What is the possibility of my heritage being Scottish, if my DNA is 48% Welsh?


Assuming it’s actually possible to separate Welsh DNA from Scottish or English DNA – not to mention Irish DNA – then … it’s hard to be sure.

The difficulty lies largely in determining the number of other nations – sovereign, non-sovereign, dependency, federation, territory (disputed or not). The usual figure of 193 regards the UK as one country, not 4. There’s a second figure of 250, which includes dependencies, but that still considers the UK as a single country, not 4.

So I’ll go with 300, which I freely agree is an under-estimate. Wales being one of the 300, if we subtract that we’re left with 299 other countries. Scotland is one option amongst that 299. The probability that the remaining 52% of your heritage is Scottish is therefore

p(Scottish)=1/(300–1), or 0.003.

You’re welcome!


A question for people who became a teacher as their 2nd (or 3rd, or 4th, etc.) career: Did your previous career(s) help you be a better teacher than you would have been without that previous career(s)? Or not really?

I was a research scientist who re-trained as a maths teacher.

What my 1st career gave me was the confidence to pick maths as my specialist teaching subject. Teaching is something I’d considered on and off from childhood, partly because I come from a teaching family: my mother, aunt, and several great-uncles and -aunts were all teachers. When I was at school, I LOVED maths and felt like I was pretty good at it, but somehow my grades didn’t reflect what I felt was my ability. As a result, I became disillusioned, and decided I just wasn’t that good at maths, and wound up doing a psychology degree. During that degree, I performed far better in statistics than I did on most of my psych classes. I did a MSc where I developed mathematical algorithms for locating and identifying vowel phonemes in speech. Then I did a PhD where I mathematically modelled brain function in the early visual cortex. Then I lectured in statistics at MSc and PhD level. Maths, maths, maths: enough to apply to train as a maths teacher, even though my school maths qualification was not great.

It was during this re-training that I was diagnosed as dyslexic for numerals. I mix numbers up, write them down backwards, forget them and/or the operands, etc., etc. On the other hand, I can visualise mathematical concepts like calculus or path analysis in my head. Fortunately, the diagnostic report was very detailed, virtually an instruction manual on how to avoid my specific problems, so I totally aced my teacher training.

It probably also helped that my BSc, PhD and subsequent research/lecturing gave me practice in standing in front of people and delivering seminar papers and lectures, but I’m not scared of public speaking anyway. Mostly, it gave me back my love of mathematics.

How can I like math?

You need to break the negative connection. This takes time, but one way to kickstart the break is to lie to yourself.

  • Every time you think of maths, SMILE.
  • Remember something awesome that happened to you (it doesn’t need to be related to maths)
  • When you’re brushing your teeth, look into the mirror and say “I LOVE maths”, like it’s your biggest crush.
  • Before you go into maths class, take a big deep breath and SMILE. Think of something funny – a joke, or whatever.

It sounds ridiculous, doesn’t it? How can you change your feelings just by smiling and thinking about happy things?

Actually, we don’t know whether our feelings are the result of our experiences, or if our feelings create the experiences. Say you’re in an accident, and you feel frightened. Are you feeling frightened because your heart is racing (a normal result of hormonal activity under the circumstances), or is your heart racing because you’re frightened?

Do you dislike maths because it’s hard – or is it hard because you dislike it?

If you can trick yourself into feeling happy and confident around maths, you will be much more relaxed and open to new experiences.

Happiness + Confidence = Success.


What would you do if you found a box containing answers to all six unsolved “Millennium Prize Problems”?

Before publishing and claiming my $6m, I’d probably extract, read, try to understand, and then roll around in ecstasy on the Riemann’s hypothesis proof. Because I just love me some Riemann.

Although – I might hide that proof, and not claim the $1m. The possibility of predicting primes represented by it could be the end of secure systems everywhere, and I’d rather be able to keep $5m safe than have $6m and possibly lose it all.

That, and the rolling around on it.

What is the most complicated math problem yet to be solved?

There’s a whole list

The Millennium Prize Problems are of particular interest, as there is a $1 million prize for solving each of the seven problems posed. So far, only one, the Poincaré Conjecture, has been solved.

Another interesting group of problems is Hilbert’s 24 Problems. These are problems that David Hilbert put forward as the most important unsolved problems in mathematics. There’s no prize for solving any of them.

Perhaps the most famous problem in mathematics is Fermat’s Last Theorem (FLT). Fermat wrote in the margins of a book that a^n+b^n=c^had no solutions for n>2, but that there wasn’t enough space for the solution. The formula is the general form of Pythagoras’ Theorem ( a^2+b^2=c^2), which elementary students can understand: and yet this proof eluded some of the finest mathematical minds for over 300 years! It was finally solved by Andrew Wiles, who spent 30 years working in secret on the proof (Simon Singh has written a readable and rather thrilling* book on the proof). It is, however, unlikely that Fermat’s ‘trivial’ proof was correct: some of Wiles’ methods were not available in Fermat’s time. Some have suggested that perhaps Fermat did have a simple proof: the science fiction writer, Arthur C. Clarke, wrote a novel about a mathematician who finds one.

My favourite unsolved proof is on both the Hilbert and Millennium Prize lists: Riemann’s Hypothesis. I did my pre-teacher training thesis on this hypothesis, which relates to the distribution of prime numbers. It’s mind-bendingly beautiful, it sings in eldritch tones, it’s a saraband in an alien landscape. It’s too exquisite not to be true, and too terrifying to be real. If it is ever solved, online security is potentially gone – it’s based on prime numbers. This isn’t just a problem for online banking and Paypal – it’s the whole international system used by banks to transfer funds. We might have to go back to bartering. I can recommend the books by both Karl Sabbagh and Marcus du Sautoy for introducing the hypothesis to an informed layperson.

* – For a given value of thrilling. I found it tremendously exciting, but I’m odd like that.

Briefly, what is algebra? How would you explain it to a 12-year-old child? Also, where would one be using algebra?

For a child beginning algebra, it can be useful to introduce the subject as a kind of “code”, where you can substitute numbers for the letters.

Then you can move on to constructing your own “codes” for ideas the child should already be familiar with – miles per gallon, speed/distance/time. This prepares the child for the idea that algebra can be used to create general rules that suit all situations. These can be expressed in words (speed=distance/time) or letters (s=d/t).

I’m not sure what 12yo translates to in grades or years in school. However, Khan Academy has lots of videos and tutorials suitable for people of this age, and the student can track their progress.

Is math better than language arts?

No. This kind of one-upmanship between disciplines is a handicap to both, and unworthy of either.

Mathematics is a tool and a language for elucidating and describing phenomena. It can be beautiful and thrilling in its own right.

Mathematics can help you be a better linguist, by, for example, providing you with analyses and models for syntax analysis, grammar, language origins, and so on.

Being a linguist can make you a better mathematician, because mathematics is a language. A limited, but highly precise and complete language with universal application.

Why do I understand conceptional information faster than math equations?

I can understand a concept very quickly. Usually I figure it out before a test, regardless of the fact I didn’t pay attention in class. But if its just a math equation (no concepts) I cannot do the same thing, regardless of how simple it is. Why is that? I’m in high school.

Concepts are relatively easy to form. We can tell each other stories to inform, use metaphors and analogies to explain, and use elaboration or imagery as well as narrative devices to reinforce.

A mathematical equation is a bare-bones formulation. Sometimes it’s hard to believe that our wonderful, thrilling, all singing all dancing concept can be reduced to a handful of symbols. Other times it’s unbelievable that simple concepts need such a huge plethora of symbols!

The trick is to imbue the symbols with the meanings from the concept. Some of us are better at this than others. The really good ones have an internal life that is god-like: the prologue to Ian Stewart’s Nature’s Numbers describes a Yahweh-like being issuing Genesis-style commands that create a universe. This segues into a sequence reminiscent of the virtual reality computers in Minority Report – though not without a hint of Homer Simpson’s Halloween trip to 3D-land – as the being explores and manipulates his new universe. It’s then revealed that this is an average morning’s work for a mathematician. On paper or with the help of computers, this is how they ‘see’ each problem they work on – as a miniature universe, twisting and turning on itself with every tweak of a symbol.

I’d love to be able to see that. Unfortunately, all I see is dancing.

Why Is math the number one subject hated by the students all over the world?


Because they’re told to hate it.

Almost everyone around them whines about how hard maths is, how difficult it is to understand. No one ever wants to admit they’re illiterate – it’s embarrassing not to be able to read or write – but people LAUGH! JOKE! about being innumerate! It’s not embarrassing at all to be useless at maths, it’s something people will actually come out and share with complete strangers! They’ll even make stupid, asinine excuses that they’re crap at maths because they’re “more artistic” or “more musical”.

And it’s all horseshit.

All the great artists were mathematicians. Pythagoras – remember him? “the square of the hypotenuse is equal to the sum of the squares of the other two sides” Pythagoras – he basically discovered the harmonics of Western music. Albert Einstein? As well as being a mathematical genius, he was an accomplished pianist and violinist. At mathematics conferences round the world, at the end of each day, many of the mathematicians unwind with a jam session, having brought their instruments with them.

As you are reading this post, your brain is doing Fast Fourier Transforms* just to figure out where each letter begins and ends.

If you can read the time, you can do maths.

If you can estimate how long it will take you to do a task, you can do maths.

If you can drive, cycle, or even walk upright, you can do maths.

If you can stack toy bricks, or live more or less within your means, you can do maths.

Maths is just a language that describes the world around us. It’s a lot easier than English, because so much of it – unlike English – is just common sense. It has a few rules, but they’re much more straightforward than grammar (especially English grammar…).

Stop listening to cowards and crybabies. You are a mathematician.

* – Maths that would scare the living tar out of you if you saw it written down.

How useful would being a master of mathematics be in a survival situation?

There’s two ways mathematical skills can enhance survival: practical and theoretical.

  1. Practical – The hero of The Martian spends much of the book doing calculations on metabolic rates, calories, soil density, etc., etc. Not for fun (although I enjoyed it immensely), but because he needed to work out what plants to grow, how many he could realistically grow given the resources available, how long he could potentially survive, and what his margins for error (or disaster) were. While the account is fictional, it exemplifies the kind of survival considerations in which mathematics is needed. Sure, he could just have leaped in and tried to grow apples and courgettes anywhere and everywhere, and he might even have survived – but his calculations gave him more realistic information.
  2. Theoretical – Even where there isn’t time for doing the calculations, mathematical habits of thought can inform decisions. Rick at the beginning of The Walking Dead takes FOREVER to realise what’s going on and to formulate a plan of action (hah – as if he ‘formulates’ anything. Stumbles from one disaster to another, more like). Then he wastes entire series on false equivalencies between ‘evade’ and ‘avoid’ as survival mechanisms. Then he virtually destroys a safe haven in Alexandria through a lack of cost-benefit analysis of culling the zombie horde. Now, he’s banjaxed Bayesian probabilistic modelling of his group’s interactions with the Saviors and the garbage people. If he’d listened with even one ear in maths class, he might be living safe and sound in a heuristic safe zone – but that would be boring.

Sorry, I went with fictional examples because they’re more fun than learned discourses on plotting arrow or bullet trajectories in calm and stormy conditions, or using vectors in navigating a life raft.