A Tribute to Euler - William Dunham

A Tribute to Euler
William Dunham
Truman Koehler Professor of Mathematics, Muhlenberg College
Tuesday, October 14, 2008, at 6:00 PM
Harvard University Science Center, Hall D
The fall 2008 Clay Public Lecture will be held at Harvard on October 14, in association with the Harvard Mathematics Department. Known for his writings on the history of mathematics, Professor William Dunham will examine the genius of one of the world's most prolific mathematicians in his talk "A Tribute to Euler" in Hall D of the Harvard Science Center at 6 pm.
Among history's greatest mathematicians is Leonhard Euler (1707-1783), the Swiss genius who produced an astonishing 25,000 pages of pure and applied mathematics of the very highest quality.
In this talk, we sketch Euler's life and describe a few of his contributions to number theory, algebra, and other branches of mathematics. Then we examine a particular Eulerian theorem: his simple but beautiful proof that there are as many ways to decompose a whole number as the sum of distinct summands as there are ways to decompose it as the sum of (not necessarily distinct) odd summands.
Condorcet, in his Eulogy to Euler, wrote that "All mathematicians now alive are his disciples." It should be clear to those who attend the Clay Public Lecture that these words are as true today as when they were first set down, over two centuries ago.
William Dunham, who received his B.S. (1969) from the University of Pittsburgh and his M.S. (1970) and Ph.D. (1974) from Ohio State, is the Truman Koehler Professor of Mathematics at Muhlenberg College. In the fall term of 2008 he is visiting at Harvard University and teaching a course on the work of Leonhard Euler.
Over the years, he has directed NEH seminars on the history of mathematics and has spoken on historical topics at dozens of U.S. colleges and universities, as well as at the Smithsonian Institution, the Swiss Embassy in Washington, and on NPR's "Talk of the Nation: Science Friday."
In the 1990s, Dunham wrote three books on mathematics and its history: Journey Through Genuis: The Great Theorems of Mathematics (1990), The Mathematical Universe (1994), and Euler: The Master of Us All (1999). In the present millennium, he has written The Calculus Gallery: Masterpieces from Newton to Lebesgue (2005) and edited The Genius of Euler: Reflections on His Life and Work (2007). His expository writing has been recognized by the Mathematical Association of America with the George Pólya Award in 1992, the Trevor Evans Award in 1997, the Lester R. Ford Award in 2006, and the Beckenbach Prize in 2008. The Association of American Publishers designated The Mathematical Universe as the Best Mathematics Book of 1994.
Our thanks to the Harvard Mathematics Department for hosting this event.
www.claymath.or...
www.claymath.or...

[@Kobe29261]

This guy is a phenomenal presenter!

[@oo88oo]

He wrote a wonderful "light" math book called "Journey Through Genius," which takes you through a large handful of big theories from Archimedes through Euler and beyond.

[@satyabratadhala4220]

Leonhard Euler...the greatest mathematician of all time, a real genius and his contribution to mathematics is beyond imagination. A nice lecture by William Dunham.

[@chasr1843]

/me votes for Euler

[@AaronHollander314]

He's no Gauss ;)

[@charlesbrowne9590]

Many mathematicians would say Gauss was greatest. Many years ago, when I was a freshman taking differential equation, we had an excellent textbook called “Differential Equations with Applications and Historical notes”. I remember reading that if Gauss had not so many theorems (and else ) named after him, it was because many were named for the first to study it after Gauss. Gauss gave us the Fundamental Theorem of Algebra and the Central Limit Theorem.

[@justonlyalta]

What about Fourier?

[@ruscul7155]

@@charlesbrowne9590 i really thought that joke was originated from euler because euler had so many theorems and discovery in every branch of mathematics

[@ninjalacoon]

This is what I would imagine a good tedtalk being if they still made them like this.

[@nickellis1553]

These days all TED Talks do is A. Stroke off the audience or B. stroke off the presenters ego

[@bojanzivkovic8934]

Great tribute to probably the greatest genius who walked the Earth - as Mr. William Dunham told quality and quantity of Euler's work were just staggering. I was told many times that some persons were geniuses (programmers, professors, engineers, doctors, ...) and some of them I know well enough or very well. If they are considered geniuses how to categorize great Euler? Alien? I have always loved math and natural sciences in general and throughout my whole education from elementary school to mechanical faculty Euler's name was mentioned so frequently in mathematics, physics, mechanics ... Producing ultimate math while being completely blind is something beyond belief. Every time I hear that fact I am left speechless and, to be honest, a few tears from my eyes start to fall. I have always been impressed by great people regardless of their profession (sport, art, science, ...) but this great man stands out from all others. There was one and only LEONHARD EULER. Many thanks to Mr. William Dunham, tribute was very interesting to watch and those 55 minutes passed very quickly. 25 000 pages of work!!! Just Euler's identity was enough to make him immortal but he did much much more with detailed explanation allowing us with decent math knowledge to follow him (up to some point of course in his more complex works) and to admire him. LEONHARD EULER RULES!!!

[@chasr1843]

That's what I say :)

[@adanicade1000]

❤

[@mauriceoreilly9955]

Hero mathematician presented by hero speaker!

[@PifflePrattle]

There are some good mathematics lectures (for general audience) online. This has got to be one of the best.

[@magicatt1]

Like?

[@PunyaDeka-yh9el]

😊😊

[@miguelcamel8079]

And on the third day God said: Let there be Euler!

[@josesaldivar655]

Right and Newton

[@davidregi7571]

@@josesaldivar655 your reply after seven years.... And i reply in 2 hours.

[@creepervideo1106]

@@josesaldivar655 and gauss

[@iLLKiD189]

There is no god

[@nrrgrdn]

On the fourth day God said: Let there be Gauss. Then I can call it an early weekend.

[@tinafeyalien]

Humorous, accessible and interesting. I was engrossed throughout. Good questions at the end too.

[@acasualviewer5861]

I believe that one of the biggest problems with Math education is the lack of a good narrative. In contrast, if you compare with Physics even school children know of Einstein and E=mc2. But the story of people like Euler is left largely unknown by the masses. And with no story, what is also lost is the fascination for math itself.

[@DRYROT124]

Great way to spend an hour on a Sunday!

[@vecter]

That is a beautiful proof of D(n) = O(n)

[@dataskin]

Euler was brilliant at math, this guy is brilliant at presenting his biography and ideas to the public. Great job, Mr Dunham!

[@IronCharioteer]

I will never forget the day i learned the Euler Identity. I was working through a book called Plane Trigonometry by Wylie; in the section on hyperbolic trig i was following the steps in a series. and came to the point where, as in the lecture, it said, "now let x equal etc.", so i did. My jaw dropped and i almost threw up from the butterflies in my stomach. I was truly astonished, and still to this day whenever i see that identity i marvel at it's elegance. Euler was truly a giant.

[@chasr1843]

Yeah, my jaw dropped when I first saw that (many years ago). And my jaw just dropped again when I saw the proof at the end of this video.

[@lalitdogra22]

Totally worth watching at 1 at night 😇👌🏼👌🏼

[@michaelbauers8800]

2:50am here, and still worth it :)

[@prabhakaranbaskar1400]

00:40 now... be back in 20

[@SAMathlete]

He is the master of us all. Terrific presentation!

[@alexnaranjo9313]

What I would give to see this man, what a treasure if he was still alive I cant imagine the tech he could create

[@aksei5786]

Great presentation Sir, I am so pleased to meet Euler. Thanks for introducing

[@taekwondoemoboy]

Euler is not genius in the sense that many others are considered genius. He is just Euler. He is in his own class!

[@silvadexter3222]

An amazing mathematician and a superb presenter

[@hrperformance]

Thank you for taking the effort to record this!

[@keniangervo8417]

This was a really great lecture. Euler was a genius. But yeah, I'd like to know more about the pattern he saw in amicable numbers!

[@voithmascarenhas]

1 hour was well spent watching this! Thanks, professor Dunham! I feel very inspired after watching this :)

[@RichardASalisbury1]

Clear, funny, even simple most of the time. What more could one ask?

[@rajendrent.k.1196]

Fantastic Dr William Dunham. It is inspiring me in this New-year. Thanks,Thanks & Thanks a lot. Love to listen more from you ,Sir Rajendren & Bhagyalakshmi

[@cerebralcereal]

incredible guy. the proof of the partitioning of numbers was amazing!

[@KetanSingh]

I love the passion of this gentleman.

[@marcgray9083]

A wonderful lecture.

[@michaelbauers8800]

Who downvoted this? This guy is a great lecturer. Of course he aimed for a lower level of audience, but that's what made it enjoyable.

[@adnankassem8114]

That was a good presentation. Euler was a phenomenal genius - i am really impressed.

[@arj123sub]

Great lecture - Prof Dunham !

[@dragonfly3139]

Euler was indeed a genius no doubt, great presentation thank you Mr. William Dunham

[@DaitoRyuDeshi]

I have been aware of Euler since my high school days and was thoroughly impressed even then. Although I had never heard of William Dunham until a couple of yrs ago due to his book (master of us all), I must say he is outstanding as an orator of mathematics esp on Euler. Much appreciation to him for popularizing Euler who is also one of my fave along with Gauss, Riemann, Galois, Abel, Ramanujan etc. Wish he put as much efforts in writing about Gauss et al as well. Thanks for the video.

[@Ratsonic]

Euler's column buckling equation is still classic in structural engineering.

[@snnwstt]

Definitively. It is called Elastic Eulerian Buckling. And it is partly based on the fact that a column, in compression, should have more than ONE solution for its shape (the straight form, and the start of the buckled form), but since it is strictly linear, a system of strictly linear equations, such system should be with a determinant possibly reaching a value of zero, leading the buckling should occur only when the axial compression force reaches a given level, Ce, C for compression, e for Euler.

[@SaveriusTianhui]

13 children and such high production with one eye thats work ethic and God God Bless

[@acetate909]

He was too smart to believe in silly things like God.

[@zinzorius313]

@@acetate909 Euler was christian, atheism was basically non existent until recently. www.google.com/url?sa=t&source=web&rct=j&url=en.m.wikipedia.org/wiki/Leonhard_Euler&ved=2ahUKEwjcubiClanlAhXEwosKHR6-CWUQFjAAegQIBhAB&usg=AOvVaw3yjZzr3A6wQC21gkvBe3fV I'm an atheist myself, but it's important to use correct facts rather than distorting the truth to promote ones own ideology.

[@kukulroukul4698]

@@zinzorius313 Panda's didnt existed back then also

[@zinzorius313]

@@kukulroukul4698 Pandas did exists back then. Although they were first discovered by europeans in 1869 by a cathololic missionary.

[@JSSTyger]

Euler was one of my greatest pupils.

[@brianmusera2485]

the way Euler proved D(n) =O(n) is nothing shot of beautiful. nice presentation.

[@majidshaalan5265]

I just came across this right now, you have no idea how late I feel I am!

[@karthickanthi1880]

Question: In the proof at 40:22, you can only use the geometric series for a Does that limit the proof to certain numbers?

[@aasrith108]

🤯

[@vikraal6974]

Are you idiot, there are no limitations

[@chasr1843]

omG OMG OMG - that proof at the end just blew my mind!

[@r.rahman12]

euler was a genius and an outstanding presentation by dunham

[@simonstrandgaard5503]

Incredibly good lecture. Great presenter. Amazing story.

[@rajnish2206]

Euler's everywhere in maths,physics, economics

[@reinowarren7880]

Remarkable person, I speak of Euler. Dunham is good too! Worthy of a look see. You will be in awe of Euler even if you "suck at math."

[@tonyoak2230]

Wow... Magnificent presentation.

[@drbonesshow1]

Euler (1707 - 1783) enjoyed rooting for the Oilers when they were in Houston under the direction of Bum Phillips (1923 - 2013).

[@CGW11]

Great lecture! Euler's funny looking headgear is called chaperon.

[@psilvakimo]

Outstanding lecturer!

[@juliomedina4171]

Great lecture....

[@gilbertogarbi4479]

Congratulations Bill Dunham!!! Your books are fantastic. Best regards from Brazil...

[@gm2407]

Anyone who ever wondered why you need to show your working out. If it was good enough for Euler, it is good enough for everyone.

[@101xaplax101]

great lecture! amazing job!!!

[@mlfnascimento]

Impressive talk done by Professor William Dunham on Euler's life and some amazing discoveries...

[@marciliocarneiro]

a little detail:the sum of the infinite series formula 1/(1-x) is valid only if the series decreases! It is easy to check.If x is 2 the series increases and the sum is -1, which is absurd,since a sum of positive terms can not be negative

[@victorlomelli]

Talented speaker. Thank you for making this video posible

[@kwonknow3869]

Delightful presentation. Delightful.

[@premal8897]

Way to go, Uncle Leonhard!

[@gm2407]

Man writes in Latin and speaks German, Russian and maybe French or Italian as well because he is Swiss. Probably knew Greek as well because of a classical education. Also can't fathom the depth of intellect of Euler just by his relevant output. It is huge.

[@deepakvenkatesh5166]

Great talk. Don’t think Euler explained why is the sky blue in his popular science book. Lord Rayleigh was born 60 years after Euler died. Rayleigh scattering is the explanation of blue skies.

[@morani789]

After a lecture about the mathematical virtue of Euler I feel I should give up doing mathematics.

[@gousemohiuddin5475]

I have no words to appreciate.

[@v.gopalakrishnan350]

Fascinating! Thanks for the excellent presentation!

[@vector8310]

Relaxed yet elegant discourse on Euler. What a pleasure to view. Pity a Kanye video draws just as many views in minutes. And what, pray tell, was there to dislike here for those 20 viewers?

[@himabratadas1577]

Inspirational...so wonderfully presented

[@75315cristina]

Happy Birthday, Euler(:

[@7425park]

While still in his twenties, Euler became fascinated with bird droppings and tirelessly searched and collected their little piles. He stacked them under his hat on the hot summer days and enjoyed their oozing flow, especially delighted how it tickled his ears.

[@djordjekojicic]

Beautiful lecture!

[@MaegnasMw]

Great presentation, from a guy who really "has this", of a guy who really "rocked" math! Euler had the luck of being born at a time when math was flowering all over Europe, with the likes of him, Gauss, Newton and others (Fermat, Bernoulli, Cauchy and some in the 19th century like Galois) really breaking boundaries and pushing math from Ancient Greek Geometry and Pythagorean Numbers along with Arabic Algebra and Trigonometry revival, towards modern math. And Euler stands head and shoulders above the rest, perhaps only looking at ONE who stands a bit above him in general contribution to math, physics AND engineering. Indeed, Euler was the closest we had to another Archimedes (for those who will disagree, remember the broader scope and the vastly bigger "leap" Archimedes took, where math is concerned. Now that the Method has been recovered from the Palimpsest, we KNOW that, had he lived a bit longer or his works had survived a bit better, we'd be taking strolls on the moon about a thousand years before we did - the man found a way to cope with infinities SEVENTEEN CENTURIES before anyone else breaking open the way for modern math 3 centuries before Christ was supposed to be born and that, in my book, is what makes him the greatest.).

[@Cats2Fat]

Euler was so clever....

[@ehgugu]

라마누잔처럼 복잡기묘한공식을 알아내는 천재도 멋있지만 오일러같이 간단명료하고 아름다운 공식을 알아내는 사람은 더욱 빛난다.

[@henrikklausen1527]

Hi Dr. Dunham. Great lecture. How come my Ti89 can't factor the polynomial X^4 - 4X^3 + 2X^2 + 4X + 4

[@EliezerPennywhistler]

+Henrik Klausen Low batteries.

[@JSSTyger]

Your TI-89 is weak, that's why.

[@tinafeyalien]

Even Wolfram Alpha is no match for Euler.

[@ujjwalrana5899]

greatest mathematician euler

[@barracuda7018]

Yes but together with Gauss !!!!!!!

[@chasr1843]

Gauss is # 2. He was very precise but nowhere near as productive as Euler.. /me says Euler is the greatest mathematician of all time. That includes Gauss, Newton, Archimedes, and anybody else.

[@smackronme]

Most entertaining video I have ever seen..

[@davidmilunic]

I'm hooked! Just ordered your book in hard cover!

[@Zagg777]

Excellent topic. Delightful lecturer.

[@alvans431able]

sir... there is one video here @ youtube that says John Neper was the proponent of number " e" . How true is that?

[@grahamashtonuk2554]

NAPIER

[@Samgurney88]

In the second volume of Die Welt Als Wille und Vorstellung Schopenhauer said something similar to the final quotation, from which I presume it must be derived: 'talent is like a marksman who hits a target which others cannot reach; genius is like the marksman who hits a target which others cannot even see.'

[@travisbaskerfield]

Loved this!

[@oxm18]

WHY DON'T YOU SHOW THE 58 MORE ???????????????????????

[@steve.T.]

Mario Mirdita but that is why google exists

[@zugzwangelist]

That was an amazing talk!

[@porttikivi]

No mention of totient function, cyclical modular exponents and modern cryptography?

[@raminarezou1009]

Euler is everywhere from Engineering to science

[@factsverse9957]

I think Euler wrote the way he tried to find out, it's to show people how he stumbled across the theorem, and so he can churn out more work quickly. Imagine writing a proof but you wrote it directly on the paper. It will be faster than doing it separately first and then copying over, it's efficient.

[@joetursi9573]

Absolutely a joy!!

[@lzuricn]

this is sooo coooooool!!! if i could do a fraction of what Euler did...man. lol Happy Birthday, Euler(:

[@davidwilkie9551]

Neuroscience has identified structures in brains that, for the want of a definitive description, demonstrate resonance in superimposed patterns of number dominance that are e-Pi-i sync-duration connectivity probability, by default, a kind of push-pull muscle memory that interprets perspective arrangements. Everyone has met others who have super memory association abilities, and some have the moving picture attribute that goes with musical chords and timing modulation, natural probabilistic integration that seems to be what Euler has exhibited in abundance.., Savant style...

[@serverhunter]

agree, that was seriously insane the way it fell together like that

[@LPSCinemaCamilleM]

Happy birthday ! We April 15, 2013, so I celebrate this anniversary !

[@henrikklausen1527]

Very good lecture !

[@ravikantpatil3398]

Excellent presenrion with raising power of homour

[@imranq9241]

He should have mentioned that the infinite series sum requires a

[@AprendiendoConBaez]

Thanks for sharing

[@comic4relief]

At 21:38-- Is not the circumcenter the center of the circumscribed circle?

[@josesaldivar655]

Euler decided to look like being in a commencenment ceremony in the first portrait !

[@krave3746]

Euler had a simple rule; Less distractions

[@steveshreeve]

Excellent!!!

[@kecl5596]

Leonhard Euler gelmiş geçmiş en büyük Matematikçidir.

[@SampleroftheMultiverse]

Is anyone familiar with Euler’s or anyone else studying this variation of Euler’s contain column studies? The video and white paper describes the mechanical properties related my unique variation of Euler’s Contain Column studies. It shows how materials (representing fields) naturally respond to induced stresses in a “quantized“ manor. This process, unlike harmonic oscillators can lead to formation of stable structures. The quantized responses closely models the behaviors known as the Quantum Wave Function as described in modern physics. The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems. The model shows the known requirement of exponential load increase and the here-to-for unknown collapse of resistance during transition, leading to the very fast jump to the next energy levels. kzbin.info/www/bejne/raOlpKSfepWpfZYsi=waT8lY2iX-wJdjO3

[@perjalananmasihjauh]

I put the euler identity into matlab, and I got this: 0.0000e+00 + 1.2246e-16i pretty close to zero but not absolute and it is not in a form of integer. I need some explanation on why it is important, this identity?

[@edukid1984]

@bur bur MATLAB doesn't return exactly zero because its underlying code doesn't actually evaluate exp^(pi*i) analytically but through a numerical algorithm. That is important for rapid computation but it comes with NEGLIGIBLE errors from time to time, such as your example. The identity per se is merely a surprising yet elegant outcome of the expression exp^(i*x) = cos x + i sin x, which I think is far more important. It allows for the sensible computation of complex exponents and also link trigonometry with complex numbers, two fields of mathematics that are essential to physics.

[@MagicBoterham]

Go back and do it with Variable Precison Arithmetic.

[@glutinousmaximus]

Produced 2008. Good post - Thanks.

[@arnehessenbruch]

Great fun!

[@atimeandaword9921]

What a brilliant lecture