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$${d}_{1}=\begin{array}{c}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\end{array}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{d}_{2}=\begin{array}{c}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\end{array}$$
SONIC PICTURE credit: By Belinda Hankins Miller from U.S.A. [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0) or CC BY 2.0 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons, from
https://commons.wikimedia.org/wiki/File:Sonic_Drive_in.jpg

https://www.youtube.com/watch?v=b6pomaq30Gg

When I started my PhD I had to take a qualifying exam in algebra
and I learned for the first time, what minus really means in math.
In math, -5 is the thing that you add to 5 to get 0.

$$\begin{array}{c}{\scriptscriptstyle -5+5=0}\end{array}$$

just like antimatter is the thing that you add to matter to get zilch

$$\begin{array}{c}{\scriptscriptstyle \left(-\mathrm{matter}\right)+\mathrm{matter}=0}\end{array}$$

just like antimother is the thing that you add to mother to make mother VANISH

$$\begin{array}{c}{\scriptscriptstyle \left(-\mathrm{mother}\right)+\mathrm{mother}=0}\end{array}$$

and -(-5) is the thing that you add to -5 to get 0.

$$\begin{array}{c}{\scriptscriptstyle -\left(-5\right)+\left(-5\right)=0}\end{array}$$

and that is why -(-5) has to be 5, because 5+(-5)=0.

Persi Diaconis is a famous and inspiring scientist, has been a great influence and mentor, and most important of all to me, a wonderful friend for more than 20 years.

"What do you want to know characters of the Brauer algebra for?"

"What do you want to know this character of the Brauer algebra for?"

You know they're wrong, but it doesn't hurt that they think so.

You know that they are wrong, but that you CAN LEARN to, when you want to.

You know that you're not really qualified, but that YOU LEARN fast, and you'll probably do just as well as anyone else that they could hire.

The secret is, ... push, ... but don't push too hard all at once or you'll break the hinges and fall flat on your face when it falls in, ... so push just a bit firmly, and don't give up. The door doesn't open right away, but it will if you keep focused and keep working on it.

This was a 45min talk as a concluding speaker at the Strengthening Engagement and Achievement in Mathematics and Science (SEAMS) program for year 11 High School students that was held at the University of Melbourne for three days 3-5 July.