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 ...
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! =)
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?
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.
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.
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!
@@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
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.
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!
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.
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...
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.
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.
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
One correction, the dating of mathematics in India seems unrealistic. It should be before Egypt or at least on same time line of Egypt and Babylonia. Archaeologists have discovered some weight and measurement devices at Harrapa (Indus Valley) which are dated more than 5K years ago.
@ Michael Asta. Actually Michael, ancient Indians did a hell of a lot of things that either others have taken and claimed as their own or simply forgotten. I can share sources with you if u want ..
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 ...
Fibonacci only please because it fits into modern narrative that today's knowledge is Eurocentric.
5 років тому+2
There are many incorrect things in this video. 2:58 Egyptians knew the concept of mathematical proof. They proved things like the result of division by multiplication, etc... They had tables of doubling fractions (which was not trivial in the way they notated fractions) and each entry in the table had a separate proof. (see Rhind papyrus) 5:20 Is giving off the impression that there was no advancement in geometry from the time of Euclid to the time of non-Euclidean geometry. This is simply not the case. Greeks had no idea of the proof of the impossibility of trisecting an angle, or the impossibility of squaring the circle. The only regular polygons with odd number of sides that Greeks knew how to construct were triangle, pentagon and pentadecagon. They had no idea whether one can construct a heptagon or decagon, let alone the famous 17-gon. The list goes on and on. A lot of that stuff is learnt in high school... 6:40 Euclid's Elements has not been in print for 2400 years, what a ridiculous thing to say. The printing press did not exist for that long. Euclid's Elements was first printed in 1482. 8:40 The myth of "dark ages". How untrue... Between 400 and 1200 we have Boethius and Fibonacci, for example. Etc... Very imprecise for a mathematician...
A great deal of mathematics from India is still not known and not addressed in this lecture. The Fibonacci Series is actually the Hemachandra Series. Infinite Series was known to Indian Mathematicians 300 years before Newton or Leibniz; and so was the concept of infinitesimal and summation. So, several elements of calculus were also known to Indians before Europeans. Apart from that, more research needs to be done on the Sanskrit texts from the Vedic era, before Thales or others in Greece, coz there is a lot of math there as well. With time, a lot of things will surely change in academic teachings of the history of math. I am sure that Egyptians also knew whatever you talked about. The problem is that the west is still obsessed with the European roots of all modern day math.
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.
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...
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.
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.
#Zero (Base of MATHEMATICS) & #Vedic_Mathematics had been developed & designed in #INDIA about thousands of years ago when #European were #nomadic...🇮🇳
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
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
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.
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 have a question. Can the history of mathematics be displayed using only mathematical symbols? The use of highlight colours may be helpful. Is this possible?
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!
My apology for asking but, what was the story from function to distribution? Which one comes first? function first or distribution first?. I need the history of distribution (mathematical distribution) in the book form if you could enlight me on that issue. Thank you very much. Please accept my apology because I am not mathematician (yet). I am learning mathematics. Thank you very much.
whactya I see. When I study mathematics, I always wonder why things happen as they are. So, my apology if I ask something rather historical and fundamental. It seems that some ideas are used rather contextually in mathematics. I am hoping that you can always guide me when I need one. Mathematics is supposed to be interesting. However, many times, probably this is the only subject which is marketed rather poorly. I am a PhD graduate in marketing by the way. I would like to study math and earn PhD in math in 8 years time, God willing.
whactya Exactly. And this is the real problem. Education system has been McDonalized so that you can only take things on the menu. Once you get the menu, it will be delivered instantly in 3-5 years time. We are going to eat that menu within that time whether we threw up or not. We are never taught how the menu is made and from what ingredients. After finishing my PhD, I finally conclude that I had probably better off going to all libraries and finish their books rather than doing my education. Although my notion is not absolutely true, but I think, within todays context where knowledge is so easy to get, where universities are only a place to get a piece of paper, and where professors just tell you to go to library to read, I believe we need to rethink the way we should educate ourselves. In the ancient times, I believe that learning was so much an involved activity. However, all of the above is only my personal opinion. Others may disagree, of course.
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.
We Indians already established our maths initial surviving proof as veda. In yajurvedha we already have counting in 10 base, edited/organised date is around 3762 bce as of now...
Kiran. You are not allowed to mention that. In the West, today's children are taught about the ancient Greeks only on the subjects of science, mathematics and philosophy. Plato, Pythagoras, Hippocrates etc. No mention of how the ancient Greeks learnt mathematics medicine and science from the Hindus because there was a huge trade between India and Greece in spices, oils, dyes, cloths, perfumes from India of the times. India or the area known as India today was the richest economic zone in the world and was a seat of learning. Students from China, Japan, Korea, south east Asia, Greece, Egypt, Arabia etc came to Indian universities to learn but today only the ancient Greeks are given prominence.
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 😃
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.
Stunning. I like his lecturing style. Much better than what I experienced most of the time...
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 wanna thank you for uploading this, and thank Professor John Dersch for his excellent presentation.
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! =)
My eyes watered several times. I wish I had Dr John as my teacher or friend! I have no words to express myself adequately.
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?
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.
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.
a first-rate exposition done in an engaging manner! ;five stars out of five!
no exaggeration , one of the greatest videos i watched all time. [ was never a good math student , but now will be ]
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.
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!
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
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
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.
Fantastic! Are there any other lectures by this professor online?
So happy to have come across this well thought out and beautifully articulated synopsis.
One of the more delightful 54 minutes and 21 seconds that I’ve spent lately!
What is amazing is the fact that multiple civilizations produced different methods to give modern mathematics!
Superb presentation, loved it. Only thing missing, for me, was the invention (or discovery) of imaginary numbers.
veritasium has it
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!
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! =).
The professor knows what hes talking about. Great lecture.
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.
Excellent presentation, congratulations, very well done.
Thank you very much professor, it was a really interesting presentation. Now I 'd love a detailed account of each century :)
Fargen brill. It is so good when lecturers know their stuff and are prepared to part with it.
You could have ten lectures like this in succession and say after each one, "and then it gets more interesting ". Thanks.
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.
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...
Audio is lower than the ocean floor
What a wonderful lecture. Thank you for posting this.
This is great! Would love to attend a lecture like this.
Great summary of the history in maths in just 50 minutes! Awesome :D
53:24 which book is his favourite?? I can't see what he's pointing at!!!
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.
Great presentation. Thanks to Professor John Dersch
Very interesting! I'm starting a module in history of mathematics tomorrow at King's College London and this was a great crash course!
Wonderful! Well paced and very interesting.
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.
He does an excellent job of conveying the, gravity, of Principia and its influence on just about everything in Science
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.
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
I wish I had more than 1 like to give this video. Give this man a raise.
Such a beautiful presentation. Great job.
He is very easy to listen to. Thank you for posting. 🙏🏾✌🏾
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?
2 years late but it’s just y = f(x) = blah blah blah, and then graph it
One correction, the dating of mathematics in India seems unrealistic. It should be before Egypt or at least on same time line of Egypt and Babylonia. Archaeologists have discovered some weight and measurement devices at Harrapa (Indus Valley) which are dated more than 5K years ago.
Once again, the ancient Hindus are leagues ahead of everybody else. Fascinating.
@ Michael Asta. Actually Michael, ancient Indians did a hell of a lot of things that either others have taken and claimed as their own or simply forgotten. I can share sources with you if u want ..
No mention of Bertrand Russel
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 ...
Fibonacci numbers are in fact Hemachandra numbers
?
Fibonacci only please because it fits into modern narrative that today's knowledge is Eurocentric.
There are many incorrect things in this video.
2:58 Egyptians knew the concept of mathematical proof. They proved things like the result of division by multiplication, etc... They had tables of doubling fractions (which was not trivial in the way they notated fractions) and each entry in the table had a separate proof. (see Rhind papyrus)
5:20 Is giving off the impression that there was no advancement in geometry from the time of Euclid to the time of non-Euclidean geometry. This is simply not the case. Greeks had no idea of the proof of the impossibility of trisecting an angle, or the impossibility of squaring the circle. The only regular polygons with odd number of sides that Greeks knew how to construct were triangle, pentagon and pentadecagon. They had no idea whether one can construct a heptagon or decagon, let alone the famous 17-gon. The list goes on and on. A lot of that stuff is learnt in high school...
6:40 Euclid's Elements has not been in print for 2400 years, what a ridiculous thing to say. The printing press did not exist for that long. Euclid's Elements was first printed in 1482.
8:40 The myth of "dark ages". How untrue... Between 400 and 1200 we have Boethius and Fibonacci, for example.
Etc...
Very imprecise for a mathematician...
A great deal of mathematics from India is still not known and not addressed in this lecture. The Fibonacci Series is actually the Hemachandra Series. Infinite Series was known to Indian Mathematicians 300 years before Newton or Leibniz; and so was the concept of infinitesimal and summation. So, several elements of calculus were also known to Indians before Europeans. Apart from that, more research needs to be done on the Sanskrit texts from the Vedic era, before Thales or others in Greece, coz there is a lot of math there as well. With time, a lot of things will surely change in academic teachings of the history of math.
I am sure that Egyptians also knew whatever you talked about. The problem is that the west is still obsessed with the European roots of all modern day math.
Very educative!! Thanks for the upload.
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.
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
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.
Hard to imagine a world without calculus and algebra. I guess that's what they all thought about geometry and counting numbers.
What an amazing teacher!
One way we still apply the sexagesimal system is that quantity of angular measure between 0 and 180 we term "degrees".
great video though the sound of grass growing outside my window made it difficult to hear his voice (I live on the second storey)
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.
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!
#Zero (Base of MATHEMATICS) & #Vedic_Mathematics had been developed & designed in #INDIA about thousands of years ago when #European were #nomadic...🇮🇳
Absolutely fantastic lecture. *Very nicely done.* :)
Awesome talk, learned a lot and it was engaging and interesting
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
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
This is amazing. It's like history of mathematics for dummies. Thank you Professor Dersch.
Brilliant presentation!
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.
Pity about the sound quality, fascinating though.
You need better headphones or speakers. Sound quality is fine
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 ...
He never mentioned Ramanujan.
30:44 I love anecdotes like this. Truly lifts me up in a humanitarian way
I have a question. Can the history of mathematics be displayed using only mathematical symbols? The use of highlight colours may be helpful. Is this possible?
I have wondered that for a very long time too , its interesting .
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!
The subject of truth ,and mystery , fortified by logic and proof is Mathematics.
Great lecture! Thanks so much!
My apology for asking but, what was the story from function to distribution? Which one comes first? function first or distribution first?. I need the history of distribution (mathematical distribution) in the book form if you could enlight me on that issue. Thank you very much. Please accept my apology because I am not mathematician (yet). I am learning mathematics. Thank you very much.
Which one that came first: Function or set?
whactya
I see. When I study mathematics, I always wonder why things happen as they are. So, my apology if I ask something rather historical and fundamental. It seems that some ideas are used rather contextually in mathematics. I am hoping that you can always guide me when I need one. Mathematics is supposed to be interesting. However, many times, probably this is the only subject which is marketed rather poorly. I am a PhD graduate in marketing by the way. I would like to study math and earn PhD in math in 8 years time, God willing.
whactya Exactly. And this is the real problem. Education system has been McDonalized so that you can only take things on the menu. Once you get the menu, it will be delivered instantly in 3-5 years time. We are going to eat that menu within that time whether we threw up or not. We are never taught how the menu is made and from what ingredients. After finishing my PhD, I finally conclude that I had probably better off going to all libraries and finish their books rather than doing my education. Although my notion is not absolutely true, but I think, within todays context where knowledge is so easy to get, where universities are only a place to get a piece of paper, and where professors just tell you to go to library to read, I believe we need to rethink the way we should educate ourselves. In the ancient times, I believe that learning was so much an involved activity. However, all of the above is only my personal opinion. Others may disagree, of course.
what did the heckler say at 3:30?
adam freilich they said “ I hate Jewish people”
A splendid evening! Thanks!
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 did the “heckler” say in the beginning.
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.
really lovely & interesting talk
Deeply, deeply fascinating.
We Indians already established our maths initial surviving proof as veda. In yajurvedha we already have counting in 10 base, edited/organised date is around 3762 bce as of now...
Kiran. You are not allowed to mention that. In the West, today's children are taught about the ancient Greeks only on the subjects of science, mathematics and philosophy. Plato, Pythagoras, Hippocrates etc.
No mention of how the ancient Greeks learnt mathematics medicine and science from the Hindus because there was a huge trade between India and Greece in spices, oils, dyes, cloths, perfumes from India of the times. India or the area known as India today was the richest economic zone in the world and was a seat of learning. Students from China, Japan, Korea, south east Asia, Greece, Egypt, Arabia etc came to Indian universities to learn but today only the ancient Greeks are given prominence.
Newton was the first Westerner to discover the concept of gravity. In India this was established in the ancient times.
Plato was a vegetarian and believed in reincarnation... Vedic philosophy.
16:30네이피어가 체계적으로 소수점이용하기 시작 . 유럽에 퍼지게 된계기. 상용로그 이후 더 퍼져서 1650년경 보편화.
26:13 미적분전야상황
And what about Euler?!
thank you professor ! it was an awesome lecture :D
I downloaded this Thank you.