By Daniel Fryer, La Trobe University

I started studying math at 25 (in January 2013). When I was 24 I wondered what the word ‘calculus’ meant, possibly for the first time in my life. I assumed it had something to do with calculators, but I knew that Isaac Newton had discovered it some time in the 1600s. Did Newton predict calculators?

I remember learning to add fractions around April 2013. By June I reached a section of a textbook that read, “we commence with the definition of a logarithm.” I was almost embarrassingly excited. I was reading through a textbook series consisting of 9 modules that would take me from zero to hero in about 8 months (hero meaning roughly the level of knowledge in a standard year 12 maths course). I knew I was ready for the definition of the logarithm, because my course was on rails and it ran at my own pace. So, whatever the definition was, I knew I was going to be able to understand it. That’s what was so exciting: I had the time, the space, and the skills. The logarithm was a complicated mathematical construction that I had heard of but known little about, and I was about to understand it.

I still get this rush now. It is the rush of truly learning something. It is the rush of climbing a mountain, when you have a map and a compass, and all the right gear and training. I crave that rush and even sometimes feel that I live for it.

By 2014, when I started my science degree, I didn’t want to make math my main course of study. Firstly, I was pretty sure I wasn’t ‘smart’ enough to do well in math. Secondly, to me math was just a tool for studying physical phenomena; it didn’t exist for its own sake. I found out how wrong I was some time during second year. To quote Paul Lockhart in A Mathematician’s Lament:

“Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.”

At this time, I saw a new world. I had been blind to it my whole life. A world in which space could have infinitely many dimensions, where everything could have distance ‘1’ from everything else, and where seemingly simple intuitive assumptions (like the Axiom of Choice) could lead to alarming and disturbing paradoxes. It is no wonder that Lewis Carol was a mathematician.

This year, 2017, I want to reach out to others who are in a similar position to the one I was in when I was 24. People who want to know, but don’t know where to start. I want to leverage the wealth of free educational tools that exist online (places like,,,, and so on) to give interested people a chance to learn introductory math and science for free in a tutored and low-stress environment, with assistance from volunteer uni students. The project is called Science Stems. Check it out at


Daniel Fryer was one of the recipients of a 2016/17 AMSI Vacation Research Scholarship.

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