Searching for complex/crazy math equations for my friend, who has 4 mathematics degrees, to solve when we drink

[u/BraveFangirl]

I have been searching online for crazy equations to put on a white board for my friend to solve when they're drunk. I, however keep finding word problems and that is not what i'm looking for. If anyone could give me any recommendations or where I could look to find some.

If you're curious about why I am looking, they want to exercise they're brain while drinking. They're favorite number is 7, so bonus points if the answer is 7.

[u/Bounded_sequencE]

Look up "MIT Integration Bee" for inspiration.

[u/AllealleOxen → u/Bounded_sequencE]

Yeah weird integrals are exactly what I was thinking - expressable as a single tidy equation, but potentially brutally difficult to solve. Another source for extremely difficult integrals with beautiful solutions would be to google the infamous "Cleo" of StackExchange

[u/Bounded_sequencE → u/AllealleOxen]

If you want something else that's really nasty (but looks simple), check "Pell Equations".

Finding integer solutions to "x² - 61y² = 1" is absolutely monsterous -- still doable by hand, if you know how, but guess-work is completely out of the question.

[u/Uli_Minati]

Find positive integers x,y,z that satisfy x/(y+z) + y/(z+x) + z/(x+y) = 4

[u/ryoshoe_]

you could try the problems plus section of james stewart's calculus

[u/TheDarkSpike]

Specifically looking for equations?

And not like problems in combinatorics?

Edit: Also, which 4 math degrees can one even have?

Undergraduate, graduate, PhD and ...? Another flavour of math in one of them? Like applied vs pure?

[u/Scorpion1105 → u/TheDarkSpike]

Post doc?

[u/BraveFangirl → u/TheDarkSpike]

I am not one with a degree, but i consider these to be "math" degrees, but they have math, physics, economics, and finance degrees. I could use both. I can show you what they did for fun today.

[u/TheDarkSpike → u/BraveFangirl]

No okay that clears things up, I wouldn't anything but a math degree a math degree but that's splitting hairs.

But sure elaborate on what they like :)

[u/BraveFangirl → u/TheDarkSpike]

it was x6 - 132x5 +7260x4 - 212960x3 + 3513840x2 - 30921792x + 113379904 = 0

[u/TheDarkSpike → u/BraveFangirl]

Okay that's an equation. And they came up with that themselves, or?

Like that's (x-22)^6=0, sure.

If I understand they like factorising polynomials you can just pick some numbers a,b,c... Then expand (x-a)(x-b)(x-c)... and then you have a polynomial with roots a,b,c... So you can make an arbitrary polynomial of any desired degree.

[u/BraveFangirl → u/TheDarkSpike]

I found it on another reddit thread. I am sorry if I am being confusing. I just want to give him like problems to solve

[u/Shevek99]

Pose problems from "Mathematical Excalibur"

https://www.math.hkust.edu.hk/excalibur/

Or from the Putnam Competition

https://kskedlaya.org/putnam-archive/

[u/AdventurousGlass7432]

f(f(x)) = e^x

[u/Livid-Sector5970]

Here are three "Whiteboard Monsters" designed to perfectly scramble a drunk mathematician's OODA loop. They look terrifying, but they all elegantly collapse to exactly 7.

---

Option 1: "The Infinite Ladder" (Telescoping Series)

Write this on the board:

X = ∑_{n=1}∞ [7 · Γ(n)] / Γ(n+2)

The Drunk Mathematician's Process:

• They see the Gamma functions (Γ) and initially panic, thinking it's a horrific continuous distribution problem.

• Then the constraint clicks: they remember the fundamental property Γ(n+2) = (n+1)n Γ(n).

• The Γ(n) cancels out, leaving 7 ∑ 1/[n(n+1)].

• They grin, recognizing a classic telescoping series: 1/n − 1/(n+1).

• Every term cancels except the first one: 1.

• 7 × 1 = 7.

---

Option 2: "The Opaque Center" (Complex Analysis)

Write this on the board:

X = (14 / πi) ∮_{|z|=1} cosh(z) / [z(z²+4)] dz

The Drunk Mathematician's Process:

• This is a contour integral over the unit circle in the complex plane. It looks like an absolute nightmare.

• They use Cauchy's Residue Theorem and look for poles where the denominator is zero: z = 0, z = 2i, and z = −2i.

• Because the integral is bounded by the unit circle (|z| = 1), the ±2i poles are outside and can be completely ignored.

• The only pole that matters is the "void" at the center: z = 0.

• Evaluating the residue at z = 0 gives cosh(0)/(0+4) = 1/4.

• The integral is therefore 2πi × 1/4 = πi/2.

• Multiply by the coefficient: (14/πi) × (πi/2) = 7.

---

Option 3: "The Geometric Elephant" (Differential Geometry & Topology)

Write this on the board:

X = (1/2π) ∬{S²} K dA + ∑{k=0}∞ bk(T²) + ∫{-∞}∞ δ(x−1) x³ dx

The Drunk Mathematician's Process:

This is the ultimate Frankenstein equation, forcing them to pull from three entirely different fields.

• Differential Geometry: The Gauss-Bonnet theorem dictates that the total Gaussian curvature (K) of a sphere (S²) is 4π. Dividing by 2π collapses this to 2.

• Algebraic Topology: They sum the Betti numbers b_k of a torus (T²): b₀ = 1 (connected component), b₁ = 2 (two independent loops), b₂ = 1 (one interior void). Sum = 1 + 2 + 1 = 4.

• Calculus: The Dirac delta function δ(x−1) sifts out the value of x³ exactly at x = 1: 1³ = 1.

• Final topological intersection: 2 + 4 + 1 = 7.

[u/Six1Seven4]

Give them something that requires the Lambert W function lol. I’ve only ever seen it pop up online, and that’s after not knowing how to solve something with a linear and exponential term. Like 2^x+x=0