AI Field Guides

Three roles, three very different relationships with the math

AI Field Guides

The same AI landscape looks completely different depending on your seat. An architect treats models as black boxes with shapes, costs and behaviors; an ML engineer opens the box and needs applied math fluency to train, tune and debug what's inside; a research scientist works where the math itself is the product. Pick your track.

How much math each role actually needs

Share of the underlying mathematics required to do the job well

AI Solution Architect system-design intuition Solution Architect — ~10% (arithmetic for budgeting and resource estimation) 10% ML Engineer applied frameworks ML Engineer — ~50% (optimization, tensor shapes, loss behaviors) 50% AI Research Scientist theoretical math Research Scientist — 100% (calculus, statistics, game theory) 100% 0 25 50 75 100%
Each track has its own guide below — from black boxes (10%) through the math under the hood (50%) to the mathematical frontier itself (100%).

Architectural Traits of AI

For Solution Architects & Product Owners — the ~10% track. Models as black boxes: which family fits which requirement, what it costs to run, and how to wire it into enterprise systems.

  • Model capabilities & selection (+ six family deep dives)
  • Operational metrics: context, latency, VRAM, evaluation
  • Integration patterns: RAG, prompting vs fine-tuning
Open the architect guide →

The ML Engineer's Math of AI

For engineers moving into ML — the ~50% track. The applied math you must actually study: what each part is, where it's used inside models and training, and how to learn it — layer by layer, deeper and deeper.

  • Linear algebra · calculus & optimization
  • Probability & statistics · losses & information theory
  • Numerics & tensor craft — plus a study roadmap
Open the engineer guide →

The Research Scientist's Math of AI

For those heading to the frontier — the 100% track. At research level the math isn't under the hood, it is the product: each mathematical field mapped to the breakthroughs it produced and what mastering it lets you do.

  • Analysis & matrix calculus · stochastic processes
  • Statistical learning theory · optimization & games
  • Information theory & the geometry of learning
Open the scientist guide →