As a 17-year old, I was whisked away from my little country town in Australia to study mathematics at the Australian National University in Canberra. Granted a marvellous scholarship, all my needs were met. Over the next ten years, with some detours along the way, all my living expenses were provided for as I proceeded to PhD level. At the age of 22 I married a woman that I met while on a bus going to Oxford who had just finished her studies at one of the London colleges. We had little money but nor had we any debt. That was 1979. In 2017, a corresponding couple will begin their lives together burdened by a joint student-related debt approaching £100,000, which they must try to repay, with interest, for most of their working lives.
It is still possible to learn mathematics to a high standard at a British university but there is no doubt that the fun and satisfaction the subject affords to those who naturally enjoy it has taken a hit. Students are constantly reminded about the lifelong debts they are incurring and how they need to be thoroughly aware of the demands of their future employers. The fretting over this within universities is relentless. To be fair, students generally report high to very high levels of satisfaction with their courses right throughout the university system. Certainly university staff are kept on their toes by being annually called to account by the National Student Survey, which is a data set that offers no hiding place. We should bear in mind, however, that this key performance indicator does not measure the extent to which students have mastered their degree subject. What is important here is getting everyone to say they are happy, which is quite another matter.
This all contrasts with the life of the main character, Sri Ramanujan in the recent film The Man Who Knew Infinity. The Indian genius of the early twentieth century had a reasonable high school education after which he was almost self-taught. It seems he got hold of a handful of British mathematics books, amongst them Synopsis of Pure Mathematics by G. S. Carr, written in 1886. I understand that this was not even a very good book in the ordinary sense for it merely listed around five thousand mathematical facts in a rather disjointed fashion with little in the way of example or proof. This compendium, however, suited the young Ramanujan perfectly for he devoured it, filling in the gaps and making new additions of his own. Through this process of learning he emerged as a master of deep and difficult aspects of mathematics, although inevitably he remained quite ignorant of some other important fields within the subject.
It would therefore be a very good thing if everyone had unfettered online access to the contents of a British general mathematics degree. Mathematics is the subject among the sciences that most lends itself to learning through books and online sources alone. There is nothing fake or phoney when it comes to maths. The content of the subject, being completely and undeniably true, does not date. Mathematics texts and lectures from many decades ago remain as valuable as ever. Indeed, older texts are often refreshing to read because they are so free from clutter. There are new developments of course but learning from high quality older material will never lead you astray.
I had thought this had already been taken care of as for ten years or more, many universities, for example MIT in the United States, have granted open online access to all their teaching materials, completely free of charge. There is no need to even register your interest — just go to their website and help yourself. Modern day Ramanujans would seem not to have a problem coming to grips with the subject.
The reality, however, is somewhat different and softer barriers remain. The attitude of these admirable institutions is relaxed but not necessarily that helpful to the private student who is left very much to their own devices. There is little guidance as to what you need to know, and what is available online depends on the decisions of individual lecturers so there is no consistency of presentation. Acquiring an overall picture of mainstream mathematics is not as straightforward as one might expect. It would be a relatively easy thing to remedy this and the rather rigid framework of British degrees could be useful. In Britain, a degree normally consists of 24 modules (eight per year), each demanding a minimum of 50 hours of study (coffee breaks not included). If we were to set up a suite of 24 modules for a general mathematics degree that met the so-called QAA Benchmark and placed the collection online for anyone on the planet to access, it would be welcomed by poor would-be mathematicians from everywhere around the globe. The simplicity and clarity of that setting would be understood and appreciated.
This modern day Ramanujan Project would require some work by the mathematical community but it would largely be a one-off task. As I have explained, the basic content of a mathematical undergraduate degree has no need to change rapidly over time for here we are talking about fundamental advanced mathematics and not cutting-edge research. Everyone, even a Ramanujan, needs to learn to walk before they can run and the helping hand we will be offering will long be remembered with gratitude and be a force for good in the world.
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