50 Centuries in 50 minutes (A Brief History of Mathematics)
2024 ж. 29 Сәу.
547 406 Рет қаралды
John Dersch (9/19/12)
How did we get the mathematics that is studied today? Who was responsible for major advances in the mathematics that we now take for granted? When and where did this work take place? Such questions will be addressed by tracing the development of mathematics from 3000 B.C. to the dawn of the 21st century. There will be time for questions and suggestions for further study will be made.
The older I get, the more I realize math is one of the most interesting subjects to learn and master.
It is impossible to master no matter how much you try
Its essential to learn
Well said my dear friend
Couldn’t agree more
The older I get, the more pain of an ass it becomes to try to study math 🙃
I can't believe myself. I actually watched the full video in one go. The professor is an absolute delight to hear.
There wasn't a single boring moment in the entire video. The whole 54 minutes passed by in an instant. Amazing lecture 😃
Excellent lecture; he did an excellent job presenting what he characterized as "fifty weeks" of information in fifty minutes. He accomplished this by not presenting any mathematics per se, but he really had no choice and his presentation definitely discusses mathematics; he just doesn't show the equations. Very interesting talk.
I wanna thank you for uploading this, and thank Professor John Dersch for his excellent presentation.
Stunning. I like his lecturing style. Much better than what I experienced most of the time...
My goodness. I was only going to tune in for 5 minutes and ended up watching it all. He is simply brilliant. Thank you Sir!
a first-rate exposition done in an engaging manner! ;five stars out of five!
WoW ~ This lecturer John Dersch is SO wonderful ... He has the knack/gift for hiolding attention and imparting knowledge in a very engaging, interesting and personable way, ie with the sensitivity and depth of charisma~ I LOVE his style. Maybe the subject and his apparant appreciation for the history of mathematics is what makes his lecture so intriguing ...
Very good, comprehensive lecture! I think you covered all the key points of the development of most of the math we are familiar with and use today. Great job!
I was completely enthralled by the story and lost in the wonder of mathematics you created, until you said we're coming to the end! Great! Thank you! KeepSmiling 😊🌺
So happy to have come across this well thought out and beautifully articulated synopsis.
What a wonderful lecture. Thank you for posting this.
He is very easy to listen to. Thank you for posting. 🙏🏾✌🏾
Clearly goes beyond brilliant. A brilliant teacher. It is one thing to understand, it is something altogether exceptional to understand and then expand the understanding of others. Brilliant. Thank you.
Hi GRCCtv =), Thank you for taking the time and effort to both upload and share this video with the youtube family. I hope you have a nice day! =).
Dear Prof John Dersch, this is great history, perspective on mathematics. Can you please do one as a sequel to this one on the 20th century mathematics development so we can tie all the new developments and new branches of development together?
Absolutely brilliant! A very well delivered lecture, thanks.
It is videos like this that tip the scales to great for the use of YT. Here's a concise and entertaining view of people who shaped our world. I can't think of better lecture to introduce young minds to mathematics. Well Done!
He does an excellent job of conveying the, gravity, of Principia and its influence on just about everything in Science
What a brilliant lecture! This is the best timeline of math and an explanation of why we use the mathematics we do. The author,epoch spacing is perfect.
Excellent presentation, congratulations, very well done.
man just think if we had more professors like this we would be the smartest people on earth. love this guy! great job!!!
Compared to who?
@@eddykohlmann471 WHY AND HOW GRAVITY AND TWO DIMENSIONAL SPACE ARE CONSISTENT WITH WHAT IS E=MC2: E=MC2 is taken directly from F=ma. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! The TRANSLUCENT blue sky is manifest as (or consistent with/as) what is BALANCED BODILY/VISUAL EXPERIENCE. Accordingly, ON BALANCE, the TRANSLUCENT blue sky is true/real QUANTUM GRAVITY !!!! THINK !!! ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. Importantly, what is GRAVITY is an INTERACTION that cannot be shielded (or blocked) ON BALANCE. Great. You didn't forget to consider what is the orange (AND setting) Sun ON BALANCE, did you !!!!? Magnificent. I have FUNDAMENTALLY and truly revolutionized physics. (Lava is orange, AND it is even blood red.) GREAT !!!! Obviously, carefully and CLEARLY consider what is THE EYE ON BALANCE, as it ALL CLEARLY makes perfect sense ON BALANCE !!! (BALANCE AND completeness go hand in hand.). Fantastic !!! The stars AND PLANETS are POINTS in the night sky. What is E=MC2 IS dimensionally consistent !!! The density of what is THE SUN is then necessarily about ONE QUARTER of that of what is THE EARTH !!! INDEED, notice what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE !!!! What is E=MC2 IS dimensionally consistent !!!! Indeed, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! CLEAR water comes from what is THE EYE ON BALANCE !!! Excellent. Think. By Frank Martin DiMeglio
Such a beautiful presentation. Great job.
Thanks, really good video - I watched the whole thing, which is rare for a 50' vid - very well presented, well paced, easy going + humor. The referrals to books at the end is appreciated. The only criticism is the camera work - - couldn't always see what you were referring to. Would have been interesting hear a little more about mathematics in the 20th century, but maybe you need another 50 minutes for that.
no exaggeration , one of the greatest videos i watched all time. [ was never a good math student , but now will be ]
Great presentation. Thanks to Professor John Dersch
Very good survey of Math History. I too have degrees in Mathematics and Engineering, but I am not even a shadow of Dr. Shannon. While in school, I missed the Math History class. It was not in my priority at the time. Dr. Dersch, I think you did a great job. You and I know one could do the work for a PhD just in Math History alone. It is amazing what you can find on KZhead today. I know you were time-limited, but if I had my choice I would have added a section on Statistics and Probability. Thanks.
The professor knows what hes talking about. Great lecture.
Wonderful! Well paced and very interesting.
Very educative!! Thanks for the upload.
What an amazing teacher!
One of the more delightful 54 minutes and 21 seconds that I’ve spent lately!
this was a brilliant lecture, thank you very much
Nice talk. I find it amazing how difficult and long the process was that shaped the face of mathematics we are now familiar with, including the establishment of symbols like = + - * / that we find trivial nowadays.
Brilliant presentation!
Great summary of the history in maths in just 50 minutes! Awesome :D
This is amazing. It's like history of mathematics for dummies. Thank you Professor Dersch.
Deeply, deeply fascinating.
Thank you very much professor, it was a really interesting presentation. Now I 'd love a detailed account of each century :)
You could have ten lectures like this in succession and say after each one, "and then it gets more interesting ". Thanks.
Amazing lecture!
Thank you. Very engaging and comprehensive .
30:44 I love anecdotes like this. Truly lifts me up in a humanitarian way
Might want to mention that Leibniz was involved with the binary number system we use today way back then. From Wikipedia: The modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de l'Arithmétique Binaire (published in 1703). Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifically inspired by the Chinese I Ching.
Amazing lecture! The one missing name from the talk that I wish was mentioned was David Hilbert. Otherwise, I think this lecture was about as comprehensive as you can get for a 50 minute lecture on the entire history of math. Well done
Very interesting! I'm starting a module in history of mathematics tomorrow at King's College London and this was a great crash course!
thank you professor ! it was an awesome lecture :D
Fargen brill. It is so good when lecturers know their stuff and are prepared to part with it.
What is amazing is the fact that multiple civilizations produced different methods to give modern mathematics!
I saw a lot of argument here about who did what first. One fascinating bit of history which I was not taught in math was the Kerala school. 14th to 16th century and they already knew some calculus and stuff on infinite series.
Interesting one to know
even probably much earlier.
Currently 26 minutes in! I'm going to pause and take a sec to write that I hope he mentions Ronald Fisher being the father of modern day statistics. It's really cool to see the variation in the age of various disciplines within math!
Superb presentation, loved it. Only thing missing, for me, was the invention (or discovery) of imaginary numbers.
veritasium has it
The great thing about this video, is that most of us will be surprised! One may think that a 50 minutes talk, may be superficial... but the surprise is to learn something important...
Does anyone (perhaps someone who attended or took his class) have the missing slide (42:36) with regards to Galois Theory? The screen was not filmed when it was initially presented. This lecture is absolutely incredible, thanks for any help! =)
Thank you very much for posting this. I enjoyed it
EXCELLENT
Profesor Dersch being in the Mathematician side throws here two or three darts to Engineers, says for example that Shannon was in the Math gang but the Engineers abducted him. He could have mentioned the scandal that Electrical Engineer Oliver Heaviside caused when in he mid 19th Century he used an outrageous (for Mathematicians) method to solve differential equations. Heaviside was using the derivative operators "d/dt" (he shorted it to "D") as if it were a variable! As if in "1+1=2" we would require to know the value of sign operator "+" !! That happens in the middle of the endeavor to rigor and formalize Calculus and solve the "Limits Riddle." The scandal gave additional fuel to the will and initiative to clarify and formalize. That effort gave fruit with Set Theory, Laplace Transform, Fourier Analysis, Complex Analysis etc... . However, the longed for "Holy Grial, Mother of All" solid rock foundations proved to be non-provable with Gödel.
really lovely & interesting talk
Cool stuff, i wish math class would be more about discovery and critical think than drilling techniques no one learns fully. I hope to teach one day once Ive learned much more
Awesome talk, learned a lot and it was engaging and interesting
Absolutely fantastic lecture. *Very nicely done.* :)
I love this stuff!
Great video,I hope he had talked about complex numbers!
A splendid evening! Thanks!
Great lecture!
Fantastic lecture
Can you sum this video up as that early math was involved functions or to applied? Given the facts were based on some concrete/tangible evidences i.e. architecture that survived the destruction of time?
If Robin Williams was a mathematician...
Good Will Hunting
I was thinking the same thing. All that Dr. Dersch needed was about 27 cups of coffee to master Robin Williams.
Nice presentation of math history!
One way we still apply the sexagesimal system is that quantity of angular measure between 0 and 180 we term "degrees".
I wish I had more than 1 like to give this video. Give this man a raise.
I like how there was the one girl who always laughed at his jokes
She wants an A. Who was hacking up their lungs? Good gravy.
That's a teachers pet
@@johnking5433 no, she wants a d
Love this guy
So fascinating! Too bad he didn't go more deeply into 20th century mathematics though.
My this was a fascinating talk
I downloaded this Thank you.
Fantastic! Are there any other lectures by this professor online?
Good, quick intro to many of the highlights in the development of Mathematics throughout the past 25, or so, centuries. A few inaccuracies; The lasting impact on math of The Elements has much more to do with the Number Theory contained therein than the geometry. The Greeks knew about and studied Perfect Numbers, for example, in the third century BC. Another detail; the Method of Least Squares, which Gauss seems to at least have allowed people to believe was his, was the work of Legendre (1752-1833), a French mathematician. In the brief discussion of 20th century math at the end of the lecture, the professor seems to blur the two separate and equally epochal contributions of Claude E. Shannon; they are: the application of Boolean Algebra to the design of electronic (digital) circuits (Shannon's master's thesis "A Symbolic Analysis of Relay and Switching Circuits" MIT (1937)) and "The Mathematical Theory of Communication" in which Shannon presented the mathematical tools, based on probability theory and a concept he introduced called information entropy, which allowed for the design of the protocols which are the electronic backbone of all digital communicationn today. It IS gratifying to have the professor acknowledge the enormous contributions of Claude E. Shannon.
24:30 How do you graph your example ( x^3 + x^2 - x = 0) if you have only 1 variable, thus only a number line will be in front of you visually?
16:30네이피어가 체계적으로 소수점이용하기 시작 . 유럽에 퍼지게 된계기. 상용로그 이후 더 퍼져서 1650년경 보편화. 26:13 미적분전야상황
Very interesting (33mins30 or so). 1600 AD - 1700 AD: a century where at the beginning of it, everything - everything, not just in the field of mathematics - was essentially recognisable to anyone living before that time. At the end of that century, everything recognisable to us today was essentially observable, in politics, languages, nation states (if not yet politically but certainly ethnically), religion etc. History is like one of those old multiple-strand, hessian ropes lying messily on the deck of a ship before it is coiled tidily away, with some strands fraying, some strands splitting and broken...
i love teachers. theyre so awake!
I'm entertained - great lecture.
This is a very nice summary, but I think you should have mentioned Gentzen, shortly after talking about Gödel.
Well done! My vote for recent math that will remain relevant in 100 years is Bayes Theorem and probability theory for it's essential roles in artificial intelligence, physics, etc.
Bayes worked in the 18th century. That's not really recent thinking.
Terrific. Puzzled that he didn’t mention Bertrand Russell
"There's two ways of doing anything, the smart way and the dumb way. When you do it the smart was, that's mathematics." --Anonymous Lexington, Mass., grade-school kid, in MIT AI Lab play-skool program.
Hard to imagine a world without calculus and algebra. I guess that's what they all thought about geometry and counting numbers.
53:24 which book is his favourite?? I can't see what he's pointing at!!!
Good lecture. Makes me want to learn more Maths.
This is the first talk I have heard Claude Shannon receive his due. Impossible to overstate Shannon's contribution. Often neglected compared to Von Neumann and Turing, Shannon not only accomplished the practical engineering of the modern computer, but went on to enunciate the essential parameters of information science which endure unchanged today.
Wayne Isaacs - True. I studied information theory ca. 1970. I don’t recall coming across Shannon’s name since, until this.
Great lecture
Good content. Enough names to check for some videos about the mentioned people.
Sumerian cuneiform tablets : 3600 bc . 100 000 bc : cave men were drawing abstract symbols on the walls & they were most probably able to count what they were hunting . They were also counting the number of full moons ( we have discovered very old bones on which stripes were made ) , this to figure out when would start the hunting season ... Counting is VERY old ...
Amazing! He didnt mention about the originator of the idea of Algorithm, historically speaking.
Between 1120 and 1160, three Europeans translated the Arabic translation of Euclid's elements into Latin, making it possible for mathematics to become part of the curriculum of the earliest universities (Bologna, Paris, Oxford, Cambridge). Euclid in Arabic was readily available via Moorish Spain. 100 years later, the first European mathematician since ancient Greece appeared: Fibonacci. The Arabic numerals diffused slowly, not becoming common knowledge among educated people until 1500. Algebra as we know it emerged between 1450 and 1620. The first trig and log tables appeared starting around 1600. Around 1620, Descartes discovered the bridge between algebra and geometry: coordinate systems, and the pace of European mathematical discovery quickened: calculus, complex numbers, modern algebra, statistics, set theory, formal logic. Now the whole world studies the mathematics discovered in Europe and the USA over the past 500 years. The methods of proof used before 1830 often invoked vague concepts, and drew on unspoken intuition. Not infrequently, proofs were outright wrong, and this afflicted even Euclid's elements. Starting with Cauchy, Riemann and Weierstrass had to rebuild calculus from scratch, in the process creating real and complex analysis. Yet despite the frequent use of sloppy hand waving methods, effectively all of calculus derived before 1830 turned out to be correct, only badly proven. This historical bit shows that mathematics is, at heart, grounded in a powerful intuition. The 19th century pedantic fascination with proofs and definitions eventually led to formal logic and set theory and transformed mathematics into a collection of axiomatic systems.
Didn't the Muslims simply catalogue earlier Greek and near East scientific discoveries in their libraries, and after the dark ages, with Europe reinvigorated, the knowledge was re-learnt? After all, why nothing of any consequence from the Islamic world once Europe started back on the road to enlightenment? Why did all the great work take place in Europe, and also later by European Americans, while Muslim nations did little of note? Surely, if they had done so much previously it would have continued? Or, is it the case that Muslim scholars reached the peak of their abilities, and had benefited greatly from the work of others, and when they couldn't catalogue and observe the work of others they fell behind...rapidly? Seems like there's a direct correlation between Muslim decline and their access to the work of others. No question, the Islamic preservation of that knowledge was vital, but keep it must be kept in perspective. Or do you disagree?
@andrew ansyon You didn't address my point.
@andrew ansyon That Muslim scholars catalogued the work done by others, preserved it, definitely built upon it, but wouldn't have been anywhere without the knowledge of others, and as soon as Europe pulled itself together we had the Renaissance and Enlightenment, we had Newton and Darwin, we had the industrial revolution, then the age of standardisation and production lines, the combustion engine, advances in medicine and vaccination, surgery and pharmaceuticals, the microchip etc...centuries of progress and innovation, whilst Islam declined as an intellectual and military force. Seems a bit of coincidence, no? Why didn't they invent the steam engine in Tehran, or discover penicillin in Baghdad, or the lightbulb in Damascus? My point, was if Islamic scholars (and the general populace obviously) were anywhere near as capable and intelligent as you make out, by rights, it should have be Muslim world which built upon such solid foundations and became the epicenter of technological development. Instead, it floundered. I say, because once it could not rely on the work of others, coupled with, I'm sure, a less open and enquiring approach to the world, it fell behind very quickly. This enquiring approach is something which, by its very nature, must question the big themes of life and the universe, which invariably means tackling the subject of God, and this is where Islam becomes inflexible and finds itself at an impasse. You could not, and still cannot, as Muslim scholars in the Muslim world, broach the subject of God as being fallible or attribute things to anything other than God. It just isn't allowed. To them, the Qu'ran is the perfect, unalterable, infallible, word of God. The merest suggestion it might have mistakes is sacrilege and will see your head removed from your shoulders. This isn't a mentality or a place where the rigours of modern science can flourish. You couldn't have had a Darwin arguing natural selection in the Islamic world, could you? Surely, the response would be, God created all things and they are perfect. Anyway, I think I've made my point and I'm veering into territory that I'm not sufficiently well read in to make assertions. I am speaking broadly, within the bigger picture. I'm glad we kept it civil and I'd be interested to see if you agree somewhat with my general point.
@andrew ansyon So, your answer is "the Mongols"? Didn't Europe, the Soviets, and America go through hell and half obliterate itself in WW2 and within 20 years was mapping the genome and put men into orbit? Didn't Japan get nearly wiped from the face of earth by two atomic bombs and within decades were producing the most advanced electronic devices on earth? All empires and nations fall...it's how quickly they rise. Why didn't Islamic scholarship revive and rebuild, and continue its work? Was it because, when it required fresh thinking and not building on much that was already done by others, they couldn't really achieve much? You say Europe took the work of Muslims, as if that validates Islamic scholarship, but don't acknowledge the same thing when Muslims took the work of others themselves and try to invalidate the work of Europeans by saying they wouldn't have gotten anywhere without Islamic works. Isn't that a bit of a double standard? My original assertion was that much of the work, and therefore the advances, made by Islamic scholars was because they collected, catalogued, and preserved the work of other civilisations - and that those civilisations deserve the credit for much of what followed as Europe fell into darkness. Do you agree or disagree? Did Muslims build on the work of others, as you claim Europeans did? I feel like you are contradicting yourself somewhat.
@@prophetascending9021 Abdus Salaam is a Muslim , an ahmadi Muslim.
Very Good. Thank you.
thank you !
11:01 Rubaiyat is one of my favourite reads and memorizations. Omar was a mathematician of considerable penetration who also gave expression in poetry to Persia's freest thought.
Cosroe Cos roe?! 😊
If you havent read it in the original Persian, you are just an orientalist. I note that Persian polymaths were much better poets than modern scientists.
I love it when I find mathematicians that can explain math without mathematics ...