F. Duncan M. Haldane's speech at the Nobel Banquet, 10 December 2016.

*Your Majesties, Your Royal Highnesses, Excellences, Dear Laureates, Ladies and Gentlemen:*

On behalf of David Thouless, Michael Kosterlitz, and myself, I would like to thank Your Majesties, the Nobel Foundation, and the Royal Swedish Academy of Sciences for honoring our early work on "Topological Phase Transitions" and "Topological Phases of Matter".

The Nobel committee have said that

*"This year's Laureates opened the door on an unknown world where matter can assume strange states."*

And they end by saying that

*"Current research is revealing the secrets of matter in the exotic worlds discovered by this year's Nobel Laureates."*

This last sentence is the key to understanding when and why this prize was awarded. Though this work has had important applications that do not involve quantum mechanics, the major recent applications have been to what has been called *"topological quantum matter"*.

As that *other* Professor Hansson of the Royal Swedish Academy of Sciences explained at the prize announcement, topology allows one to count the number of holes in a Swedish pretzel using a wonderful mathematical formula due to Gauss, (as an alternative to the rather banal method of just looking at it).

These words "*topological quantum matter*" combine the elegant mathematics of topology, with the word "*quantum"* that evokes the mysteries of quantum mechanics, and the deeply practical word "*matter*", out of which we are made, as are our treasured new smartphones.

Quantum mechanics is notoriously difficult to explain to the general public. Even the physics community, who have understood the laws of quantum mechanics for nearly a century, were initially surprised by what our research revealed. And when others built upon the foundations we helped to lay, even more unexpected results emerged.

Just knowing the correct laws of quantum mechanics does __no____t__ mean that one understands all the strange phenomena that it allows. What ** has** been learned is that it can do "

I am amazed at how this new field of topological matter seems to have excited and inspired a whole generation of young physicists in many different subfields.

I think I also speak for my co-Laureates when I say that just to have participated in changing the way people think about physics in our field would have been reward enough, but of course we are thrilled by today's award! And more exciting developments are sure to come!

Finally, not to be outdone by Professor Hans Hanson, I will leave you with a metaphor to explain how weird topological matter can be: while there are clear differences between American football and the other varieties, their balls have the ** same** topology. Now just imagine how strange these games would become if the ball was replaced by a large leather bagel!

Copyright © The Nobel Foundation 2016

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