Our Aim

We aim to offer the opportunity to challenge yourself and learn. To achieve this, we create interactive puzzles where you can verify your answers before seeing a solution and explanation. We also post articles explaining various interesting models and issues in applied mathematics.

The articles follow areas of our own interest predominantly in machine learning with a particular focus on the fundamentals of probabilistic modelling, deep learning and reinforcement learning.

The puzzles have been created to offer a challenge with inspiration drawn from areas including Economics, Finance, Computer Science, Logic and mathematics. However, there is no assumed knowledge. For SolveSmart curiosity, perseverance and ingenuity are all you need.


Our articles are designed to have a similar style to the popular blog posts of leading research labs such as OpenAI, DeepMind and Berkeley Artificial Intelligence Research (BAIR). We aim to provide informative, entertaining and accessible articles which are built on sound research and the real-world experience of the author. These articles will be updated through time and in some cases will act as a survey of particular areas and in other cases will act as a deep dive into the inner workings of areas of interest.

We are building our library of articles over time to ultimately form a useful reference for anyone interested in applied mathematics and machine learning. We started out with a map of machine learning and will aim to cover a wide range of topics at sufficient level to then delve deeper on your own. In cases where we have the expertise and interest, we will provide our own deep dives.

Our particular areas of interest include probabilistic learning, game theory, reinforcement learning, multi-agent systems, deep learning and microeconomics. These themes will be considered more deeply when they arise. Where we can, we will provide example code to accompany any blog posts to support reproducing and expanding on our work.


Under puzzles you can find a selection of mathematical challenges and brainteasers designed to entertain and educate. All puzzles have detailed explanations and solutions provided (including python code in many cases). The puzzles are inspired by real life challenges, academic papers and classic logic puzzles. Please share the puzzles with like-minded friends being sure to cite this website in the spirit of the problems' academic origins.

We provide solutions to enable different uses of the website. Should you want to simply learn and read on the commute then show the solutions and read on. However, if you are looking for a challenge or preparing for technical problem-solving interviews then have a go at solving the puzzles and check your answers. We do not assume that our solutions are perfect so if you spot any errors or potential for improvement then please get in touch.

Who are we?

At present this entire website from the name, the concepts and the content (down to the logo) has been produced by Ian Davies. You may note however that throughout the website we refer to "we". This is aimed to encourage inclusiveness and openness to collaboration. While this is a portfolio of work, we are open to submissions of possible challenges and articles to include and will help anyone with an interesting article to prepare it for publication here.

Ian Davies is a Machine Learning Research Engineer with an academic background in Economics, Mathematics and Computer Science.

Other References

Wherever possible we will link to relevant external sources from our articles and puzzles. Below is a list of many popular websites which may be useful more generally for your own reference (in no particular order).