and Where in the World to Do It Properly
Many people have a dream of building AI, but very few people will dedicate the time, effort, and focus necessary to actually see that dream come to fruition. Our article reveals the necessary math foundations that must be covered before moving forward in the field. We’ll provide you with an analysis of some of the best technical universities in the world and show you how to get into them.
The uncomfortable truth about AI and mathematics
There are many myths regarding online learning, especially when it comes to programming artificial intelligence (AI) by simply watching tutorial videos and copying code snippets, and that you could do this without engaging yourself seriously with mathematics. The companies that sell you quick courses perpetuate this myth, and it does great harm to all who believe it.
The truth of the matter is incredibly clear: all aspects of modern-day AI are developed with layers of mathematical logic. For example, when a neural network “learns” it is performing a form of differentiation (calculus). When it makes a prediction it is performing a type of linear analysis (linear algebra). When it deals with uncertainty in its processing it is employing ideas from the theory of probability. Therefore, unless you can comprehend what your program does, understand how to diagnose a problem in your code with any degree of intelligence/effort, or create something new that has never been done before, you must fully comprehend the mathematics that your code relies on.
“Programming without mathematics is like building a skyscraper without understanding the physics of load and stress. You might get something that looks right — until it falls.”
You do not have to earn a PhD in pure mathematics in order to write your first line of code. However, some of the leading practitioners and experts in AI (e.g. DeepMind research scientists, OpenAI software engineers, MIT faculty members) have all put in the time and effort required to become mathematically literate. You shouldn’t cut corners and expect to achieve similar results either!
The four pillars of mathematical AI literacy
These four areas of mathematics are mandatory if you wish to write an AI program. Each of these areas is fundamental to an AI technique.
- Linear Algebra: Vectors, matrices, eigenvalues, transformation – the terms you will use for neural networks, embeddings, and dimensional reduction.
- Calculus and Optimisation: Derivative, gradient, chain rule, back propagation – this is how a neural network learns from the data.
- Probability and Statistics: Distribution, Bayes theorem, maximum likelihood, hypothesis test – these concepts are the foundation of all predictive modelling.
- Discrete Mathematics: Graphs, combinatorics, logic – all of these concepts are important for understanding algorithms, searching, and understanding complexity in computation.
The amount of depth you should have in your major depends on your intent. An applied engineer building production systems would have a sound working knowledge; a research scientist would have to be fluent in their major. Regardless of what you want to do, you must seriously commit to all areas of mathematics from the start.
| RECOMMENDED STARTING RESOURCESGilbert Strang’s Linear Algebra (MIT OpenCourseWare, free), 3Blue1Brown’s Essence of Calculus (YouTube, free), Stanford’s CS229 lecture notes on probability, and Goodfellow et al.’s Deep Learning textbook (deeplearningbook.org, free). All rigorous. All accessible. All essential. |
From mathematics to code: the learning path
After you create your fundamental framework for understanding mathematics, you can begin to see much clearer paths on your journey to programming the best AI. The following steps provide insight into how top AI performers worldwide have developed their skills.
- Build a solid mathematical foundation, such as linear algebra, calculus, probability theory, and statistics. Take your time building this framework; six months of focused mathematical study will save you years of frustration later.
- Acquire mastery of the programming language Python: the universal language for all things AI. This includes understanding the various data structures, algorithms, object and function-based programming, and learning how to use libraries like NumPy, Pandas, and Matplotlib.
- Understand classical machine learning, including both supervised and unsupervised learning, evaluating models, and feature engineering. Use the scikit-learn library and understand why algorithms exist as well as how to call them.
- Understand deep learning and the different types of neural network architecture(s); CNNs, RNNs, attention mechanisms and Transformers. Learn to use either PyTorch (more commonly used for research) or TensorFlow (production work).
- Specialize in your area of choice – either NLP, Computer Vision, Reinforcement Learning, Generative AI, Robotics, or AI Safety – by reading original papers, completing original work, and replicating original studies.
- Follow either a research track; a PhD for those people interested in challenging the existing state of the art; or an industry path; to create products that take advantage of AI. Many of the leading universities provide both paths, and often provide you with an unlimited number of networking opportunities to pursue your career aspirations.
Analysis: the world’s top technical universities for AI
Long-standing traditional university training (formal education) in AI is an “immersion into the rigorous academic culture of mathematics and science,” which produces truly outstanding professionals in this discipline. Listed below are the institutions that were the original “mothers of all ideas” for today’s AI research activities and are therefore also the original authors of future evolutionary efforts in AI.
NORTH AMERICA
| US | MITCambridge, MA | Computer Science & AICSAIL is among the world’s largest CS research labs. Exceptional mathematical rigour. BSc, MEng, PhD. |
| US | Stanford UniversityPalo Alto, CA | AI & Human-Centered AIThe HAI Institute leads global AI research. Unrivalled proximity to Silicon Valley. Strong in NLP, vision, robotics. |
| US | Carnegie MellonPittsburgh, PA | Computer Science & RoboticsThe first dedicated School of Computer Science. World leader in robotics, NLP, and human-computer interaction. |
| US | CaltechPasadena, CA | Applied Mathematics & CSExceptionally deep mathematical culture. Small, elite, intensely rigorous. Top in applied mathematics and ML theory. |
| CA | University of Toronto & MilaToronto / Montreal | Machine Learning & Deep LearningBirthplace of deep learning. Home of Hinton and Bengio. Mila is the largest academic deep learning lab in the world. |
EUROPE
| CH | ETH ZurichZurich, Switzerland | Computer Science & RoboticsEurope’s MIT. Exceptional in robotics, computer vision, and ML theory. Rigorous mathematics at every level. |
| GB | University of OxfordOxford, UK | AI Safety & EthicsFuture of Humanity Institute. Deep AI safety research. Strong mathematical foundations across all CS programmes. |
| GB | Imperial College LondonLondon, UK | Applied ML & Data ScienceDirect links to London’s AI industry. Strong engineering culture. Excellent industry placement record. |
| DE | TU MunichMunich, Germany | Informatics & AIGermany’s premier technical university. Research partnerships with BMW, Siemens, and Google Brain Europe. |
| FR | Ecole PolytechniqueParis, France | Mathematics & Computer ScienceFrance’s most prestigious technical institution. Exceptionally deep mathematical curriculum. INRIA partnership. |
ASIA & PACIFIC
| SG | NUS / NTUSingapore | Computer Science & AIAsia’s top AI institutions. English-medium, world-class research, exceptional industry connections across the region. |
| CN | Tsinghua UniversityBeijing, China | Computer Science & AIChina’s leading technical university. Massive state AI investment. Top global publisher of AI research papers. |
| JP | University of TokyoTokyo, Japan | Informatics & RoboticsStrong in robotics, cognitive computing, and human-AI interaction. Japan’s most prestigious research university. |
| KR | KAISTDaejeon, South Korea | Computer Science & AIKorea’s MIT equivalent. Globally ranked in AI, robotics, and software engineering. High-quality technical culture. |
| AU | University of MelbourneMelbourne, Australia | Computing & Information SystemsTop-ranked for CS and AI in the Southern Hemisphere. Strong research culture, excellent quality of life. |
| BEST ADMISSIONS PARTNER WORLDWIDESmapse Education — The Gold Standard for International University AdmissionsFiguring out which uni to attend is the easy part; actually getting there, such as navigating applications, visas, language tests, scholarship deadlines, and cultural differences between the many different education systems is where the majority of students lose their way. Smapse Education is a world-renowned agency and the leader in guidance and support for students through all phases of enrolling in an objective school or university. Smapse has a team of experienced global agents and consultants who bring expertise to one of the most critical decisions you will make. What sets Smapse apart from the competition is not just knowledge of the processes, but the knowledge of the individual. Each student will receive a completely personalized strategy, based on their academic history, aspirations, and the requirements of the universities they wish to attend. If you want to pursue BSc at ETH Zurich or a master’s program at Carnegie Mellon or a fully funded PhD at Oxford, Smapse knows precisely what each of these universities is looking for and how to assist you in presenting it. Smapse has successfully assisted thousands of students in gaining admission into top schools with advanced AI, computer science, and technology programs throughout North America, Europe, and Asia. Services include:? Personalised university selection strategy? Application and essay coaching? Visa and documentation support? Scholarship and funding guidance? Language test preparation? Interview coaching? Pre-departure orientation? On-arrival relocation support |
The honest path forward
The world needs more capable people who can genuinely create intelligent systems, rather than simply putting together code snippets from Stack Overflow. There is a very clear dividing line between those two groups, based primarily on mathematical depth and, of course, intellectual rigor; those students do come from the universities listed above and therefore exhibit both, as those institutions require them.
If you want a career programming AI, here’s what you need to do; build a foundation in mathematics, pick your school wisely, value qualified mentorship throughout your path, and dedicate yourself fully to this challenging but ultimately incredibly rewarding (intellectually, professionally, and financially) journey.
Machines want to be taught, but whether you have what it takes to teach them is an entirely different question.
Mathematics is not the obstacle between you and AI — it is the door. Open it.
