Equations take a bit of working out

Aug 28, 2012
Leonhard Euler (Basel, 1707 - St Petersburg, 1783.

The myth that mathematical theorems suddenly come together in the most elegant and smooth proofs will be busted at an upcoming lecture.

Associate Professor Hans Lausch, an adjunct senior research fellow in Monash University's School of , will be discussing how mathematical theorems come to exist at his upcoming 'Euler, Gauss and someone else—who got it right and who didn't'.

"This lecture is to illustrate once more that celebrated mathematical results can have, perhaps more often than not, a long gestation period, with leaps and bounds, with errors and dead ends, and with frustration," Associate Professor Lausch said.

"These issues are usually not, or only sparsely, mentioned in text books, so a young student may get the impression that mathematical theorems suddenly come down upon us from heaven together with the most elegant and smooth proofs.

"On the other hand, there have been results, or proofs of results, correct ones as well as erroneous ones that were left unnoticed for a long time and not surprisingly, were rediscovered."

Associate Professor Lausch's lecture is looking at some work of the famous mathematicians Leonhard Euler and Carl Friedrich Gauss and specific theorems they worked on to determine who originally proved those theorems, in comparison to who was thought to have been first to have flawlessly proved them.

His talk is the second of the ', Mathematics, Philosophy and Technology' lecture series, organised by Dr Alan Dorin from the Monash Faculty of Information Technology.

"I hope my lecture will illustrate that great mathematicians are not supermen, but 'only' highly gifted human beings," Associate Professor Lausch said.

Explore further: OK, computation

More information: 'Euler, Gauss and someone else—who got it right and who didn't' will be held from 2-3pm on Thursday, 30 August 2012 in Seminar Room 135, Building 26, at Monash University's Clayton campus.

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AWaB
not rated yet Aug 28, 2012
A perfect example of this is Maxwell's EM equations. He spent a lot of time deriving his results as can be seen from his papers. Once he had them, the originals were horrendous and quite cumbersome. It took even more time to generalize them into what we have today.
natello
1 / 5 (4) Aug 28, 2012
Once he had them, the originals were horrendous and quite cumbersome.

Maxwell's original theory was based on 20 equations in 20 unknowns. The original quaternion form of Maxwell's equations was more consequential and exact, than the later form reduced by Heaviside, Hertz, and Gibbs. The exclusion of scalar component from quaternions removed the description of spin-2 component of EM waves and scalar waves from Maxwell's theory. It's similar, like if we would neglect the elastic deformation of underwater and underwater waves from description of surface ripples with deforms of elastic fluid. The energy density of underwater waves is indeed minute with compare to the energy of surface ripples - but in many connections it cannot be neglected.
defactoseven
5 / 5 (1) Aug 29, 2012
"...Ye cubic surfaces! By threes and nines, Draw round his camp your seven-and-twenty lines- The seal of Solomon in three dimensions....."

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