))]
Yangqing Jia & Berkeley AI Research · UC Berkeley (BAIR)
A fast, declarative CNN framework with a model zoo of pretrained weights. It normalised the idea of downloading someone else’s network — the habit that became Hugging Face.
Kaiming He et al. · Microsoft Research Asia
Skip connections let gradients flow through 150+ layers. Residual streams are the backbone of transformers too — the idea outlived the architecture it was built for.
y = F(x, W) + x
John Schulman, Sergey Levine, Philipp Moritz, Michael Jordan & Pieter Abbeel · UC Berkeley
Constrain how far a policy may move in one update and deep reinforcement learning stops collapsing. Simplified into PPO, this is the optimiser behind RLHF in nearly every chat model.
max_θ E[ π_θ(a|s)/π_old(a|s) · Â ] s.t. KL(π_old ‖ π_θ) ≤ δ
The trust region that PPO clips instead of constrains
DeepMind (David Silver, Demis Hassabis et al.)
Deep networks plus Monte Carlo tree search plus self-play. Move 37 showed a machine producing genuinely novel strategy, not just faster search.
Sergey Levine, Chelsea Finn, Trevor Darrell & Pieter Abbeel · UC Berkeley (BAIR)
BRETT learned to fit blocks and hang hangers by mapping camera pixels straight to joint torques, with no hand-written perception stage. Every vision-language-action robot model follows this template.
π_θ: image → torques, trained jointly
No separate perception, planning and control stack
2017 — 2021
Attention replaced recurrence, scaling laws turned research into an engineering budget, and pre-trained models became general-purpose infrastructure.
Boston Dynamics
Model-predictive control plus hydraulics, later electric actuation, produced a bipedal machine that recovers from shoves and does backflips. Locomotion stopped being the hard part; deciding what to do did not.
Vaswani, Shazeer, Parmar, Uszkoreit, Jones, Gomez, Kaiser & Polosukhin · Google Brain / Google Research
Recurrence dropped, attention kept — and suddenly sequence models were fully parallel on GPUs. This single formula is the load-bearing wall of the entire current industry.
Attention(Q,K,V) = softmax(QKᵀ/√dₖ)V
Scaled dot-product attention
Philipp Moritz, Robert Nishihara, Ion Stoica & RISELab · UC Berkeley
A task and actor runtime built for reinforcement learning that became the default way to orchestrate large training and serving jobs, including OpenAI’s.
Google AI Language / OpenAI
Train once on unlabelled text, adapt cheaply to anything. The foundation-model business model — and the API pricing pages Tomorrow’s Tech tracks — starts here.
Google Quantum AI
A 53-qubit processor sampled a random circuit in 200 seconds that Google argued would take a supercomputer millennia. Contested repeatedly by classical simulation — but the era of real experimental benchmarks started here.
Jared Kaplan, Sam McCandlish et al. · OpenAI
Loss falls as a smooth power law in parameters, data and compute. Research turned into a capital allocation problem — and the reason model releases now track GPU shipments.
L(N) ≈ (Nc / N)^αN
Power-law loss versus parameter count
OpenAI
175B parameters behind a REST endpoint. Few-shot prompting replaced fine-tuning for most tasks, and an application layer of thousands of products became possible overnight.
DeepMind (John Jumper, Demis Hassabis et al.)
A 50-year-old grand challenge in biology closed by an attention-based model. The proof that these methods generalise far beyond text and images.
2022 — today
Instruction tuning turned models into products, diffusion made pixels cheap, and tool use turned chat into agents that act. This is the era Tomorrow’s Tech tracks live.
Robin Rombach, Björn Ommer et al. (CompVis) / OpenAI · LMU Munich
Denoise Gaussian noise into an image, but do it in a compressed latent space so it runs on a consumer GPU. Open weights turned image generation into a commodity within months.
xₜ₋₁ = (xₜ − εθ(xₜ,t)·βₜ) / √αₜ + σₜz
Reverse diffusion sampling step
Long Ouyang et al. · OpenAI
Human preference data turned a raw text predictor into something that follows instructions. The gap between 'model' and 'product' is mostly this step.
max_π 𝔼[r(x,y)] − β·KL(π‖π_ref)
Preference optimisation with a KL leash
OpenAI
A research preview reached 100 million users in two months. Distribution, not capability, was the breakthrough — and every segment Tomorrow’s Tech tracks was reshaped within a year.
Meta AI
Competent weights anyone could run locally reset the price floor and seeded Mistral, Qwen, DeepSeek and the whole self-hosted tooling stack.
OpenAI
Images in, expert-level exam scores out, and a long enough context to be useful in production. The moment enterprises started budgeting for AI rather than experimenting.
Google DeepMind
Fine-tuning a web-scale vision-language model to output robot actions as tokens let robots generalise to objects and instructions they were never trained on. Robotics inherits the scaling curve.
π(aₜ | oₜ, ℓ) — actions emitted as text tokens
Action as another output modality
LMSYS / Sky Computing Lab · UC Berkeley
Berkeley showed a cheap fine-tune could approach frontier quality, then built the crowdsourced Elo arena that became the industry’s de facto scoreboard for model releases.
R′ = R + K(S − E), E = 1/(1+10^((R_b−R_a)/400))
Elo, applied to blind pairwise model votes
Woosuk Kwon, Zhuohan Li, Ion Stoica et al. · UC Berkeley (Sky Computing Lab)
Treat the KV cache like virtual memory pages and serving throughput jumps several-fold at the same GPU count. It is the reason inference prices kept falling through 2024–25.
KV cache = 2 · L · H · d · tokens · bytes
Paging the term that dominates serving memory
European Union
The first comprehensive, risk-tiered AI law. Compliance obligations for general-purpose models now shape release notes, model cards and pricing tiers worldwide.
OpenAI, Kuaishou, Google DeepMind, Runway
Diffusion transformers extended to time. A segment that barely existed in 2023 became one of the fastest-moving markets on the radar.
OpenAI, DeepSeek
Spend compute at answer time, not just training time: the model thinks in tokens before replying. DeepSeek-R1 then showed it could be reproduced open-weight for a fraction of the cost.
quality ∝ log(inference compute)
A second scaling axis, alongside training compute
Google Quantum AI
The first chip where adding more physical qubits made the logical qubit better rather than worse. That crossing is the precondition for useful, fault-tolerant machines.
Λ > 1 (error suppression per code-distance step)
Below the surface-code threshold
Anthropic and the wider ecosystem
A common protocol for connecting models to tools and data turned bespoke integrations into plug-ins, and moved the competitive frontier from model quality to what the model can reach.
IBM, Quantinuum, QuEra, Microsoft, PsiQuantum
Vendors stopped quoting raw qubit counts and started quoting logical qubits, error rates and fault-tolerance dates. Neutral atoms and trapped ions became credible rivals to superconducting chips.
Figure, Tesla, Agility, Unitree, 1X
Warehouse and factory pilots, unit prices falling toward the cost of a car, and Chinese vendors undercutting Western ones by an order of magnitude. The constraint is manipulation data, not hardware.