Frequently Asked Questions

Hi, this is Tiago here. I created this page so that people can find out more about what got me interested in mathematics and why I love mathematics proofs. On this page there are also tips about how to navigate more efficiently. Enjoy reading!

What got you into mathematics?

Well, when I was at school (at the age of 16) – I was already OK with numbers. I managed to get a GCSE B grade in maths. I’d say I was always naturally good at it – but because I was pursuing a football career, it wasn’t something I cared about much. Teachers used to complain about my lack of effort in studying the subject.

I only started to take mathematics seriously in my mid 20’s, when I was almost certain I wasn’t going to become a footballer. I knew that to safeguard my future (job wise) I’d have to study a very technical subject – hence I decided to work towards obtaining A Level mathematics qualifications.  Many people told me (including my younger brother who became an accountant) that I could get virtually any top job with advanced mathematics skills. I think that had I not been given this advice, I wouldn’t be here today with a Pure Mathematics A Level certificate in my hands. I’m very fortunate I was guided down this path.

What made you become so interested in mathematics proofs?

When I was in college doing my maths A Levels (back in 2013) I’d ask my teacher why certain formulas / equations were true and where they originated from. He couldn’t answer these types of questions and that made me really annoyed, so I decided to search for answers to these questions myself.

One of the first proofs I found was related to Pythagoras’ theorem. Its beauty and logical precision astounded me. When I figured out how to derive Pythagoras’ famous theorem from scratch, I felt absolutely euphoric. The realisation that I could reach such profound and rigorous mathematical conclusions just by manipulating algebraic expressions (derived by thinking / conceptualising)  – was life transforming. It completely shattered my old beliefs about what should be considered ‘true’. I think it was this ‘eureka’ moment which inspired me to search for more mathematics proofs. Somewhere along this journey or quest, finding proofs became an addiction and my own brand of escapism. I was just hooked.

Why should people learn mathematics proofs?

To me, there are 3 obvious reasons (well, at least in my own mind) why people should learn mathematics proofs:

  1. This endeavour will help you get used to thinking more logically / coherently. People who study mathematics proofs tend to be good at breaking problems down into parts and solving them step by step.
  2.  I’m a believer that mathematical truths are the only truths that exist. If something can’t be proven mathematically, then it’s probably just an idea, opinion or perspective. I think that learning mathematics proofs will encourage you assess truth claims more rigorously and with plenty of scepticism, just like an established scientist. Remember, it’s the mathematics used to describe the physical laws in our universe that help us put aeroplanes in the sky, not ideas, opinions and perspectives. You can’t develop advanced technology based on your beliefs or personal views about the universe.
  3. Those ‘eureka’ moments you get to experience… When you discover why a certain formula / equation is true… When all the pieces of the puzzle come together and the picture is complete… That moment when everything just clicks.

I could come up with plenty of other reasons why one should learn mathematics proofs, but I don’t want to bore my readers! Also, 3 reasons sounds better than 14 reasons, no?

"In the mathematics I can report no deficience, except it be that men do not sufficiently understand this excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures, so in the mathematics that use which is collateral and intervenient is no less worthy than that which is principal and intended." - Sir Francis Bacon

What makes so different to the other mathematics websites on the internet?

Most websites out there teach you how to solve mathematics problems… They show you which equations / formulas to use – depending on the problem you have to solve… You then get these equations / formulas and plug numbers into them in order to come up with solutions / results. Here on, things are completely different. Here we just want to show you proofs… Why certain equations / formulas are true and why they work. We aren’t really concerned about helping students solve problems. There are already plenty of teachers out there that do this… Plenty of websites teaching the same thing. Plenty of Youtube channels that help you solve maths problems. is supposed to be unique; the first of its kind. Oh and by the way, it isn’t littered with advertisements!

What’s the best way for people / students to navigate

I’d say visit the site tags page. There you can find links to posts about various mathematical topics. It’s the first place I go to when I’m looking for something specific on my site. If you want to watch mathematics proofs videos, then just head over to ‘videos playlists‘ or ‘all Youtube videos‘. For articles, go to ‘navigation (page by page)‘ or ‘all posts (archives)‘. If you still can’t find what you’re looking for, use the search bar or visit the site map.

Where do you want to take this project? What are your plans for the future?

I just want to continue providing GCSE and A Level students (based in the UK), plus students around the world,  with mathematics proofs and tips. I’ll soon be adding Further Pure Mathematics proofs to this website – and also to my Youtube channel. Let’s see what happens… Perhaps this project will transform into something really big and popular? Who knows? I don’t want to make any predictions about the future because in life, anything can happen. Right now, I’m just trying to live in the present moment. I don’t really want to try to see beyond it.

Page last updated: 13/02/2019 @23:19 hrs (UK Time)

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GCSE + A Level Mathematics Proofs, Videos and Tutorials.