# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# 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 anyncomplex numbers z_{1}, โฆ, zthat are linearly independent over the rational numbers Q, the field extension Q (_{n}z_{1}, โฆ,z_{n},e^{z1}, โฆ,e^{zn}) has transcendence degree at leastnover Q

Source :Wikipedia

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

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 Irrational numbersplugin-autotooltip__plain plugin-autotooltip_bigIrrational numbers

unknowable

An irrational number is a real number that can't be expressed as a ratio of integers, i.e. as a fraction.

Put another way, it can never be specified with absolute accuracy.

Well known examples are ฯ and โ2

For many irrational numbers, relatively simple mathematical proofs exist which show that it's impossible to ever arrive at a finite solution. For example, such as **ฯ** and the natural logarithm ** e**.

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