Thomas Oléron Evans @Mathistopheles

Maths. Puzzles. Lecturer at @CASAUCL. I've also written a book w/ @Fryrsquared on the merry Maths of Christmas! https://t.co/A3Y2uf96yi mathistopheles.co.uk London Joined October 2011

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Thomas Oléron Evans @Mathistopheles

2 years ago

@MattBecker82 Well done. I did prove that these were the only solutions, but I had to prove for a>c>1, a>1 c<-1, c<a<-1 separately, all for |b|>1, having already considered all cases with |a|, |b|, |c| <2. Might post if I get the time, but this margin and all that.

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Thomas Oléron Evans @Mathistopheles

2 years ago

There are three families of solutions. One very easy to find, one fairly easy, and one a bit more tricky. (And then there's the rigmarole of proving that there are no others, which was less straightforward than I'd anticipated...) #puzzle #puzzles #maths #math

Thomas Oléron Evans @Mathistopheles

2 years ago

MATHS PUZZLE: Find all integer solutions of: a^(b^c) = c^(b^a) Some clarifications in the following tweet. #maths #math #puzzles

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Thomas Oléron Evans @Mathistopheles

2 years ago

MATHS PUZZLE: Find all integer solutions of: a^(b^c) = c^(b^a) Some clarifications in the following tweet. #maths #math #puzzles

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Thomas Oléron Evans @Mathistopheles

2 years ago

PS. I should have said "greatest" rather than "largest". Basically, always return the positive real root when there is also a negative real root.

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Thomas Oléron Evans @Mathistopheles

2 years ago

If there are no solutions, why? If there are finitely many solutions, can you list them? If there are infinitely many solutions, can you describe them all?

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Thomas Oléron Evans @Mathistopheles

2 years ago

@MattSingh_ You should hear their Eurovision commentary...

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Thomas Oléron Evans @Mathistopheles

2 years ago

@Jay42_SD @keiranpedley Yes, my understanding is that polls were particularly accurate overall in both 2018 & 2022: fivethirtyeight.com/features/2022-… This poses a question of whether there is some specific issue of polling when Trump is a candidate, and whether pollsters might (over?)correct for that in 2024.

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Thomas Oléron Evans @Mathistopheles

2 years ago

@keiranpedley Do we have any idea how aggressive pollsters are being on trying to correct for underestimates of Trump's vote in 2016 and 2020? Fingers crossed for a Labour 2015 to 2017 type polling effect...

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Thomas Oléron Evans @Mathistopheles

2 years ago

A plot of Labour & Conservative polling errors in all final GB general election voting intention polls, 1945-2024. 2024 polls in red. Data from PollBase (@markpack). #GE24 #politics #stats

Steve Akehurst @SteveAkehurst

2 years ago

Definitely agree with @Dannythefink that GE24 polling miss should be taken more seriously. But in fairness to pollsters: - Several averages had Lab at 37-38%, wide on their lead by ~6% not 10. Bad not catastrophic. - They did pick up late dip in Lab’s vote; it was ignored

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Thomas Oléron Evans @Mathistopheles

2 years ago

Finally, an honourable mention to the organisation who published the most inaccurate final poll in UK election history in 2010 (in terms of absolute error), underestimating both Labour & the Conservatives by a collective 15.6 %pts. They predicted a Lib Dem win... #GE24 #politics

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Thomas Oléron Evans @Mathistopheles

2 years ago

CONCLUSION: The consistency of the polling bias towards Labour and against the Conservatives in 2024 across EIGHTEEN final polls from EIGHTEEN different organisations (at least three times as many as in any of the above examples) is unprecedented. #GE24 #politics #stats