The first step is to solve the math problems. The solutions are shown in this PDF.
As noted in the above document, each problem involves a theorem or other mathematical concept which is named after a mathematician. There are 14 such mathematicians, each associated with a pair of problems. As clued by the flavortext, the two answers for each pair should be added together, giving a sum which can be indexed into the alphabet to get a letter. Within each pair of problems, one problem assigns a variable letter between A and N to the value it asks for, and the pairs can be ordered in this way.
Thus, we get the following extracted letters:
| Variable Letter | Mathematician | Problem #’s | Answers and Sum | Extracted Letter |
|---|---|---|---|---|
| A | Minkowski | 5, 14 | 2+1=3 | C |
| B | Gauss | 12, 21 | 3+6=9 | I |
| C | Weierstrass | 4, 6 | 3+15=18 | R |
| D | Euclid | 10, 27 | 2+1=3 | C |
| E | Euler | 15, 25 | 13+(-1)=12 | L |
| F | Cauchy | 2, 17 | 3+2=5 | E |
| G | Abel | 1, 19 | 1+2=3 | C |
| H | Lagrange | 18, 23 | 7+8=15 | O |
| I | Fermat | 3, 28 | 2+12=14 | N |
| J | Legendre | 13, 20 | 1+18=19 | S |
| K | Frobenius | 8, 9 | 5+15+20 | T |
| L | Riemann | 22, 24 | -12+13=1 | A |
| M | Dedekind | 11, 16 | 6+8=14 | N |
| N | Cayley | 7, 26 | 4+16=20 | T |
This gives the cluephrase CIRCLE CONSTANT, which clues the final answer, PI.
This was one of my earliest puzzle ideas for Mystery Hunt, and I made a prototype of it for our internal puzzle potluck. With the theme of overloaded mathematical names, I was deciding between math concepts named for mathematicians and those named for regular English words (e.g., normal, simple, or regular). I eventually decided that the former was more interesting, since there were more options.
I really enjoyed studying math during my undergrad. However, I haven’t had much time to do it in recent years, which is why I was glad to be able to write this puzzle. Typing up the problems and solutions in LaTeX was a nostalgic throwback to when I typed up my math homework back in college. In fact, I typed up some of this puzzle’s content in the same college library that I frequented all those years ago.
It was probably clear from the distribution of problems that I prefer and have more experience with algebra compared to analysis. Dummit and Foote was one of my favorite math textbooks, and I once went through all of its chapters. I apologize to those who would have liked more problems in analysis and other areas.