a question a day keeps the stupid away 26

Abel’s impossibility theorem states that there is no general algebraic solution (that is, a solution using the algebraic functions, which are addition, multiplication, and taking n-th roots) to polynomials of degree five or higher.

Which isn’t to say that every polynomial of degree five or higher can’t be solved algebraically. For example, the 16th degree polynomial 0 = (x - 2)^16 can be solved trivially using the algebraic functions.

Solve the general polynomial of arbitrary degree using the non-algebraic (in other words, transcendental) functions, as well as the algebraic functions as necessary.

?

Our Indiegogo campaign just got more interesting.

No name in voting theory has hit households like Nobel laureate, Dr. Kenneth Arrow, developer of the Impossibility Theorem. Our first phone interview with him went really well. So we decided to follow up.

During our recent phone conversation, Dr. Arrow graciously offered to autograph a reprinted copy of the first journal to publish his theorem, Journal of Political Economy (1950). And now it could be yours.

One of his autographed first edition books sold for \$5,200.

This perk is going for a one-time donation of 3,500 (multiple donations adding to this doesn’t count). Now, if no one has claimed the perk by the end of the campaign, then the person with the highest total in public donations gets it. (No board members can win.)

Who would’ve guessed it? We (of all people) have created a game theory problem for you!

Some of you are already in the running for total public donations:
Frank Atwood: \$800
Brian Hauer: \$500
Robert Jochim: \$500
Robert Norman: \$500

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