Academics From The United Kingdom

"If there wasn't air around me, I'd die very very quickly... and math is like that for technology. Take the math away, the technology fails, but just like the air around us it's invisible, and lots of people don't know it's there."

"Who was the most famous female mathematician? ...Emmy Noether, [was an] excellent... fantastic mathematician, but if I went into the street, who would know Emmy Noether? ...Even more famous than Marie Curie. Films have been made about this woman. Ada Lovelace... famous, but not as famous as this one. I've seen films, books have been written about her. Hugely famous, most children would know her name. I'm going to put her picture up and it's going to surprise you. ...Florence Nightingale's an incredibly famous woman because... she basically founded modern nursing. ...The story ...she was sent to Crimea and... set up hospitals... which saved huge number of lives, and when she went back to England she developed modern nursing and her practice... are used all over the world, and everyone thinks she's a nurse, but... she was a . She was one of the first members of the and was a really good statistician... [T]he way she cured people wasn't so much through medical care. It's through the... more modern approach, which was to try to work out what was causing people to be ill. ...[S]he gathered loads and loads of data on this and... produced graphs of this data... essentially to convey what she was doing to politicians, because politicians then and sadly now, don't know what numbers are... [S]o she did this through graphical information and she developed... rose diagrams which are very like pie charts... [S]o she not only developed ... she also developed graphical presentation of data, which is universal, and she's incredibly famous, but noone knows she was a mathematician. ...The Royal Statistical Society ...building is called the Nightingale building, after her."

"Various things happened in 1917. We had the Russian Revolution, the Great War was going on in Europe, and America came in on the side of the allies... and so a lot of people were being injured, and they had s... Madame Curie was driving... an ambulance X-raying people. ...You could see some detail, but not very much, and it was realized that Radon's [object] formula... if it could be made to work, could turn an X-ray into a really good image that could show you what was going on. ...[T]hey didn't have the technology to do that. You had to wait 50 years for computers to be powerful enough to use that, and a company called EMI with a guy called Cormack developed the computers... the scanner... and that was the first scanning device. ...[T]he scanner that relies totally on Radon's formula, with a lot of other stuff. Cormack got the , quite rightly, for doing that. So that's all based on math. ...Medical imaging has utterly transformed medicine, hugely reliant on maths. ...[I]t's an area I work in myself."

"[A] ton of math was involved as well. You have to produce tables of the motions of the sun and the stars... These ephemerides... were calculated by computers. ...A computer in those days was a room full of people who computed. ...They were typically youngish people, often students, and it was found ...that women were better at it than men ...[T]he midshipmen on the boat doing navigation had to do long [tedious 22-step mathematical] calculation based on these [tables] to [plot a ship's position] find where they were. But those calculations changed the world."

"In the 18th century... people traveled... by boat, but the problem... was... that they were finding it very difficult to know where they were. ...[O]ne of the big problems of the 18th century was finding your position at sea. ...We have , which is the angle from the equator, and , which is the angle measured round... from London. ...I've stood on the zero longitude line in . ...[T]he first thing they cracked was latitude. So you could work out your latitude... by using... the , which measures angles very accurately... [T]hey realized that if you measured the angle between the sun and the horizon, or between the pole star and the horizon, you could... accurately find your latitude. ...[Y]ou had to use a ton of ... [i.e.,] more math, in fact trigonometry on the surface of a sphere, which is... ... [T]rigonometry and the sextant combined... meant that navigators could work out their latitude... how far above the equator they were."

"Why is America such a powerful nation? Because you could reliably sail your ships to Europe and sell all your stuff, and that reliability came from navigation, and that navigation relied on math."

"People often say there's a close link between math and music, and mathematicians and musicians, and that's absolutely true. Music uses a lot of math. So some musical notes sound better when you play them together. ...The reason was discovered by... Pythagoras. ...He is very very famous for Pythagoras' theorem, which was invented by the Chinese about 1,000 years before him. ...But he absolutely did do the work on musical notes. ...[H]e measured the length of strings of instruments and he compared the lengths with notes that sounded good together. ...He realized that the octave [C:C] corresponds to two strings, one being twice the length of the other [2:1], C:G ... 3/2 and C:E proportion 5/4, and Pythagoras found an incredible link between musical harmony and fractions."

"Pythagoras... took the idea further. He said... let's suppose that we have a sequence of notes with simple fractional relationships. So he came up with notes with these relationships [the Just scale] [C] 1 : [D] 9/8 : [E] 5/4 : [F] 4/3 : [G] 3/2 : [A] 5/3 : [B] 1/ 5/8 : [C] 2 So Pythagoras invented the scale... the basis of modern Western music..."

"The calculations were tedious. They took a long time. They were also very error prone, and so people thought... can we automate these using machines? So... Babbage, working with Ada Lovelace... a very very fine woman computer programmer, essentially the first ever computer programmer, worked together to design the machines which would automatically calculate these tables [the Ephemerides.] Sadly they never managed to build them properly due to engineering problems, but Babbage's machine has been recreated... at Science Museum. You turn the handle, all the cog wheels go round and it calculates the tables for you. Brilliant! ...[B]abbage's ideas led directly on to the invention of the modern computer, with Turing, von Neumann and people like that, and that all came directly by navigation and the need to do that."

"I would argue that mathematicians save hundreds, if not thousands, if not millions of lives, almost every day. ...Medical scanners have revolutionized medicine because you can be scanned and... find out what's wrong... without cutting you open. ...[T]he medical scanner was basically invented by ...Radon ...one of my favorite mathematicians ...[H]e did brilliant maths which is used in medical imaging and saves millions of lives. He's a fantastic mathematician, and he was studying in 1917 a kind of abstract problem. He was looking at shadows. You know, objects cast shadows, and he wanted to know if you know what the shadows were, can you find out what the object was that cast them... [H]e wrote down a formula for taking an object and the shadows it cast, and then with a bit of genius, he worked out another formula saying, if you know what the shadows are, this is what the object is. f is the object, R is the object.{{center|1=Shadow \quad R(\rho,\theta) = \int f(\rho \cos(\theta) - s\sin(\theta),\rho\sin(\theta) + s\cos(\theta))ds Object \quad f(x,y) = \frac{1}{(2\pi)^2} \int\limits_{-\infty}^{\infty} \int\limits_{0}^{\pi} \int\limits_{-\infty}^{\infty} e^{ik(x\cos(\theta)+y\sin(\theta)-\rho}) R(\rho,\theta) \left\vert k \right\vert dk d\theta d\rho}}"

"Maths is universal."

"[I]n the 18th century the idea behind the labyrinth was evolved into... the modern maze, and people... used to build mazes in their large houses... designed to trap the unwary. You'd go into them and... occasionally get lost... People would try to puzzle how to get from the entrance into the center."

"Euler... worked out the math of how you could get into the center and... back out again, and that math led him into the theory... of networks, and that all came out of mazes. What do we use networks for now? ...[T]he biggest network in the world is the internet ...and Euler's work on mazes is directly used to help us do the internet. ...[W]hat uses that, Google. Understanding networks, combined with Matrix Theory (due to Cayley) also forms a major part of the algorithms behind Google."

"Math was... invented to count things with. What was it then used for? ...Once you have numbers 1,2,3,4,5, and 6... and you want to start using them, you... find they're not useful for everything. You have to invent... more numbers... to include things like 0... invented around the year 0, and negative numbers were invented to deal with things like debt, and s were invented... I suppose you've got 3 fields and... 5 children, then each child will inherit 3/5 of a field. So they were invented to deal with that."

"The ians were a little... more advanced. They used the knuckles as well. They counted not only in 10s but in 60s... and that's why we have 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle."

"What was the first application of numbers? ...[W]e're pretty sure that the first application... was ...the tax man. Why can we be sure... because if you go to museums... you can find Babylonian cuneiform tablets... and the [Egyptian] Rhind papyrus... where there's loads of wonderful maths developed, and it's all to help the tax man."

"We had a... newspaper competition in the U.K.... to identify the greatest ever invention... and I wrote in ...calculus. ...It didn't win. ...The greatest ever invention was apparently the ...the second was the , and the third was fire... which was misguided because calculus is, without a doubt, the best tool that we have... But of course, I am biased."

"The great triumph of maths around... 1690 was the development of calculus... and calculus is now probably the best tool that we have in math to tackle the problems of the real world."

"[A] lot of maths doesn't develop by solving problems of practical importance. A lot of it... develops purely out of curiosity, of from doing stuff for fun! ...You're doing maths when you do Sudoku, and it's good fun ...[S]olving puzzles ...and having fun is ...an extremely good way of doing math, probably the best way."

"[[w:Recreational mathematics|[R]ecreational math]] is a huge... subject... [A] particular favorite of mine... s and labyrinths, which were originally recreational. One of the earliest examples... involves... the ... the product of a between the queen of King and... Zeus, dressed up as a bull... turned into a bull, or whatever they do. The product... was the Minotaur... half man and half bull... [H]e was... ferocious and... lived in the center of a labyrinth underneath the palace of King Minos. ...Theseus... said I will go with the 9 young men and 9 young women and... attempt to kill the Minotaur. So when he went to Crete he was met by one of my heroes... ... the first female mathematician... recorded in the classical literature. ...[S]he gave him a sword. By the way she fell in love with him. ...[S]he also said ..."I will give you an algorithm for cracking the labyrinth ...and using this algorithm, he went into the labyrinth, found ...[and] killed the Minotaur, got out of the labyrinth and took the young men and... women back to Greece... [O]n the way he stopped off at an island... where they had a great party... and only after they had sailed off did they realize they'd left Ariadne behind, and she died of a broken heart and turned into a spider... [T]he real hero of the story is the labyrinth. ...[T]his design, although they've found it everywhere in the ancient culture, is universal. There are clear examples of Native American populations in the U.S. having essentially discovered the same design."

"I want to tell you a little... about some of the algorithms that have been used to solve mazes. ... ...was a mathematician and a computer scientist, because she came up with [an] algorithm for solving the maze or the labyrinth, and her algorithm was beautifully simple, but remarkably effective. She gave Theseus a ball of thread... and as you go into the labyrinth you unwind it and... to get out, you wind it up again... It worked very well, and that is the basis of a modern computer algorithm called the Flood algorithm for solving the labyrinth."

"On the whole, mathematicians don't have a particularly great image."

"Another algorithm is, if you... read the book '... they try and solve , and... Harris... says you solve it by always turning left, or... you put your left hand on the hedge and keep it there, and that will actually work... and it will solve a lot of mazes. It won't solve all of them, but it's... a very good algorithm to try. It will always get you out of a maze, even if it won't get you into the center. So always turning left is a good algorithm."

"A labyrinth with this of [King Minos] design is... unicursal, which means that you can go in and out without making any decisions... So you didn't need the thread after all, but the other mazes like Hampton Court and , and all the other ones, you have to do a little... more. So a labyrith is something where you don't have to make decisions..."

"This scale was used... up to about the 18th century... [when] keyboards were invented. ...It was found that this scale worked brilliantly for one key, but terribly in another key... because the ratios differ... and so the mathematicians developed a different [[w:Equal temperament|[well tempered] scale]] where the notes were constantly varying in frequency [in the same proportion, a geometric progression of the semi-tone frequencies], so the ratio is this wonderful number 1.059.. = 2^\frac{1}{12} which is the number when multiplied by itself 12 times gives 2, which works well in all keys."

"Bach was very familiar with this work going on, and he so liked the well tempered scale that he wrote... ' where you go through every key on the harpsichord... and it's all based on maths, and it's the maths of s... [I]t all goes back to mathematicians working with musicians. We're not evil, souless people at all."

"So one way to get to America was that you would sail from England on the same latitude, and when you got to something big that was probably America, or possibly Canada."

"was the big problem... Many mathematicians tried to solve it using math alone, but the solution was a beautiful one, and it's the sort of math I do... a combination of sums on paper, but also a lot of work with a computer, so it's combining technology with formulae. ...[T]he solution ...was due to ...Harrison, who was a clockmaker... [I]t was based on the observation that the earth goes once around every 24 hours and so if you can time when the noonday sun is, and measure that time on a clock which is the same as the clock in Greenwich, for example, then by measuring that time you could... work out how far around the earth you are. You have to do a whole ton of other stuff as well, but that's the basic idea. ...[T]hat was math, but it was also linked up with technology because you needed the clock ...[H]arrison's clock, called H4 ...was the first clock ...accurate enough to make that possible."

"View #1 about math: Math is completely useless. Another one... Mathematicians are evil, soulless geeks... [A]nother... everyone seems to believe: All mathematicians are mad! ...Unfortunately, they are views quite commonly held."

"Where did math come from? ...Early people counted on their fingers, and numbers basically came from that. ...There's no other reason for choosing ten. Ten isn't a great number for a base. Very few numbers divide into it. If we had 12 fingers we would have been better..."

"But then he did something which mathematicians can do... [i.e.,] what-if experiments. You can say... what if these equations have other solutions, and he found... waves with the same speed as light, but a different and than light... and we now call them radio waves. ...Maxwell discovered radio by pure mathematics alone. It was later... that... Hertz found them experimentally, and... later... Marconi and others took the theory and turned it into practical means of communication."

"Faraday... wasn't a mathematician and so he relied on other people to do his math... and Maxwell... took Faraday's experimentally derived results, and... turned them into mathematical equations.{{center|1=\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} - \mathbf{M}, \quad \nabla \times \mathbf{H} = -\frac{\partial \mathbf{D}}{\partial t} + \mathbf{J}, \nabla \cdot \mathbf{D} = \rho, \quad \nabla \cdot \mathbf{B} = 0.}} ...and these are called Maxwell's equations, and if you go to Edinburgh and you see his statue, on the base of the statue you will see these equations... which link electricity \mathbf{E} with \mathbf{B} and \mathbf{M}, which are magnetism, and \mathbf{J} is current, and \rho is charge, and these are... vector operations, and that's a derivative. ...Maxwell ...took those equations and looked for solutions, and... discovered that there were solutions... where you have an electric wave and a magnetic wave... paired... and traveling together, and he worked out the speed of those waves... exactly the speed of light. ...[I]n those equations he unified electricity, magnetism and optics all in one setup."

"I'm going to show a picture of a mathematician... that has changed your life profoundly more than anyone I could possibly think of. ...Whilst I'm a great admirer of Washington and Franklin and... all these wonderful people, I reckon this guy's changed your life even more... This is Maxwell, but... most audiences haven't a clue who this is."

"Much of industry has problems which can potentially be formulated and solved using mathematics. ...It's numbers. It's information. It's mathematics."

"[T]he shame about all of this is not only is it not true. It's really, really, really not true! ...Math is basically the basis of the modern world. The modern world would simply not exist without mathematics."

"[S]ome people are... quite frightened of math, or even... suspicious of math."

"But they then discovered something else, and... had to extend numbers a bit more. Suppose a farmer has a field and that field grows 100 cabbages. ...[T]he king wants to have a war so they need... 200 cabbages. How much bigger should my field be? ...It needs to have twice the area, and the area... is proportional to the square of the length of the field, so... how much bigger should the length of the field be, and the equation that you have to solve... is[W]e know the ns were interested in this problem because... a cuneiform tablet, which I believe is in the ... is... trying to solve this equation.... and... gives the answer. ...[T]hey tried to solve this using fractions and they... couldn't. There was no fraction which equaled the answer... and so they had to invent... what we call an irrational number to give a solution... 1.4142135623730950488... That's to 20 decimal places, and it goes on and on and on. ...[T]hese were numbers called s, and were originally invented for the tax man to work out how to double the area of fields."

"So... [who needs math?] Thirty years ago [traditional industrial users] typically using mathematics... [were] telecommunications, the aircraft industry [aerospace], power generation, oil, iron and steel, weather forecasting... a big user since the 1920s, security-code breaking... and of course, finance."

"The way maths is used... has... changed enormously, essentially in my own lifetime. ...The whole thing has changed remarkably, largely because of the develoopment of computers."

"Math is also developed by curiosity, and just pure abstract reasoning as well, so there's lots of ways it works."

"So this is error correcting, which brings us right up to date with the information age, sending huge amounts of information around the world, sending stuff around with Google. Absolutely fantastic."

"The way you... deal with... a problem from industry is you take all the math that you know... and you try and solve the problems with it. ...[A]fter a while you find that you've run out of math. The math that you've learned isn't enough to... solve the problem. So...you have to... invent new math, and... that new math can be... abstracted and turned into other stuff, and then... used to solve new problems, and... you look at those new problems and... find that you need new math from that... and so it... cascades, with problems generating maths, generating problems, and so on. ...[I]t's a really good virtuous circle, and this is... how math is developed over many years."

"So film, entertainment, graphic design, the retail industry uses lots of mathematicians. When you go and buy something... sadly, they're collecting data... If you go to Amazon and... buy a book, it will say, "People who bought this book also were interested in this!" ...[T]here's a mathematical algorithm that's doing that. ...It's great news for young people, because... there's vast numbers of jobs, if you stick with the maths."

"Seventy per cent of the funding of the World Health Organisation comes from commercial entities…. As long as the WHO is getting industry funding or funding from vested interests, it should not be considered independent and the Indian government should ignore its advice. Those commercial entities are not interested in your health, they will make money by deception."

"Wherever the Aryans originated, whether their culture was a development of indigenous cultures or whether they migrated from elsewhere."

"the Sutlej ‘flowed southwards from the Himalāya . . . and onwards, through Sind, to the sea’—until, for some reason, a prince-turned-ascetic named Puran, a hero of many Punjabi legends, cursed the river to leave its bed and move westward. ‘The stream, in consequence, changed its course more and more towards the west, until, six hundred and fifty years ago, it entered the Beas valley . . .’, which would take us to the thirteenth century CE; but leaving aside the date, the consequence was ‘a terrible drought and famine in the country on the banks of the Hakra, where [large] numbers of men and cattle perished. The survivors then migrated to the banks of the Indus, and the country has ever since been desert’... ‘the traditions of all the tribes bordering upon it [the Rann of Kachchh] agree that this expanse of salt and sand was once an estuary’... The course of the ‘lost river’ has now been traced from the Himalaya to the Rann of Kach . . . We have also seen that the Vedic description of the waters of the Saraswatī flowing onward to the ocean, and that given in the Mahabharata, of the sacred river losing itself in the sands, were probably both of them correct at the periods to which they referred."

"Although the river below the confluence [with the Ghaggar] is marked in our maps as Gaggar, it was formerly the Saraswatī; that name is still known amongst the people."

"The first person who attempted to correlate the textual descriptions of Sarasvati with empirical paleogeology was C. F. Oldham, in 1874. He surmised that "the waters of the Sarasvati [are] continuous with the dry bed of a great river [Hakra], which, as local legends assert, once flowed through the desert to the sea"."

"(the Rig Veda in one of its hymns clearly places the river) ‘between the Yamuna and the Satudri [Sutlej] which is its present position’. ... ‘it was formerly [known as] the Saraswatī; that name is still known amongst the people . . .’ Its ancient course is contiguous with the dry bed of a great river which, as local legends assert, once flowed through the desert to the sea. In confirmation of these traditions, the channel referred to, which is called Hakra or Sotra, can be traced through the Bikanir and Bhawulpur [Bahawalpur] States into Sind, and thence onwards to the Rann of Kach. The existence of this river at no very remote period, and the truth of the legends which assert the ancient fertility of the lands through which it flowed, are attested by the ruins which everywhere overspread what is now an arid sandy waste. Throughout this tract are scattered mounds, marking the sites of cities and towns. And there are strongholds still remaining, in a very decayed state, which were places of importance at the time of the early Mahommedan invasions. Amongst these ruins are found not only the huge bricks used by the Hindus in the remote past, but others of a much later make. All this seems to show that the country must have been fertile for a long period . . . Freshwater shells, exactly similar to those now seen in the Panjab rivers, are to be found in this old riverbed and upon its banks... ... ‘great changes in the course of the Sutlej have occurred in comparatively recent times. Indeed, only a century ago [that is, in the late eighteenth century], the river deserted its bed under the fort of Ludiana, which is five miles from its present course’... the ‘old riverbed generally known as Narra. This channel, which bears also the names of Hakra or Sagara, Wahind, and Dahan, is to be traced onward to the Rann of Kach59 . . . The name Hakra . . . is also applied to the Narra, as far as the Rann of Kach, so that the whole channel is known by this name, from Bhatnair [Hanumangarh] to the sea’...."

"Provisional age data now show that between 2000 and 3000 BCE, flow along a presently dried-up course known as the Ghaggur-Hakkra River ceased, probably driven by the weakening monsoon and possibly also because of headwater capture into the adjacent Yamuna and Sutlej Rivers."