Recently, I gave some lectures based on a general-audience personal tour across four (plus one) mathematical puzzles that I encountered during my career. Here is a paper based on these lectures which is meant for a very wide audience (in English)

Puzzles on trees, high dimensions, elections, computation and noise.

A videotaped lecture is here. An earlier Hebrew version is

**חידות על עצים , ממדים גבוהים, בחירות, חישוב ורעש **

(It deals only with the first four puzzles.) A short videotaped Hebrew lecture (where I only discuss the first two puzzles and touch on the third) is here.

A drawing by my daughter Neta for puzzle number 3. (Based on a famous Florida recount picture.)

**Summary:** I will talk about some mathematical puzzles that have preoccupied me over the years, and I will also reveal to you some of the secrets of our trade. The first puzzle we shall discuss is about high-dimensional trees: what they are and how to count them. The second puzzle deals with high-dimensional geometric bodies, and a question of Borsuk. The third puzzle is about errors made when counting votes during elections, and the fourth puzzle raises the question: are quantum computers possible? I will conclude with a puzzle that I am currently thinking about: random RNA trees.

I am very curious about how accessible the paper is, and comments both on the presentation and content are most welcome. I plan to devote soon one post to a fresh look on each puzzle, and I also have posted about them in the past- Puzzle 1 (1,2,3,4,5), Puzzle2 (1,2,3), Puzzle 3 (1,2), and Puzzle 4. The fifth puzzle is closely related to TYI 29 about the diameter of various random trees. (Since writing the paper, I have learnt more about earlier relevant research.) I am also planning to write a similar but more technical version for mathematicians (perhaps for the ICM2018 Proceedings).

### A few more figures from the paper:

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