The Clay Institute was kind enough to compile a list of my small mathematical projects (I would like to solve at least 5 before the age of 40). David Hilbert did the same, but his list is arguably less focused.
Disclaimer: as pointed out by some keen-eyed (-minded?) visitors, the countdown should end not on the date of my 40th birthday, but rather on the date of the last Fields Medal ceremony before it (which should take place a good one year before). Thank you for bringing this to my attention, as I did intend to do most of the work in those last few months…
Because we all need to use more LaTeX symbols than we can remember… this page guesses a bunch of possible LaTeX commands when given a mouse-drawn symbol.
The following is a list of mathematics-related YouTube channels I particularly enjoy:
- 3Blue1Brown has some of the best mathematical animations I have ever seen. The content skews towards analysis but touches on other areas too.
- Numberphile is a source of hundreds of short odds-and-ends videos presented by mathematicians all around the world. They also have extended-format interviews in their podcast channel.
- standupmaths combines mathematics and humour in a humorously mathematical way.
- Graduate Mathematics provides advanced lectures in mathematics in physics.
The notes by Keith Conrad make a wonderful read, as does the rest of his personal site.
Anki is a spaced-repetition-based software aimed at self-study. It has been widely used by university students (with particular popularity among Medicine undergraduates, it appears), language learners (such as me and, statistically, probably you) and countless other curious minds. It is free (except on iPhone, with Mac still being an option), self-regulated and quite convenient – for instance, it synchronises across the various devices using the same account. You can create your own “deck” of flashcards or use one of the thousands people have shared over on the official site.
Computer-science celebrity M. Nielsen makes here a more convincing case for the system than I could ever hope to. Nonetheless, as a frequent user myself, I cannot recommend it enough. In addition to relying on it for language learning, I am in the long-term process of building (and studying) a mathematical deck with concepts close to my research: Iwasawa modules, homological algebra, algebraic number theory, etc.
Some of my hobbies include languages, guitar, board games and volleyball. I am quite computer-oriented (I double-majored in Mathematics and Computer Engineering) and love creating small digital projects, whether they involve programming, web design, audio/video/image edition, etc. I have lived in Spain, Sweden and Germany and have close personal ties to Poland.
At the mountain range of El Bierzo in the Camino de Santiago