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# The pons asinorum of modern mathematics

 Posts: 2,762 Add as FriendChallenge to a DebateSend a Message 2/4/2016 5:26:18 PMPosted: 3 years agoThe pons asinorum of Greek mathematics was Proposition 5 of Book I of Euclid's Elements: The base angles of an isosceles triangle are equal. Its proof was believed to be a 'bridge': Anyone who can cross it is not a donkey, hence the name pons asinorum (yeah, 'asinorum' has to do with the word @ss). But times have changed and so have mathematics. What should the new pons asinorum be?I think it should be the first-order linear differential equation. It require you to apply nearly all knowledge of algebra, trignometry and calculus up to that point (I guess geometry is less relevant, but I don't like geometry...) It's not the easiest to learn, but also not hard once you get the hang of it.Here are some other possible pons asinorums (or whatever the correct Latin plural is) I thought of. What do you think?Quadratic equationsCentral limit theoremPolynomial equations and the Fundamental Theorem of AlgebraEquations of circlessin^2 a + cos^2 a = 1Taylor seriesDefinite integrals and the Fundamental Theorem of CalculusGeometric seriesProof of AM >= GM >= HMPythagorean theorem (any proof)Expoential and logarithmic equationsLogarithmic differentiationEpsilon-delta proofsVolume of a sphereInverse of a 3x3 matrixSimultaneous linear equations and Gaussian eliminationEuler's formula/De Moivre's TheoremPolynomial division and the remainder theoremI think it is well established that the only reason aliens come to earth is to slice up cows and examine inside peoples' bottoms. Unless you are a cow or suffer haemerrhoids I don't think there is anything to worry about from aliens. - keithprosser Don't be a stat cynic: http://www.debate.org... Response to conservative views on deforestation: http://www.debate.org... Topics I'd like to debate (not debating ATM): http://tinyurl.com...
 Posts: 6,033 Add as FriendChallenge to a DebateSend a Message 2/10/2016 9:39:25 AMPosted: 3 years agoAt 2/4/2016 5:26:18 PM, Diqiucun_Cunmin wrote:The pons asinorum of Greek mathematics was Proposition 5 of Book I of Euclid's Elements: The base angles of an isosceles triangle are equal. Its proof was believed to be a 'bridge': Anyone who can cross it is not a donkey. But times have changed and so have mathematics. What should the new pons asinorum be?DC, I wonder whether it's being able to explain why science:1) Relies on empiricism, yet continuously changes its model and methods;2) Is the continuing elimination of ignorance and error from knowledge, and not the conclusive proof of truth;3) Having derived from natural philosophy, and while still being stimulated by it and occasionally challenged by it, is no longer accountable to philosophy alone;4) While making extensive use of logic and math, is not created by either.In support for this contention, I find that members who understand this, can: understand a sketched rationale behind almost any accepted scientific result, recognise the difference between science and pseudoscience quite easily, and make a decent fist of understanding the philosophy of science and science history.Meanwhile, those who miss one or more of these seem to be missing critical knowledge in the discussion, critique and appreciation of science, while those who miss all of them seem to be missing the fundamental concepts of what science -- or knowledge -- are at all.I hope that may be useful.
 Posts: 2,762 Add as FriendChallenge to a DebateSend a Message 2/10/2016 6:02:55 PMPosted: 3 years agoAt 2/10/2016 9:39:25 AM, RuvDraba wrote:At 2/4/2016 5:26:18 PM, Diqiucun_Cunmin wrote:The pons asinorum of Greek mathematics was Proposition 5 of Book I of Euclid's Elements: The base angles of an isosceles triangle are equal. Its proof was believed to be a 'bridge': Anyone who can cross it is not a donkey. But times have changed and so have mathematics. What should the new pons asinorum be?DC, I wonder whether it's being able to explain why science:1) Relies on empiricism, yet continuously changes its model and methods;2) Is the continuing elimination of ignorance and error from knowledge, and not the conclusive proof of truth;3) Having derived from natural philosophy, and while still being stimulated by it and occasionally challenged by it, is no longer accountable to philosophy alone;4) While making extensive use of logic and math, is not created by either.In support for this contention, I find that members who understand this, can: understand a sketched rationale behind almost any accepted scientific result, recognise the difference between science and pseudoscience quite easily, and make a decent fist of understanding the philosophy of science and science history.Meanwhile, those who miss one or more of these seem to be missing critical knowledge in the discussion, critique and appreciation of science, while those who miss all of them seem to be missing the fundamental concepts of what science -- or knowledge -- are at all.I hope that may be useful.Hi RuvDraba :) I agree that the above may well be the pons asinorum of modern science, or indeed of a modern intellectual, but my OP was actually asking about the pons asinorum of modern maths. Which mathematical concept do you think could play the same role that Euclid's proof did in Ancient Greece?I think it is well established that the only reason aliens come to earth is to slice up cows and examine inside peoples' bottoms. Unless you are a cow or suffer haemerrhoids I don't think there is anything to worry about from aliens. - keithprosser Don't be a stat cynic: http://www.debate.org... Response to conservative views on deforestation: http://www.debate.org... Topics I'd like to debate (not debating ATM): http://tinyurl.com...