Well, this is it: the final of The Big Internet Math-Off. Just one more match stands between the two remaining competitors and their destiny: the title of World’s Most Interesting Mathematician (modulo the previously described factors of knowing me, interest in taking part, and availability in July to indulge my whimsy).

Nira Chamberlain and Matt Parker each have one pitch left to wow you and get your little grey cells a-quivering. So what have they picked? Find out below!

There’s no twist in the format for the final round, the rules are the same as always: take a look at both pitches, vote for the bit of maths that made you do the loudest “Aha!”, and if *you* know any more cool facts about either of the topics presented here, please write a comment!

So, with all that said, let’s begin the final round of **THE BIG INTERNET MATH-OFF!**

### Nira Chamberlain – Mathematical modelling

*Dr Nira Chamberlain is an applied mathematician and maths outreach expert, and Vice President, Professional Affairs and Industry at the IMA. You can find him on Twitter at @ch_nira, or at nirachamberlain.com. In round 1 he saw off James Tanton with an application of the Reynolds equation to Formula 1 cars, and then in round 2 gave us a history lesson on the black heroes of mathematics. He won an incredibly closely-fought semi-final with a video on Schelling’s model of segregation.
*

Nira has made a video about mathematical modelling.

### Matt Parker – Naively adding fractions

*Matt Parker is a standup mathematician with a lot of jobs. He’s one third of the scientific comedy group Festival of the Spoken Nerd, author of the book Things to Make and Do in the 4th Dimension, he sells mathematical toys at Maths Gear, he frequently features on Numberphile, and he does stuff for schools through Think Maths. You can find him on Twitter at @standupmaths, on YouTube, or at standupmaths.com. He got through round 1 with a pile of matchboxes that can play noughts-and-crosses, lost his sense of direction in round 2 with the projective plane, and upended the entire concept of competition in the semi-final with a pathological voting strategy that made the referee’s head hurt.*

For me, the greatest joy in Mathematics is spotting something interesting and playing with it. Even the small and near-trivial. Anything is fair-game for a bit of extra mathematical exploration.

Anyone who has taught maths has seen students try to add fractions with the naively obvious method:

\[ \frac{a}{b} + \frac{c}{d} = \frac{a+c}{b+d} \]

One day I wondered what this ‘naive fraction sum’ actually represents.

It turns out it is always a new fraction between the two fractions $a/b$ and $c/d$.

I thought that was really nice. I’m sure there is some computing etc. reason why this might be useful but I saw it as something interesting to look into. So I set about to prove it and it’s a lovely little proof (for nice, non-pathological values of $a$, $b$, $c$ and $d$).

So it’s not big or profound and it’s not a massive crowd pleaser, but I like it. Do have a play with it yourself to find a proof. Or you can watch this video of me proving it:

So, which bit of maths has tickled your fancy the most? Vote now!

**The final!**

- Nira Chamberlain with mathematical modelling (56%, 1,207 Votes)
- Matt Parker with naive fraction addition (44%, 960 Votes)

Total Voters: **2,167**

**The poll is now closed. Nira won!
**

Vote Nira

Both candidates are really good. I’m not mathmatian but as a marvel fan I love how mathmatic modelling theory was applied to black Panther armoured suit

Excellent work by all

Matt: For not too much more work, you could have shown that by iterating the naive sum, you can generate the Farey sequence. A much cooler result since you don’t merely get fractions in numerical order — you get absolutely every positive rational number, in reduced terms, and in numerical order.

Indeed! I also wanted to post a comment that the Stern-Brocot tree is very interesting and based on the “naive sum” (and the Farey sequence).

Matt, you might enjoy this paper on how naive fraction adding relates to Ford Circles, and thus to rational approximation (In Fig 1.1 on pg 2, the X position of each circle is equal to the “naive sum” of the X positions of its two tangent neighbors!).

Loved both videos! For Matt’s another way of looking at it is…

Assume $a/b < c/d$ (without loss of generality). Rearranging you get $a/c < b/d$. Add 1 to each side to get $(1+a/c) < (1+b/d)$. Now write $\frac{a+b}{c+d} = \frac{(a/b)(1+c/a)}{1+d/b}$ which is greater than $a/b$ based on the results above. Similarly $\frac{a+b}{c+d} = \frac{(c/d)(1+a/c)}{1+b/d}$ which is less than $c/d$ based on the results above :)

Isn’t a nicer proof of the fraction thing obtained by drawing a parallelogram with vertices $(0,0)$; $(a,b)$; $(c,d)$; $(a+c,b+d)$ and just observing that the diagonal from $(0,0)$ has slope in between the slopes of the sides from $(0,0)$?…

Yes

Andrew, that is stunning. I would have voted for you except…

I vibe for Nira. His model explains concepts in depth and his model is practical and can be duplicated to be used with any level.

Dr Nira Chamberlain is a great guy in Mathematics with special focus on mathematical modelling with applications in real world situations.

Aside many other recognitions, in the year 2017 Myself and Dr Nira were recognised as inspirational Mathematicians which is available at https://www.lms.ac.uk/news-entry/03102017-1422/october-black-mathematician-month or https://www.theguardian.com/science/blog/2017/oct/02/why-were-adding-black-mathematician-month-to-our-calendars.

He is someone who can’t be cheated when it comes to mathematical modelling and applications!

Love that I could try my hand at proving Matt’s assertion about fractions (& I understood Matt’s proof, plus Nathan’s and Andrew’s given here in the comments). My version used common denominator fractions. A big thank you to Matt and the other competitors for making so many of their pitches *accessible* to all!!

Really admirer both gentlemen. Their theory’s are sound my vote how ever is for Nira

I am voting for Dr Nira Chamberlain who has charisma and a large Personality

Great competition

Good luck as you deserve the award with your brilliance.

Great achievement and incentive for our future generation

And here, I thought Matt was doing this in his kitchen…

I wish to vote for Nira Chamberlain.I know nothing about Maths but thought The Black Panther was amazing

I don’t know much about Maths but I could learn it easily from Nira

I enjoyed reading candidates profile and think both are worthy champions, but, my vote goes to Nira Chamberlain.

My vote is for Nira Chamberlain. A fascinating video – fantasy related to truth.

Ive know about 30 yrs

Absolutely simplest 1-1 mapping rationals Q onto natural nos. Z+. ALT.MATH 10-MILLIONTH rational in mcdonals scheme 1987 etc. Add fractions wrong way. Nz mensa journ aug 2018 iss 556.