Euler's Equation: 'The Most Beautiful Theorem in Mathematics' - Professor Robin Wilson

Eulers pioneering equation, the most beautiful equation in mathematics, links the five most important constants in the subject: 1, 0, , e and i. Central to both mathematics and physics, it has also featured in a criminal court case, on a postage stamp, and appeared twice in The Simpsons. So what is this equation and why is it pioneering?

Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 2,000 lectures free to access or download from the website.

[marc-andrebrunet]

Great thanks from Montreal, Canada ! I'm 37, and I unfortunately never been to school. But now I learn English and I have some of the best public lecture on earth with Gresham College! !! I'm getting rich of knowledge now!!🤓🤓🤓.

[kzgcyn]

So much knowledge and history on display. Thank you.

[ZeedijkMike]

I got quite lost in the equations here and there but I still enjoyed every minute.

[ExistentialistDasein]

More professors should dress like professor Wilson.

[deborahkeesee]

At 14:57 you provide 22/7 as an estimate of the value of pi; but the ratio 355/113 is much closer as it varies from pi only in the 7th decimal place!

[beannathrach]

I found the law of cosines the most beautiful. It combines algebra through the inner product to geometry through cosines of angles. If a system has inner products other than zero and one, you can do angles and distances and geometry with the system. I wonder what the geometry of continuous functions is.

[kokomanation]

Euler and Gauss are the two greatest Mathematicians ever I think

[TomLeg]

@11:08 12*20 + 13 = 240 + 13 = 253, rather that 273. Proofreaders are still important.

[LawrencRJUTube]

This is all very well done -- but I object strongly to the "bum rap" given to the simple Liebniz equation for Pi/4 that alternately adds and subtracts the reciprocal of consecutive odd numbers. It is true that if you depend only on the SINLGE sum after n terms are added, it takes a great number of terms to give you 3 digits of Pi. However only a FOOL would fail to notice that Pi is being gradually squeezed between an upper bound and a lower bound so if, after (say) 50 terms are added, you AVERAGE the sum of 50 terms with the sum of 49 terms the average of the two sums gives you the value of Pi/4 to almost 3 decimal digits. And (though only a dimit-wit would fail to notice this fact) someone who is only slightly smarter would realize that the weakness of the series is also its greatest strength BECAUSE if you were to graph the sums of only the positive values of n and another graph of the sums of only the odd values of n, you would get two lines that approach each other so gradually that the point half way between them gives you points that are alternately above and below the value of Pi. So that you can take the average of the averages of 3 sums and get an even better approximation or the average of the averages of the averages of 4 consecutive sums and get an even better approximation ... and it turns out from a study that I did in high school back in 1955, that if at any even number n you go back to n/2 and work with the average of the averages of the averages of the averages ... until you are down to a single average derived from the n/2 terms, the leibniz series leads to a value of Pi which is far more respectable than the "bum rap" that it gets. And if you take some of the other infinite sums that also jump back and forth above and below Pi, but converge more rapidly than the Liebniz series (considering any given sum of n terms) the steepness of the asymptotes does not guarantee any improvement beyond the first order average of two consecutive sums, so that it turns out that fewer calculation are involved in determining a 6 digits of Pi using compound averaging with the Liebniz series, than the first order average with some of the simple series that converge more rapidly. This is especially true if you happen to have access to a table of recipricals of the natural numbers -- the greatest labor on finding the sum of n terms of the Liebniz series is caculating the reciprocals of the odd numbers. When I was in school we had to memorize four decimal digits of the square root of the prime numbers up through 11 and also their reciprocals.

[almablanca]

i study history, i am completely lost here. so i did not get the joke in 6:00
it was a joke about superposition?

[rider]

Wasn't it meant to be 'e i e i "oh" '?

[davidwilkie]

If e^ix=(sinx+cosx), then the cause-effect reason is the "containment" property of i, ..e^iPi would be an inclusion x set in "imagined" (possible calculation of) potential-transverse or tangential exclusion beyond the radius of probability. (Goes with the polygon measure of Pi methodology)
Could word that better? Because if the reason Pi is irrational is the requirement for closure of probability one (1-0D eternally-now interval), then the Pi ratio has to be an identity of infinity, by way/path to (Quantum Calculator) calculate eternity. The Quantum Calculator is both machine and product, ..cause-effect of temporal superposition.

The possible relative positioning of the trig relationship, is potentially summed to be the area of the "circle of infinity" determined by the Pi ratio. (Goes with the needle drop experiment)

It is identifiable as the actual phase-state potential relationship of constant creation.(?)
Just for fun, reality is perceived as, "something sometimes somewhere somewhen, in nothing, probably".

All the properties of the singularity, of the vanishing point of temporal superposition, have mathematical identities related to these "rational" fractal ratios of existence; ie it's possible to resolve a proportionate relative timing position of historic intensity in the irrational eternally-continuous QM field of projected probability by natural condensation of superimposed "e" logarithm. Just add-imagine the actual mathematical "energy of calculation" to the structure of naturally occurring "static" constants...

Excellent lecture. If Euler's Formula is pioneering, it's because it's the crankshaft and main bearings of the Quantum Fields Mechanism too.


If QFM is reality, then all educational substantiation of knowledge is, is a closing of the connection between a point location of information-existence, and the discovery of the relevant reciprocal connection, via the Mathematics and "imagined" correlation of evidence. (In terms of direct experience or, "learning by doing")

Because, if mathematical abilities are characteristic of a particular family, then there's a practical reason for it.


This video provided the "Rosetta Stone" translation of the core mathematical connection with QM-Time modulation principle, that is where Group Theory and practical applications of controlled modulation devices meet.., Intuitively.
Thank you.

[lerneninverschiedenenforme]

So why is it called 'beautiful'? E.g. compared to e^(iτ) = 1

[maxheadrom]

There are 10 types of people: those who can count and those who can't. Very funny!!!!

[snoortpod]

Blimey. I remember Robbo presenting Open University programmes during its heyday in the 70s and 80s - with those framed glasses you couldn't get more serious. That would be the Countdown To Mathematics series comprising the then Foundation Course, etc, etc. They did away with that course in the end. Wrong way to go IMO.

[dreamingguy]

why is so much made about the number of numbers after decimal in the pi value.Of course more and more accuracy in calculations of the area of a circle. can some one talk about why the need to have so many digits for pi and why so much is made of it or talked about it.

[FlockOfHawks]

Anybody ever heard of Augustus de Morgan ? George Airy ? Exactly .

[moppleinga]

ok so liked immediately on his snappy dressing-first class Sir!

[topilinkala]

There are 10 types of people: Those who do not know binary, those who do and those who did not expect this to be in trinary.

[vinylzappa]

This is why I've hated every job I've had