====== Schanuel's conjecture ======

In the mid 1960s American mathematician Stephen Schanuel devised a complex mathematical conjecture regarding the 'transcendence degree' of certain 'field extensions' of the rational numbers.

Formally stated :

>Given any //n// complex numbers z<sub>1</sub>, ..., z//<sub>n</sub>// that are linearly independent over the rational numbers Q, the field extension Q (//z//<sub>1</sub>, ..., //z//<sub>n</sub>, //e//<sup>z<sub>1</sub></sup> , ..., //e//<sup>z<sub>n</sub></sup>) has transcendence degree at least //n// over Q\\
>Source :[[https://en.wikipedia.org/wiki/Schanuel%27s_conjecture|Wikipedia]]

At present, the conjecture has neither been proved or disproved.\\ 

If it //is// eventually proved, it could have profound implications for exploring the nature of [[content:mathematics:irrational_numbers]] such as **π** and the natural logarithm **//e//**.