Addictive Number Theory, Vicky Neale | LMS Popular Lectures 2013

For hundreds of years, mathematicians have asked intriguing questions about adding whole numbers, for example concentrating on particularly important sequences such as the prime numbers and the square numbers.
In this talk, Vicky discussed some of these problems (solved and unsolved), and some of the elegant techniques from across mathematics that have been used to tackle these problems.
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[@deeprecce9852]

A great mathematician, but a even greater educator!! Respect!!

[@Shaolin-Jesus]

unfortunately deceased, just watched her here for the first time and found out, made me so sad

[@umerbinshabir6561]

Her way of explaining is so amazing

[@tronghai55]

Great lectures, this lecture is the mandatory cross roads for future advanced research in the fields of applied quantum physics at the Cern.

[@magicsqr3414]

Although I am already a number theory junkie, my beast of choice being the 3x3 magic square of integer squares (maybe my name gives that away), your enthusiasm is truly infectious. Many thanks for sharing this lecture.

[@KaelynWillingham]

Really good lecture here.

[@ytyewtc]

Hardy & Wright is one of my favourite books. I didn't know there was a new edition. Just ordered it. I can't wait.

[@ryacoli]

Is it any good?

[@ytyewtc]

@@ryacoli Slightly disappointing. Mainly a new chapter on elliptic functions probably covered better elsewhere these days.

[@mathschoolonline]

The field is principally devoted to consideration of direct problems over (typically) the integers, that is, determining the structure of hA from the structure of A: for example, determining which elements can be represented as a sum from hA, where A is a fixed subset.[1] Two classical problems of this type are the Goldbach conjecture (which is the conjecture that 2P contains all even numbers greater than two, where P is the set of primes) and Waring's problem (which asks how large must h be to guarantee that hAk contains all positive integers, where A k = { 0 k , 1 k , 2 k , 3 k , … } {\displaystyle A_{k}=\{0^{k},1^{k},2^{k},3^{k},\ldots \}} A_k=\{0^k,1^k,2^k,3^k,\ldots\} is the set of k-th powers). Many of these problems are studied using the tools from the Hardy-Littlewood circle method and from sieve methods. For example, Vinogradov proved that every sufficiently large odd number is the sum of three primes, and so every sufficiently large even integer is the sum of four primes. Hilbert proved that, for every integer k > 1, every nonnegative integer is the sum of a bounded number of k-th powers. In general, a set A of nonnegative integers is called a basis of order h if hA contains all positive integers, and it is called an asymptotic basis if hA contains all sufficiently large integers. Much current research in this area concerns properties of general asymptotic bases of finite order. For example, a set A is called a minimal asymptotic basis of order h if A is an asymptotic basis of order h but no proper subset of A is an asymptotic basis of order h. It has been proved that minimal asymptotic bases of order h exist for all h, and that there also exist asymptotic bases of order h that contain no minimal asymptotic bases of order h. Another question to be considered is how small can the number of representations of n as a sum of h elements in an asymptotic basis can be. This is the content of the Erdős-Turán conjecture on additive bases. en.wikipedia.org/wiki/Additive_number_theory

[@hochathanfire0001]

breathtaking

[@koenth2359]

46:40 ...On the twin prime conjecture.... Any of you sorted that excercise out yet? LOL very fine sense of humor!

[@alaskaj9786]

I have no idea what’s going on but her accent is awesome

[@alastairbateman6365]

Simon Singh, 'Fermat's Last Theorem' prime page 47 says ' Fermat's greatest love was for a subject which is largely useless - the theory of numbers.' Launcelot Hogben, 'Mathematics For The Millions' said words to the effect that ' when clever people lose contact with the common man they are in danger of becoming a priesthood. I agree with them both! Welcome to 'The Holy Tabernacle of Useless Mathematics' where within resides 'The Holy Arc of The Covenant of Abstract Mathematics'.

[@BRYDN_NATHAN]

thank you between four and seven is one prime number

[@shivamtrivedi1684]

👌👍👍

[@chowdhury1987]

I don't know whether i am attending a lecture on number theory or visiting a circus ! Mr. Perelman must have seen her "performing" to have said "...the animal on zoo.." comment !

[@powong4136]

Dr Vicky Neale should be congratulated for her summarizing many theorems in the past for all audiences who attended her lecture sponsored by the Institute of Education in London. I would like to take this opportunity to share with all audiences by sending to you a very interesting problem relevant to the number theory to watch by clicking the following website: plus.google.com/118141546473679947918/posts/6LWrsti19n1

[@jake180289]

Sorry Vicky, I can't let it go. Why is 1 not a prime number?

[@titanarmy4116]

because we said so. Maths is generated from some arbitrary made up axioms.

[@deniztunayalcin]

prime numbers are numbers that cannot be factored by any other prime than itself by definition. if 1 was prime then no number other than 1 would be prime that's why 1 is not prime. If 1 was prime (say) 13=13.1 which is obviously a prime wouldn't be a prime because it would be a product of ''two different'' primes.

[@Shaolin-Jesus]

@@titanarmy4116 not all of mathematics is the product of made up axioms

[@Wemdiculous]

Would have made more sense to use 32 columns

[@dsapienza2000]

With squares, I think 8 columns are better because quadratic residues mod 8 (remainders of the division of a square by 8) are just 0, 1 and 4; while mod 32 there are 7 quadratic residues (0,1,4,9,16,17,25) so with 8 columns it should be easier to find patterns. Is there a reason why you suggested using 32? I'm just curious, maybe I'm completely wrong...

[@mrboyban]

The rushy train

[@yujaehyun1925]

The first 30 minutes is WAFFLE But yes it is okay But not as amazing as I thought it would be :D I liked it hough any suggestions on what I should watch next?

[@PHILLYMEDIC69]

I think you’re a prime number

[@NothingMaster]

Anyone who could put on a pants like that can’t be all that bad. 😉 By definition, there can be no negative primes. The very fact that there is no prime number symmetry extended to the negative axis probably implies that the whole notion of primes is a baseless man-made pipe dream, with no underlying significance. And they are always looking for the largest prime number and checking to see if they would ever run out or not, and yet they could hardly extend the search to the transfinite realms! Yes, we’ve found some curious patterns and interesting observations regarding prime numbers, but so what? You look hard enough, you could find interesting patterns in just about anything, some even with corresponding observations in nature (the Fibonacci numbers etc.). The reveries of number theorists has always been highly entertaining.

[@brokenbauccner3945]

She said "particularly positive whole numbers" so are there any negative whole numbers?? Lol 😂😌

[@happyhanabi1632]

Whole numbers are numbers without a fraction or decimal place, AKA integers. And integers can be negative.

[@keepsmiling1304]

She is very fast where she makes the point to think..Only i hear blah blah multiple of eight.. blah blah multiple of eight. blah blah multiple of eight. blah blah multiple of eight....ANd i rewind what point is she making...Its really hard to understand who goes quick where a little time is required to atleast understand verbally ,what she is saying

[@chowdhury1987]

It seems she is the only 1 understanding whatever she is blabbering!

[@v.prestorpnrcrtlcrt2096]

Stop barking