# The Mathematics Department

After a whirlwind tour of the English department, the tour entered the Mathematics department.

Upon entering, I immediately heard some interesting conversations:

"It's like a puzzle, that game..."

"I think the key is to rationalise it, by making a recurrence..."

"You have to use Cantor's diagonal argument, and take it from there..."

I stopped, looking into the classroom they seemed to be referring to. There were many students and a couple of teachers. One of them I recognised from computer science department.

The other teacher, who I assumed was a mathematician, wrote several things on the whiteboard:

The aim of the game is to find out: WHO AM I?, from investigating WHAT AM I? in the following clues:

graph of a tetrahedron

9-sided polygon

The mathematician addressed the class, saying something along the lines of: "You'll need Morse's eye on this one." I couldn't hear well from outside the room. The mathematician started writing again:

$f$ in $f:\mathcal{A}\rightarrow\mathcal{B}$

product notation

The mathematician said somethings to the computer scientist, who took the market and wrote on the board:

ints, but with more storage

Handing the marker back, the computer scientist announced something about taking pears. The mathematician started writing again:

likelihood of an event

symbol for discrimininant

Here the mathematician stopped, and whispered something to the computer science teacher again. Looking around, I realised that the tour had gone off without me. I decided to stay put until they found me - surely someone would notice.

Taking the marker from the mathematician, the computer science teacher wrote:

ordered multiset

Then the computer science teacher handed the marker back. The mathematician continued to write more things on the board:

symbol for root of unity

process of dividing an angle into two equal parts

rhombus with equal diagonals

symbol for the golden ratio

multiply-1

property that $A\equiv B$

symbol for infintisemal

sum notation

Again, the mathematician whispered to the computer science teacher, who wrote:

linear running time

The mathematician took over again, writing:

person who the binomial triangle is named after

point on a graph

$\frac{d}{dx}f(x)$

circle excribed around a triangle

Then the mathematician asked, "Have any of you got it yet?" A student came up and whispered something into the mathematician's ear.

"That is correct. Would you like to show how you got this?" The student nodded, but just as they were about to write something on the board, I was interrupted.

"There you are! We've been looking for you. Quick, come along now, we have to hurry!" I was dragged along, but inside was burning with curiosity. What was the student going to write on the board?

Hints:

1.

As I left, I heard someone say, "They could have just used modular indexing, it would have been a lot easier..."

Again, this story is fictional. No knowledge of prior puzzles in the series is needed.

Each of the lines of text on the blackboard seems to represent a single symbol or word:

graph of a tetrahedron

$K_4$ or K4 (thanks @Volatility)

9-sided polygon

nonagon or enneagon

"Morse's eye"

"I" in Morse code is ..

$f$ in $f:\mathcal{A}\rightarrow\mathcal{B}$

function or map

product notation

$\Pi$ or Pi

ints, but with more storage


This one was written by the computer scientist, so presumably we're looking for a symbol used in computer science rather than mathematics. The correct answer is longs (thanks @Volatility).

"taking pears"

something to do with pairs

likelihood of an event

probability?

symbol for discrimininant

$\Delta$ or Delta

ordered multiset


maybe list?

symbol for root of unity

$\omega$ or omega (or maybe $\zeta$)

process of dividing an angle into two equal parts

bisection

rhombus with equal diagonals

square

symbol for the golden ratio

$\phi$ or phi

multiply-1

divide

property that $A\equiv B$

congruence or equivalence

symbol for infintisemal

$\epsilon$ or epsilon

sum notation

$\Sigma$ or Sigma

linear running time


$O(n)$ or On (thanks @Silenus)

person who the binomial triangle is named after

Pascal

point on a graph

vertex (thanks @TheGreatEscaper)

$\frac{d}{dx}f(x)$

derivative?

circle excribed around a triangle

circumcircle

Putting all of these together, we get something like:

K4 nonagon function pi longs probability Delta list omega bisection square phi divide congruence epsilon Sigma On Pascal vertex derivative circumcircle

Now, using the clues given at the very beginning about "recurrence" and "Cantor's diagonal argument", we

write these words out in order and choose the $n$th letter of the $n$th word (if it's shorter than $n$ letters, write it out multiple times until we have enough letters).

This yields:

K4
nonagon -> ö (adding Morse's eye)
function
pipipi
lo|ng|sl|on|gs (taking pairs)
probability
arrayarray
omegaomega
bisectionbisection
squaresquare
phiphiphiphi
dividedividedivide
congruencecongruence
epsilonepsilonepsilon
SigmaSigmaSigmaSigma
OnOnOnOnOnOnOnOnOnOn
PascalPascalPascalPascal
vertexvertexvertexvertex
derivativederivative
circumcirclecircumcircle