There is no denying that the Internet has created a revolution in learning. If one, moreover, focuses on subjects which by virtue of their nature are well-suited to objective assessment imparting validity to any reasonably popular article on them (among those subjects are natural sciences and mathematics), the usefulness of the web becomes nothing short of phenomenal: Instead of having to read from a limited collection of books, you are free to wander in the corridors of this imposingly large yet friendly labyrinth of knowledge, picking tomes on your subject of interest along the way.
In the case of mathematics, there is a plethora of high-level material one can study online, even without buying one of the many available seminars. All sorts of books, ranging from famous to obscure, are already in the public domain – their list always expanding – and even for more recent work there’s nothing easier than to search for free lectures provided by prestigious universities.
Regarding video material, it is interesting how in our time we have seen the rise of something analogous to the popular philosophers of old, but now slightly refurbished as popular mathematicians. On YouTube alone there are major channels dedicated to this type of promotion of mathematics, including 3Blue1Brown, Mathologer and Numberphile. One is more likely than not, to arrive at a video of interest simply by typing the subject in a browser search, thus the days of skimming through a book in a library or a bookstore, feeling unsure whether the topic you wish to know about is hiding somewhere in the pages, are long gone.
Therefore the material itself is accessible – but what about the learning process? Can such sites, videos and e‑books provide one with everything needed to learn, in the absence of a tutor? The question is very important, since it is about whether the Internet can indeed better the chances of an autodidact to both acquire knowledge and put it to use.
E‑learning as a career boost
The answer depends on how the knowledge to be acquired is to be used. While there is nothing at preventing an intelligent autodidact to comprehend fully the material he or she is exposed to online, it remains true that the lack of a formal degree will limit professional use of this knowledge. This is why a number of online seminar hosts work in conjunction with universities or other educational institutions and grant certificates to anyone attending their course. Even so, those certificates may still lack marketable value, depending on the subject of learning: While in the not very distant past, amateur mathematicians could rise to prominence – one great example would be Pierre de Fermat – nowadays this would be quite difficult to achieve! Still, it is certainly easier to market art-related skills acquired online: the majority of graphical artists and creators of computer game assets to be sold online are skilled autodidacts. Sites where one’s 2D or 3D game art can be sold include Turbosquid, Itch.io and Creative Market.
E‑learning for recreation and self-improvement
This is where online learning excels. There’s no limit to what one can learn, and no requirement in order to start learning. The non-compulsory nature (one isn’t studying for school or university) of recreational learning can lead to better results. After all, by following your passion you already possess an overabundance of incentives; all it takes is interest and will to discover more about a subject already dear to yourself. And, if one is to fail as an autodidact, it’d still be only because, somewhere along the way, their interest shifted to other subjects – with some luck, that shifting interest will already have led to self-improvement, to realizations about what you actually like. To quote the novelist, Franz Kafka: “New powers will arrive – as long as life itself continues” – likewise, new knowledge can always be gained, as long as one still feels like learning.
