AI (and Robotics) From Scratch in 2026

• 10-202 Intro to Modern AI so you can modify any open source LLM as this will take off soon with new hardware. You can easily get paid insane amounts of money doing this right now.
• 10-714 DL Algorithms & Implementation teaches how to build your own PyTorch stack from scratch and trust me you want to use types and toss out Python into the dustbin of history because right now types are making agentic coding very simple to use and for AI-assisted "lightweight formal methods" to verify the code.

Almost everything in those courses is self-contained or you can ask Gemini/Grok/ChatGPTx to help you. The only math you really need is understanding the beginning of this single video Matrix Calculus from MIT's 2020 18.06 course on linear algebra which we will take here too as our first math lecture.

Does there exist a unified theory of modern AI yet or something close to it?

• These 30 Lectures were recently put together by MIT's leading Neuroscience researcher by that I mean he's the world's most cited Neuroscience researcher. He used the assistance of a research paper Agentic Investigator. Give it a research topic and it gives you back an entire paper on that topic.

These lectures show current AI provides a generic mean or 'smoothing' effect on everything it generates. The human user has to provide the sparse logical jumps to escape the annoying politeness and homogenizing of scientific thought that AI defaults to. They also show compositionality which means a complex thing is constructed of many small reusable basic things and these are (as described in the prologue) mathematically implied to be sparse for the simple reason that we can compute them efficiently. Genericity is another trait of modern AI and means a learning function being defined by any set of coordinates is invariant to transformations and defining it in different spaces where you 'shift' the function doesn't really matter. There will be many lectures about this in detail and we will take them.

AI also can't be sentient (yet) no matter what AGI marketing these companies claim. This is another theme of these lectures.

Things we have to take to understand these lectures:

• The mathematical model of Machine Learning which hasn't changed.
  • All lectures are taught by the author of the book and there's undergrad notes (MIT).
  • Some optional short lectures from the perspective of theoretical neuroscience.
  • A book Understanding Deep Learning though we will mostly only use the MIT Lectures

We will also have to incrementally take various lectures from 15-251 CMU's Great Ideas in Computer Science such as boolean functions and some complexity theory because deep learning is a deep topic touching many theoretical fields.

Throw out almost all math learned in undergrad. As per Tomaso Poggio in his 30 lectures on Deep Learning the Real Numbers don't exist. Everything must be done by numerical analysis/approximations which means no limits, no Riemann integral, no pivots or echelon forms, no inverting matrices, limited use of eigenwhatever, and exclusively using SVD factorization for linear algebra. Even gradient descent isn't really used anymore as it 'zig-zags'.

The following is very similar to CMU's Math Foundations for Robotics course as well:

• Matrix calculus
• MIT Numerical Methods and large scale linear algebra.
  • Infinitesimal calculus book
    • We will only ever use dy/dx

You can use the Agentic Investigator to help you research these fields by yourself.

Real numbers are mostly undecidable and even worse the way they are taught is over 100+ years old and obsolete. There exists a 'Natural Integral' on the real (imaginary continuum) line invented in 1960s or so that is sometimes called the gauge integral, or the Newton integral, or the Henstock-Kurzweil integral and it includes the Lebesgue integral as a special case. It is vastly more simple than Riemann limiting sum constructions. There are a few undergrad level books by analysis experts written for beginners about this such as Brian S Thomson and Andrew Bruckner written books I suggest you search for them if you want 21st century real number theory. They are called 'DRIPPED' or 'Drop the Riemann Integral'. Bruckner is still doing derivatives research in his 90s and uploading papers such as what actually characterizes the derivative? Turns out the Darboux property is still the only characteristic and there is functions that are discontinous everywhere yet still have derivatives. They also blow out Rolles' theorem and other junk you have to take in a modern calculus course in undergrad. The integral ends up being basically the mean value theorem. AI is killing this entire obsolete abstraction right now.

Real numbers have this (fake) idealized construction where compactness exists however we will learn in the deep learning lectures that basically almost every real number is undecidable so there's no actual compactness. You can approximate e, pi, phi, a very few other real numbers using a stream algorithm but the rest of them (the vast majority in fact) are not computable at all. Ergo the entire theory is just trash in 2026 and we shouldn't even bother entertaining it here.

Instead we will learn the infintesimal calculus with modern definitions though I am now denying you the satisfaction of working through an elementary text and realizing it's too easy for you which provides motivation and encouragement. I plan on using linear algebra for that. For example the David Poole book used by CMU where you will do enough applications that math undergrad problems become trivial. You need this win and I will provide it just not silly calculus that even Newton himself would object to.

TODO

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