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.
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 ...
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 😊🌺
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.
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 UA-cam today. I know you were time-limited, but if I had my choice I would have added a section on Statistics and Probability. 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!
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?
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!
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.
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.
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.
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.
@@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
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.
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.
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
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 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
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 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.
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! =)
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...
#Zero (Base of MATHEMATICS) & #Vedic_Mathematics had been developed & designed in #INDIA about thousands of years ago when #European were #nomadic...🇮🇳
Whether people use rulers, clocks, money, gold, bricks, diamonds, coppers, bronzes, irons, steels, silvers, crystals, platinums, calenders, timers, watches, loans, fees, debit cards, credit cards, gift cards, express cards, checks, balances, cash, coins, bars, receipts, IOU'S, it all has some form of mathematical abilities involved
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.
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.
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.
"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.
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!
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.
This video is good and it tells a big truth. The elementary calculus rules and even the fundamental theorem of calculus were known intuitively long before Newton and Leibniz published their work, and it was communicated in a verbal form. Scientists, one century before Newton and Leibniz, knew that calculus rules were valid on polynomials. In fact, you can discover or guess all calculus theorems, intuitively, by working with polynomials, as the video says high school students do that all time. The problem was the notation to represent the calculus operations and its application. The correct notation for calculus was created by Leibni(t)z and the applications to difficult physical problems (the easy ones were solved by Galileo and his followers) was Newton's achievement.
Ah, I was hoping he would talk about our progression from whole numbers to all the other kinds of numbers. For a long time, people denied negative numbers, saying that you could not go behind zero. And then, once that was accepted, it took a long time for people to accept irrational numbers as well! Only pi was accepted, but things like the square root of 2 were thought to be non-numbers, and they denied irrational numbers for the sake of purity. And finally the imaginary numbers came along, and some of the greatest mathematicians of the time dismissed them in the same way that previous numbers were dismissed. In fact, I recall that the term "imaginary" was given to these numbers to be a derogatory term! It's interesting how, with each new generation of humans, we continue to progress in our thinking.
+Niflheim Actually the Indian mathematician, Brahmagupta did understand the concept of negative numbers and the number system and did call it debt as notation in the 7th Century. Further, the mathematician Madhava worked on the concepts of infinite series for calculating the value of pi to 16 decimal places; again 100s of years before European mathematicians. An 8th century mathematician, Aryabhatta used trigonometry(essentially defining the sine cosine and tangent fns) to calculate the distances of astronomical bodies, and even calculated the circumference of Earth correctly with an error of just 70 miles. So its actually sad that all India is remembered for and mentioned in this lecture for is the numeric system(and actually, zero the base 10 decimal system, fractions, 1/0, formal notations and many other concepts), credit for which we have to share with the Arabs . I guess that is how the West justifies undermining the achievements of those they oppressed and called heathens, deserving of subjugation.
+Drinko76 Yup, actually that's exactly what we have been for 4000 years. Pacifists to a fault. Probably why everyone else managed to fuck us over for so long. Not anymore though thankfully.
Amazing talk! Thank you! But referencing math and its influence to digitisation referencing Shannon, atleast if you think of computers, you missed for that the most important mathematician ... Alan Touring ... ! ...
Indians (Hindus) had significant advances in arithmetic, geometry, trigonometry in 3000 BC or earlier. Sulba Sutras talked of (so called) Pythogarous theorem, since then till 18th / 19th century there were significant developments in India on different aspects of mathematics including arithmetics, geometry, trigonometry, algebra and calculus... notable names of Indian mathematicians (and astronomers) include Aryabhata, Bhaskara, Brahmagupta, Panini, Pingala, Madhava, Mahavira, Varaha Mihira, Nilakanta.... and so on. Many of the details are available in web if one searches.!!!
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.
Bashing Fermat is common among modern mathematicians, but Fermat was CENTURIES ahead of his time in mathematics and physics. Fermat invented calculus (Newton STOLE Fermat's work), statistics, principle of least action/time, number theory (including Fermat's Little Theorem (used in modern cryptography) and numerous theorems, optics, etc... including his now famous "Last Theorem") and MANY other things. He was FAR beyond any "professional" mathematicians of his time. Modern mathematicians call him an "amateur" as a way to relegate him to the corners of history, because they want retribution for him not write down his proof to his Last Theorem (which is called the "Fermat's Last Theorem" because it was the LAST of his numerous theorems to be proven, since he left proof for only a few, and commonly challenged other mathematicians to prove things he had already proven). We also do not have the proof to his polygonal number theorem, yet mathematicians always conveniently sweep that fact under the rug (or simply are not even aware, but they get the standard line fed to them from the top of the mathematical community "food chain", and they never bother to question it).
apburner1 "There is nothing in Fermat's work that approaches the calculus that Newton developed." That is simply not true. Fermat developed all of the concepts that Newton used. He developed both differential and integral calculus. Newton fleshed it out a bit more, but he did not develop the core ideas which are the main hurdle. The core concept of infinitesimal rise over run is entirely due to Fermat. The core concept of area under the curve is entirely due to Fermat. Mathematicians tend to focus on the person that assigned arbitrary symbols. I think it is much easier to formalize a concept that is already developed than to developed an entirely new concept. And, Fermat, developed far more new concepts than any mathematician that has ever lived. Fermat invented calculus (Newton STOLE Fermat's work), statistics, principle of least action/time, number theory (including Fermat's Little Theorem (used in modern cryptography) and numerous theorems, optics, etc... including his now famous "Last Theorem") and MANY other things. It took several hundred years to prove all of Fermat's theorems. We *still* do not know how he proved his polygonal number theorem. We simply have NO IDEA. Some people have proposed he somehow used geometry, but we really have no idea. That is the entire mathematical community over the past 350 years or so. "He was a great mathematician, not a god." I don't think he was a "god", but he was a superhuman. Definitely no other human in history has had such great intelligence and creativity.
Euler... perhaps the greatest of the 18th century... but Lagrange should also be mentioned as a contender shouldn't he? I always hear Euler mentioned with regards to the 18th century... rarely Lagrange. Don't understand why.
+otakurocklee Euler may be the most influential mathematician who ever lived. His colleagues called him "Analysis Incarnate." Laplace, famous for denying credit to fellow mathematicians, once said "Read Euler: he is our master in everything." Euler was the most prolific mathematician in history and is often judged to be the best algorist of all time.
Yup, Euler is by far the most productive mathematician ever (Gauss being no.2). So many things come from Euler that we don't even know, but use every time we exercise mathematics. For example: f(x) - a notation for a function, Σ - symbol for sum; sin,cos - symbols for sine and cosine, Δ - symbol for difference, e - base of natural logarithm etc.. etc...
Very well done, both the mathematics and the presentation, which held my interest for the full program. I learned a great deal. I would like to see Prof. Dersch speak on the topic of the square root of 2. especially the proof that the SQRT(2) is truly a random number. I copied one of the 1 million-digit expansions of SQRT(2) and ran an FFT analysis, and was befuddled to see a flat noise spectrum, meaning to me random data. How can an algorithim produce random data ? Didn't know such was possible.
Yankton, do you know about the concept of normal numbers? That might be what you are seeing - that the digits seem to be equally distributed. Check here: mathworld.wolfram.com/NormalNumber.html
David Kotschessa Thank you for the normal-number referral. This is interesting. My interest in this area is related to the big effort which is going on to produce "truly random" numbers for encrypting valuable data. If it is true that the square-roots of certain numbers are irrational, are they not also random? My FFT of the expansion of the SQRT(2) showed no pattern. If the said irrational square-roots are random, then why waste big resources on seeking that which is easily had by invoking a very simple algoritim, which will easily crank out an infinity of "truly random" numbers ? Are random numbers normal ?
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 😃
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!
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.
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 ...
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 😊🌺
My eyes watered several times. I wish I had Dr John as my teacher or friend! I have no words to express myself adequately.
a first-rate exposition done in an engaging manner! ;five stars out of five!
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.
I wanna thank you for uploading this, and thank Professor John Dersch for his excellent presentation.
Excellent presentation, congratulations, very well done.
Superb presentation, loved it. Only thing missing, for me, was the invention (or discovery) of imaginary numbers.
veritasium has it
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 UA-cam today.
I know you were time-limited, but if I had my choice I would have added a section on Statistics and Probability.
Thanks.
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!
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?
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!
The professor knows what hes talking about. Great lecture.
Very interesting! I'm starting a module in history of mathematics tomorrow at King's College London and this was a great crash course!
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.
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.
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.
So happy to have come across this well thought out and beautifully articulated synopsis.
He is very easy to listen to. Thank you for posting. 🙏🏾✌🏾
Wonderful! Well paced and very interesting.
Thank you very much professor, it was a really interesting presentation. Now I 'd love a detailed account of each century :)
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.
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
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! =).
One of the more delightful 54 minutes and 21 seconds that I’ve spent lately!
Great summary of the history in maths in just 50 minutes! Awesome :D
What a wonderful lecture. Thank you for posting this.
Such a beautiful presentation. Great job.
What is amazing is the fact that multiple civilizations produced different methods to give modern mathematics!
Great presentation. Thanks to Professor John Dersch
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.
Very educative!! Thanks for the upload.
no exaggeration , one of the greatest videos i watched all time. [ was never a good math student , but now will be ]
Fargen brill. It is so good when lecturers know their stuff and are prepared to part with it.
Absolutely fantastic lecture. *Very nicely done.* :)
You could have ten lectures like this in succession and say after each one, "and then it gets more interesting ". Thanks.
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.
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
Brilliant presentation!
What an amazing teacher!
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 ...
Great lecture! Thanks so much!
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
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.
This is amazing. It's like history of mathematics for dummies. Thank you Professor Dersch.
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! =)
He does an excellent job of conveying the, gravity, of Principia and its influence on just about everything in Science
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...
#Zero (Base of MATHEMATICS) & #Vedic_Mathematics had been developed & designed in #INDIA about thousands of years ago when #European were #nomadic...🇮🇳
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
Whether people use rulers, clocks, money, gold, bricks, diamonds, coppers, bronzes, irons, steels, silvers, crystals, platinums, calenders, timers, watches, loans, fees, debit cards, credit cards, gift cards, express cards, checks, balances, cash, coins, bars, receipts, IOU'S, it all has some form of mathematical abilities involved
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.
really lovely & interesting talk
Someone said "if you want to know any subject well, knows its history". This is not just someone, it is Chairman Mao. Thanks for the professor!
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.
Fantastic! Are there any other lectures by this professor online?
Amazing lecture!
"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.
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!
A splendid evening! Thanks!
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.
I wish I had more than 1 like to give this video. Give this man a raise.
Awesome talk, learned a lot and it was engaging and interesting
I downloaded this Thank you.
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.
30:44 I love anecdotes like this. Truly lifts me up in a humanitarian way
The subject of truth ,and mystery , fortified by logic and proof is Mathematics.
So fascinating! Too bad he didn't go more deeply into 20th century mathematics though.
This video is good and it tells a big truth. The elementary calculus rules and even the fundamental theorem of calculus were known intuitively long before Newton and Leibniz published their work, and it was communicated in a verbal form. Scientists, one century before Newton and Leibniz, knew that calculus rules were valid on polynomials. In fact, you can discover or guess all calculus theorems, intuitively, by working with polynomials, as the video says high school students do that all time. The problem was the notation to represent the calculus operations and its application. The correct notation for calculus was created by Leibni(t)z and the applications to difficult physical problems (the easy ones were solved by Galileo and his followers) was Newton's achievement.
What about Brahmagupta who found zero and four fundamental operations the way we do today, negative numbers, fractions, etc
R rar. Yes but this doesn't fit into modern narrative. Civilization and knowledge must be shown to come from the ancient Greeks only.
Deeply, deeply fascinating.
Ah, I was hoping he would talk about our progression from whole numbers to all the other kinds of numbers. For a long time, people denied negative numbers, saying that you could not go behind zero. And then, once that was accepted, it took a long time for people to accept irrational numbers as well! Only pi was accepted, but things like the square root of 2 were thought to be non-numbers, and they denied irrational numbers for the sake of purity. And finally the imaginary numbers came along, and some of the greatest mathematicians of the time dismissed them in the same way that previous numbers were dismissed. In fact, I recall that the term "imaginary" was given to these numbers to be a derogatory term! It's interesting how, with each new generation of humans, we continue to progress in our thinking.
+Niflheim Actually the Indian mathematician, Brahmagupta did understand the concept of negative numbers and the number system and did call it debt as notation in the 7th Century. Further, the mathematician Madhava worked on the concepts of infinite series for calculating the value of pi to 16 decimal places; again 100s of years before European mathematicians. An 8th century mathematician, Aryabhatta used trigonometry(essentially defining the sine cosine and tangent fns) to calculate the distances of astronomical bodies, and even calculated the circumference of Earth correctly with an error of just 70 miles. So its actually sad that all India is remembered for and mentioned in this lecture for is the numeric system(and actually, zero the base 10 decimal system, fractions, 1/0, formal notations and many other concepts), credit for which we have to share with the Arabs . I guess that is how the West justifies undermining the achievements of those they oppressed and called heathens, deserving of subjugation.
+Sujay Pillai Cry me a river. Its not like your own culture has been pacifistic saints throughout history.
+Drinko76 Yup, actually that's exactly what we have been for 4000 years. Pacifists to a fault. Probably why everyone else managed to fuck us over for so long. Not anymore though thankfully.
Nice presentation of math history!
Amazing talk! Thank you! But referencing math and its influence to digitisation referencing Shannon, atleast if you think of computers, you missed for that the most important mathematician ... Alan Touring ... ! ...
this was a brilliant lecture, thank you very much
Though it is Euro-centric Presentation but gives good bit of a history of European maths.
Great video,I hope he had talked about complex numbers!
Great lecture!
Good lecture. Makes me want to learn more Maths.
Indians (Hindus) had significant advances in arithmetic, geometry, trigonometry in 3000 BC or earlier. Sulba Sutras talked of (so called) Pythogarous theorem, since then till 18th / 19th century there were significant developments in India on different aspects of mathematics including arithmetics, geometry, trigonometry, algebra and calculus... notable names of Indian mathematicians (and astronomers) include Aryabhata, Bhaskara, Brahmagupta, Panini, Pingala, Madhava, Mahavira, Varaha Mihira, Nilakanta.... and so on. Many of the details are available in web if one searches.!!!
You have to follow the modern narrative, knowledge and civilization began in the West with roots in ancient Greece.
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.
thank you professor ! it was an awesome lecture :D
Fibonacci numbers are in fact Hemachandra numbers
?
Fibonacci only please because it fits into modern narrative that today's knowledge is Eurocentric.
Audio is lower than the ocean floor
Thank you. Very engaging and comprehensive .
EXCELLENT
Bashing Fermat is common among modern mathematicians, but Fermat was CENTURIES ahead of his time in mathematics and physics. Fermat invented calculus (Newton STOLE Fermat's work), statistics, principle of least action/time, number theory (including Fermat's Little Theorem (used in modern cryptography) and numerous theorems, optics, etc... including his now famous "Last Theorem") and MANY other things. He was FAR beyond any "professional" mathematicians of his time. Modern mathematicians call him an "amateur" as a way to relegate him to the corners of history, because they want retribution for him not write down his proof to his Last Theorem (which is called the "Fermat's Last Theorem" because it was the LAST of his numerous theorems to be proven, since he left proof for only a few, and commonly challenged other mathematicians to prove things he had already proven). We also do not have the proof to his polygonal number theorem, yet mathematicians always conveniently sweep that fact under the rug (or simply are not even aware, but they get the standard line fed to them from the top of the mathematical community "food chain", and they never bother to question it).
apburner1 "There is nothing in Fermat's work that approaches the calculus that Newton developed."
That is simply not true. Fermat developed all of the concepts that Newton used. He developed both differential and integral calculus. Newton fleshed it out a bit more, but he did not develop the core ideas which are the main hurdle. The core concept of infinitesimal rise over run is entirely due to Fermat. The core concept of area under the curve is entirely due to Fermat. Mathematicians tend to focus on the person that assigned arbitrary symbols. I think it is much easier to formalize a concept that is already developed than to developed an entirely new concept. And, Fermat, developed far more new concepts than any mathematician that has ever lived. Fermat invented calculus (Newton STOLE Fermat's work), statistics, principle of least action/time, number theory (including Fermat's Little Theorem (used in modern cryptography) and numerous theorems, optics, etc... including his now famous "Last Theorem") and MANY other things.
It took several hundred years to prove all of Fermat's theorems. We *still* do not know how he proved his polygonal number theorem. We simply have NO IDEA. Some people have proposed he somehow used geometry, but we really have no idea. That is the entire mathematical community over the past 350 years or so.
"He was a great mathematician, not a god."
I don't think he was a "god", but he was a superhuman. Definitely no other human in history has had such great intelligence and creativity.
I love it when I find mathematicians that can explain math without mathematics ...
Wish I payed more attention in my calculus classes.
Terrific. Puzzled that he didn’t mention Bertrand Russell
Euler... perhaps the greatest of the 18th century... but Lagrange should also be mentioned as a contender shouldn't he?
I always hear Euler mentioned with regards to the 18th century... rarely Lagrange. Don't understand why.
+otakurocklee Euler may be the most influential mathematician who ever lived. His colleagues called him "Analysis Incarnate." Laplace, famous for denying credit to fellow mathematicians, once said "Read Euler: he is our master in everything." Euler was the most prolific mathematician in history and is often judged to be the best algorist of all time.
Yup, Euler is by far the most productive mathematician ever (Gauss being no.2). So many things come from Euler that we don't even know, but use every time we exercise mathematics. For example: f(x) - a notation for a function, Σ - symbol for sum; sin,cos - symbols for sine and cosine, Δ - symbol for difference, e - base of natural logarithm etc.. etc...
Lagrange was good, but not a contender in the league of Euler.
nneisler ramjnajan numbah 1
Very well done, both the mathematics and the presentation, which held my interest for the full program. I learned a great deal.
I would like to see Prof. Dersch speak on the topic of the square root of 2. especially the proof that the SQRT(2) is truly a random number. I copied one of the 1 million-digit expansions of SQRT(2) and ran an FFT analysis, and was befuddled to see a flat noise spectrum, meaning to me random data. How can an algorithim produce random data ? Didn't know such was possible.
Yankton, do you know about the concept of normal numbers? That might be what you are seeing - that the digits seem to be equally distributed. Check here: mathworld.wolfram.com/NormalNumber.html
David Kotschessa Thank you for the normal-number referral. This is interesting.
My interest in this area is related to the big effort which is going on to produce "truly random" numbers for encrypting valuable data. If it is true that the square-roots of certain numbers are irrational, are they not also random? My FFT of the expansion of the SQRT(2) showed no pattern.
If the said irrational square-roots are random, then why waste big resources on seeking that which is easily had by invoking a very simple algoritim, which will easily crank out an infinity of "truly random" numbers ?
Are random numbers normal ?
Fantastic lecture