Great video. Also, a bit of related news; A new Mersenne prime was announced today and discovered a few days prior, the 48th we know of, and it's M(57,885,161). It's thanks to Dr. Curtis Cooper but mainly also thanks to the huge amount of GIMPS volunteers.
Since 2017 the largest is now M(77,232,917) , the 50th so far - there may be more between 47 and this one . Source / further reading : en.wikipedia.org/wiki/Mersenne_prime
The "Goldbach Conjecture" (26:00 in video) can be asked equivalently as: "Is every integer halfway between two primes?" The Goldbach Conjecture is equivalent to saying that for each integer N, we can find d so that N-d and N+d are both prime (when N is prime, then d=0). This just suggests a different way of thinking about the problem.
If I may make a suggestion to the camera-men and the editor... When the speaker is referring to a slide, it is much easier for those of us who are not in the room to be able to see the slide as well. Not so much time needs to be spent with the camera on the speaker. Thank you.
Just checked Fermat's Prime Generating function for the case where n = 5. At 19:08 the slide shows 2 raised to the 32nd power + 1 = 4,274,967,297. This is not divisible by 641 as shown on the slide. Because the correct answer is 4,294,967,296 + 1 = 4,294,967,297. Which is divisible by 641. Just sayin' ..... :)
Alternatively, could you make the slides available for download? Then it's up to us viewers which one we want to look at. Thanks for all the great videos, I subscribed last year so that I would not miss any uploads :-) (PS: How about 720p recording? Not a huge priority, it would just look better)
Mathematics translated into artistic harmonics reveberating from a single note this beauty abstract with imagery of non concrete intangibles within the finente are understandable as it is the philosophic under carriage silently bourne by the leviathan beneath the waves
infinity is a symbol though representing the "ongoingness" of numbers, and can't be quantified. Numbers go on forever, so as they do, there will always be more factors for them.
Noticeable about primes.., is the way they assume dominance by "phase-locked" probabilities in continuity with the common unity, in continuing connection, so the search for conformity - the uncertainty principle -, generates a moving number sequence condensing out of the most probable existing primes in the selected circumstances, such as the resonant vibration of structures in everything from quarks to elephants. Each prime is a probability number coordinate system of other primes. At the limit of the process are the numbers that are innately constant algebraic functions, e, i, Pi etc "fitted" to the one connection in eternally shifting patterns of math, physics and chemistry, collectively called "Time". The symbol is not the thing, to believe in absolute proofs is a form of magical thinking, but in balance, not to attempt a proof is to avoid the dominant probability. Pedantic, and it takes the magic out of it so it's bad for fantasy. In the spirit of mathematics, opinion statements are the first guess approximations that introduce food for thought to exercise the mind. IMO Excellent presentation of core concepts.
My dear Kanvij - Ms. Winder was evidently referring to Professor Flood's presumed sexual orientation, rather than a serious classification of mathematics as a science or a non-science. Please refer to Zanzibar native Freddy Mercury of the British rock group Queen for further edification.
Right at the beginning of the lecture, he cites Gausee as calling mathemtaics "the Queen of the sciences" and "number theory is the Queen of mathematics".
I think of maths as the cement that holds the whole of Science in its proper place. Ie, it gives the most precise structure to Science that is available to us.
The slides ARE available for download, and the transcript too - we put up everything we have on our website (follow the link in the video description above). We're always fighting to up the quality and we have a route to improving it over the coming month or so...
