University Of Cambridge Alumni

"You have to decide whether you always want to be Thierry Henry or Arsene Wenger. When I was younger, I thought I was always going to be Henry but someone opened my eyes to realise that overseeing the whole team, thinking about the strategy and getting the best out of others was much more satisfying."

"I've learned through difficult periods as a CEO that resilience is everything. I believe the ability to quickly recover from setbacks, rally for longer, and remain positive is a key differentiator for many top CEOs."

"Making everyone in the organisation you work in feels as though they can be the very best version of them at work as happy, engaged people are always more willing to go the extra mile, think the creative solution and engage more positively with customers."

"Empathy is absolutely critical for CEOs. In a politically uncertain world—with increasing divergence between the “haves” and “have nots,” you have to think carefully about how you show up as a leader and ensure you’re in touch with your customers, employees, and wider stakeholders."

"Being a purposeful company is all about corporate character, not corporate add-ons. A purposeful company will have a very clear sense of its long-term social mission and will be guided by that in its decision-making."

"But I think backgammon is even more beneficial because it revolves around managing probability, risk and reward"

"CEOs have always had to focus on running their company well, but, unquestionably, a CEO needs to increasingly focus on purpose, investing time and resources in making a wider contribution to the environment and to the communities where their company operates. They need to focus more on culture, as culture is the enabler of any upside, and it should guide you as a leader."

"A ship is sooner rigged by far, than a gentlewoman made ready."

"Catch occasion by the foretop."

"My Lord," a certain nobleman is said to have observed to the bishop, after sitting next to Bentley at dinner, "that chaplain of yours is a very extraordinary man." Stillingfleet agreed, adding, "Had he but the gift of humility, he would be the most extraordinary man in Europe."

"Different media of publication—textbooks, monographs, quarterlies, abstracts, and ‘review letters’—have been introduced, one after another, to meet new professional needs; and the historically changing operations of a scientific profession are reflected once more in the transfer of influence from one medium to another. The ‘s’ of seventeenth-century Europe were initially linked by the circulated correspondence of men like Henry Oldenburg. With the foundation of national academies, emphasis shifted to their Transactions and to treatises such as Newton’s Principia, which were published under their auspices. In subsequent centuries, the balance has again shifted several times: to quarterlies, to twice-monthly periodicals, weeklies, and even shorter-term publications. The proliferation of journals and the acceleration of publication are effects, in part of the fragmentation of sub-disciplines, in part of the sharpened competition for priority; but they are associated also with a great decentralization of scientific authority. Where no one can hope to master all the available concepts and theories, scientific professions were bound to move towards a pluralistic pattern of authority. On the very frontiers of research, indeed, we are now back not only with ‘invisible colleges’ but with a multiplicity of Oldenburgs, who circulate duplicated ‘prepublication’ material in highly specialized subjects to an international circle of equally specialized devotees. In the more self-consciously original branches of science—it has even been suggested—only out-of-date ideas ever actually get into print!"

"In Pascal's view, casuistry was the denial of true morality. It held out no vision of the ideals to which humans should aspire. It commanded no sacrifice, insisted on no heroic dedication. Not only did it trivialize the lofty precepts of the Gospel, it did not even hint at the "natural life of virtue" that had been espoused by Aristotle and Cicero. It was a mere farrago of excuses, loopholes, and evasions."

"Nothing enlarges more the gulf of atheism, than that wide passage, which lies between the faith and lives of men pretending to be Christians."

"If someone was to ask us to describe our , we might be hard pressed to find anything to talk about that we might say was at all interesting, because daily life suggests routine, and routine by definition involves things that are not out of the ordinary."

"... most sociologists who would want to talk about wine for one reason or another probably have some personal interest in it. Why spend so much time building up a for something you cannot stand, or which—if you are an alcohol-abstainer—you are opposed to on moral or some other grounds? After all, if you publicly present yourself as an analyst of wine, you are publicly associating yourself with it, and audiences will read you as linked to wine in some way. (The hostile reception to wine talks I have given, by students who seemed to be of a religious fundamentalist persuasion, is a case in point.)"

"At the heart of the Stoic doctrine lay a conviction which was...highly favorable to the development of a systematic natural science. For, first and foremost, the Stoics believed in 'determinism'; there was nothing willful about Nature, and everything happened according to law. The secret of human life was to fathom the general character of this universal order and to live in harmony with it. This conviction led certain of the Stoics to elaborate the scientific ideas inherited from their predecessors, but at the same time it reinforced them in beliefs which, to our eyes, appear superstitious. (Their belief in astrological divination...was justified by appealing to the harmony and interaction between celestial and terrestrial events.)"

"are marshalled in the service of satire against powerful individuals and s, to degrade and belittle them; excreta are not on the whole used as images of celebration and festivity ..."

"[E]ven in his academic work it is clear that Budd enjoys breaking out of the university bubble and getting his hands dirty in the real world, working on problems that he hopes can "benefit society directly"."

"This technology is used all the time now. If you have a CD player, then you're using that technology. ...[O]n the CD you put lots of extra information to make sure that when you play the CD it doesn't get distorted or destroyed. [Error correcting codes... store the numbers... and other data... such that any errors can not only be detected but corrected. They work by asking extra questions to make the answers as different as possible so we can still tell the right answer even if it has mistakes in it.] This technology... was invented by a marvelous American mathematician working at Bell Labs... Hamming, one of my heroes, a fantastic mathematician, a brillian inventor of... error correcting codes [using... ()], which he used to send all the information... essentially he created the mobile phone and the internet technology which could which could send the information around... But... it goes back even further... to a branch of math called Galois theory... invented at the end of the nineteenth century by a guy aged 19, and Galois's stuff is heavily used in modern technology now."

"This was the first photo of Saturn that was taken by a satellite. It was taken in the early 70s by the Voyager satellite. That was... beamed to earth by a transmitter with 30 watts of power... less than that light bulb. That light bulb, well you can see it, but imagine from Saturn, which is millions of miles away... [T]hey took this picture, turned it into numbers and... turned those numbers into a code, and that code had lots of [redundant] information put into it, so it didn't matter how far it went and how much it was distorted. You could reassemble it at the other end, into the picture... ...[I]t's absolutely wonderful. It's a combination of math, and technology and brilliance."

"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."

"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..."

"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."

"and are basically the same maths as scanning. [If you solve Killer sudoku you are using the math of .]"

"Mathematicians have changed the world."

"[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."

"Maths is universal."

"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."

"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."

"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."

"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}}"

"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."

"What is often called pure math, which is maths developed for interests only, suddenly finds applications in remarkable ways and leads to whole new technologies. Google was invented by two mathematicians who are now very wealthy. Let that be a lesson to us all."

"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."

"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."

"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."

"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."

"[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'm going to take you through this, looking at the way history of the way math has impacted our civilization. ...I'll try and take you right up to where we are at the moment, and beyond."

"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..."

"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..."

"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."

"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."

"[T]here are incredibly exciting times ahead and the great thing is that there is going to be young people driving us forward, and I can't wait to see where we get to next."

"For the last 20+ years, Dr. Budd has run a module at the University of Bath designed to help undergraduate students communicate mathematics to broader audiences while providing mathematics masterclasses to young aspiring mathematicians at the Royal Institution."

"But it all started with Maxwell. Let's think where we'd be without radio. We wouldn't have radio... ... TV... ... our s, we wouldn't have microwave cookers. The world would be utterly different without radio! In fact, the modern world simply would not exist without radio waves, and it was Maxwell who discovered them, purely from mathematics, and... very, very few people know who he is. This guy should be on the bank notes... It took us a long time to get his statue up. ...One of the other things he's... noted for is his work in . He essentially invented color photography. He also wrote poetry... He was a... very good guy."

"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."