If you could be responsible for any single mathematical achievement what would it be /sci/ ?
can be something already achieved or something not already achieved
>>8041842
[math]e^{i \pi} + 1 = 0[/math]
>>8041858
why Euler's identity
>>8041861
Not only is it a beautiful equation, but also the most famous mathematical equation after 1 + 1 = 2, and one with many applications.
>>8041842
Probably the Barnett cohomology.
>>8041842
Nice pic op, i like it.
Also Fibonacci sequence probably.
Pic rel.
>>8041842
I'll be responsible for abolishing complex numbers
>>8041842
resolving Hilbert's 8th problem.
>>8042061
Resolving Hitler's Solution.
>>8041877
Such a beautiful subject.
We just start with the famous space of Barnett triple integrable functions:
[math] \mathcal{B} \equiv \left\{ {f \in C\left( \mathbb{R} \right)|\iiint\limits_{U \subset {\mathbb{R}^3}} {f\operatorname{d} {\lambda ^3}} < \frac{{{e^{i\pi }}}}{{11.999...}}} \right\} [/math]
And then generalize this space to include functions values on general manifolds and classify by their differentiability:
[math] {\mathcal{B}^k}\left( M \right) \equiv \left\{ {f \in {C^k}\left( M \right)|\iiint\limits_M {f\operatorname{d} \mu } < \frac{{{e^{i\pi }}}}{{11.999...}}} \right\}[/math]
We then define the cochain complex, [math]... \leftarrow {\mathcal{B}^{k + 1}}\mathop \leftarrow \limits^{{\mathfrak{d}_k}} {\mathcal{B}^k}\mathop \leftarrow \limits^{{\mathfrak{d}_{k - 1}}} {\mathcal{B}^{k - 1}} \leftarrow ...\mathop \leftarrow \limits^{{\mathfrak{d}_1}} {\mathcal{B}^1} \leftarrow 0[/math]
and with only that the kth Barnett cohomology group is realized as:
[math]H_\mathcal{B}^k\left( M \right) \equiv \frac{{\ker {\mathfrak{d}_k}}}{{\operatorname{im} {\mathfrak{d}_{k - 1}}}}[/math]
.
What a magnificent man that Barnett.
>>8042092
>the meme gets deeper
>>8041842
Stationary action principle
>>8042092
kek
Fermats last
Translation of Inter-Universal-Teichmuller-Theory.
