The economists have had another terrible year. It's time for a complete re-think

Jeremy Warner in The Telegraph


This may or may not be a good time for democracy, but one thing is certain about the past year of political upsets; it’s heaped further humiliations on the economics profession.

A substantial majority of economists thought the mere act of voting for Brexit would pole-axe the economy. Not only did voters ignore these warnings, but so far the “experts” have proved almost wholly wrong.
Internationally, the story is much the same. The profound shock to global confidence anticipated by the International Monetary Fund, the OECD , Uncle Tom Cobley and all, failed to materialise; Brexit had no discernible impact on the world economy. Having cried wolf over the short term consequences, the profession should not be surprised if rather more credible warnings of pain delayed are widely disbelieved.

Similarly with Donald Trump, where the widely expected economic and market mayhem his election would supposedly unleash has so far been conspicuously absent. This collective misreading has been widely attributed to the perils of “groupthink” – where opinion hugs the consensus for fear of derision - or more conspiratorially, to vested interest and deliberately misleading intent.

But there is in fact a more prosaic explanation; that as a discipline, the dismal science has quite simply lost the plot. All over the shop, economics seems incapable of answering the great questions of our time. Are we heading for deflation or inflation? Are we locked in secular stagnation or have we finally put the financial crisis behind us?

The conceit of modern economics is that it sees itself as an evidence-based science, yet if it could ever be such a thing, it is today no nearer its goal than when Adam Smith penned the Wealth of Nations, and in some respects, a good deal less so.

In a devastating recent analysis, the American economist Paul Romer asserted that macro-economics has been going backwards for more than three decades, with economic modelling succumbing to what he has called “mathiness”, an obsession with mathematic laws and equations which bear very little relation to the real world, ignore the lessons of other disciplines and are frequently out of touch with the inherently unpredictable nature of human behaviour.

When he wrote his treatise, Adam Smith was not an economist at all, but a professor of moral philosophy, yet many economists have come to believe that they should be as divorced from moral judgement as scientists – that economics should be a technical discipline free of ethical concerns. In the battle between moralism and mechanism, mechanism won. Unlike science, however, it doesn’t appear to have delivered anything remotely useful.

Few of the profession’s more recent failings should have come as any great surprise, for they merely follow the monumental breakdown in economic analysis exposed by the financial crisis. The Queen’s faux naïve question of economists at the time – “how come nobody saw this coming” – has yet to be answered.

As Andy Haldane, chief economist at the Bank of England, pointed out in a recent lecture, economic models provided an exceptionally poor guide to economic dynamics at the time of the financial crisis. Even after the crisis erupted, the profession seemed oblivious to its likely consequences. Virtually all the economic forecasts produced in the final quarter of 2007 – that’s after the collapse of Northern Rock - were not just mildly wrong about the coming year, but spectacularly so. Few saw any possibility even of a downturn, let alone the worst recession since the 1930s.

Mainstream economic modelling failed spectacularly during the financial crisis and has largely failed since

This failing has been explained by the Nobel prize winning economist Robert Lucas thus: “The simulations were not presented as assurances that no crisis would occur, but as a forecast of what could be expected to occur conditional on a crisis not occurring”. Thanks for nothing.

A somewhat similar excuse is proffered by HM Treasury for its ill judged analysis of the short term consequences of a vote for Brexit. This was not a prediction, but a “scenario”, it is claimed, based on two assumptions that turned out to be wrong – that Article 50 would be immediately triggered, and that there would be no countervailing monetary action by the Bank of England. Yet in truth, it was always obvious both that Article 50 would not be immediately triggered, and that the Bank of England would indeed take action to support the economy.

A stone when dropped will always fall to the ground. Human behaviour is by contrast far less certain, the result of a complex series of interactions which will always be inherently unpredictable, or what Mervyn King, former Governor of the Bank of England, has called “radical uncertainty”. The trouble with much modern economic modelling is that it assumes the laws of physics can indeed be applied to economics, or that behaviour will always respond to given inputs in a particular way. Time and again this has been proved incorrect.

The risks of this serial inability to diagnose what’s happening in the economy lie not just in the social costs of extreme events, or in wrong-headed policy response to them. It has also made mainstream macro-economics the object of political derision, which is in turn undermining public trust in key aspects of institutional and policy orthodoxy, including central bank independence and inflation targeting, which by and large have served us well.

Already we see some of this backlash in Trumponomics, where established norms, evidence and constraints are rejected in favour of policy based on instinct and narrowly perceived American self interest, including protectionism. These cranky alternatives threaten even worse outcomes than the faulty economics of the past.

Mr Haldane sees some reason for hope in reformed modelling, and in particular in so-called “Agency Based Models”, which take account not just of the observable environment, but also the behaviour of other agents which interact with it. Big Data promises to give these models even better predictive qualities.

Long applied to air traffic control, disease prevention, pharmaceutical drug trials and many other practical fields, use of ABMs in macro-economics is still very recent and far from commonplace. We can but hope they represent the great leap forward proponents claim.

One notable sceptic is the economist Paul Krugman, who claims that the old models didn’t fail, or rather that his own relatively simplistic Keynesian modelling predicted almost exactly the failure in post-crisis macro-economic policy. Ah, the path not taken. The beauty of this line of argument is that we’ll never know whether a different approach would have worked better.

Whatever the answer, economists need to be far more circumspect about prediction, as well as the uses their work are put to by the political class, where there is a growing tendency to cite the “experts” who seem to support the party line as true visionaries and dismiss the ones who don’t as useless propagandists. Pick your poison.

But let’s not entirely despair; undeterred by the low regard in which the discipline is held, there are apparently more students applying to do economics at university than ever. Economics may have lost its mojo, but plainly not yet its fascination.

Our fixation with maths doesn’t add up

Simon Jenkins in The Guardian


Who will win the Varkey Foundation’s million-dollar “best teacher” prize this week in Dubai? Hot favourite is Britain’s star maths teacher,Colin Hegarty, whose videos are followed by a million viewers worldwide. Hegarty has been hailed as the great hope for British maths.

Like much of the public realm, British maths is “in crisis”. The country is languishing alongside America way down every league table. Evidence of this was cited in a new poll from YouGov, measuring the public’s knowledge of maths, science and English. In maths, roughly a third of those surveyed had no idea how to calculate a mode, a median, a “line of best fit” or the area of a circle.

I seriously doubt this poll, since it implies that two-thirds did know the answers. All on whom I tested it failed, including myself. Nor could they see the point. With one voice they replied: “That’s the sort of thing you learned at school.” So what is the point? It merely ensures that many pupils, like the bright child of a friend of mine with maths blindness, have their schooling undermined by the government’s fixation with maths.



Colin Hegarty has been shortlisted for the $1m Varkey Foundation teacher prize. Photograph: Linda Nylind for the Guardian

There is nothing, except religion, as conservative as a school curriculum. It is drenched in archaic prejudice and vested interest. When the medieval church banned geography as an offence against the Bible, what had been the queen of the sciences never recovered. Instead Latin dominated the “grammar” curriculum into the 20th century, to the expense of all science. Today maths is the new Latin.

Science at least improved. In 1988 Thatcher hailed a “dash for science” to halt the decline in young people opting for science subjects. It failed completely. Then in 2006 a radical new GCSE syllabus dragged school science away from test tubes and Bunsen burners towards everyday life, to pollution, global warming, additives, health and diet. Since then the reactionaries have turned to maths as the talisman of educational success. It is in maths that we must beat the Chinese, the Singaporeans and the Finns. Pisa league tables of “top nations” are pored over. Maths teachers are paid more, have their loans written off, are entered for global prizes. No one dares mention the calculator.

Any league table that has China at the top, Britain at 26th and America at 36th tells me something more important than merely who is good at maths. If the US and Britain – among the most vigorous economies and most successful at science – are so bad at maths, it suggests their young people are applying themselves to something more useful. Chinese students are rushing to British and US universities to join them.

No one would argue that pupils should not be able to add, subtract and multiply. But I studied higher maths, from calculus to number theory, and have forgotten the lot. All the maths I have needed comes from John Allen Paulos’s timeless manual, Innumeracy. It is mostly how to understand proportion and risk, and tell when a statistician is trying to con you.

I agree with the great mathematician GH Hardy, who accepted that higher maths was without practical application. It was rather a matter of intellectual stimulus and beauty. A new book by Michael Harris, Mathematics Without Apologies, goes to the extremes of this stimulus, to the categorical ladder, incompleteness theory and the Black-Scholes equation, used to assess financial derivatives. It ends in the “inconsistency nightmare”, that nought might possibly equal one.

We accept the need for maths in advanced physics and in computing algorithms, much as we accept Greek for archaeology and Anglo-Saxon for early literature. The “mathematics of finance” school at Columbia University is lavishly sponsored by Wall Street firms, for good reason. But that does not mean every primary pupil must spend hours, indeed years, trying to learn equations and πr2, which they soon forget through disuse. Maths is for specialists, so why instil arithmophobia in the rest?
Charge the maths lobby with the uselessness of its subject and the answer is a mix of chauvinism and vacuity. Maths must be taught if we are to beat the Chinese (at maths). Or it falls back on primitivism, that maths “trains the mind”. So does learning the Qur’an and reciting Latin verbs.

Meanwhile, the curriculum systematically denies pupils what might be of real use to them and society. There is no “need” for more mathematicians. The nation needs, and therefore pays most for, more executives, accountants, salesmen, designers and creative thinkers.

At the very least, today’s pupils should go into the world with a knowledge of their history and geography, their environment, the working of their bodies, the upbringing of children, law, money, the economy and civil rights.

This is in addition to self-confidence, emotional intelligence and the culture of the English imagination. All are crowded out by a political obsession with maths.

The reason is depressingly clear. Maths is merely an easy subject to measure, nationally and internationally. It thus facilitates the bureaucratic craving for targetry and control. The prominence of maths in the curriculum is education’s version of Orwell’s imaginary boot, “stamping on your face … forever”.

------ Reply from a Maths teacher

Maths isn’t the problem - the way it’s taught is

Tim Gowers in The Guardian


A county council gathers data about where road accidents take place, identifies an accident blackspot, places a speed camera there, and notices that the frequency of accidents decreases. Moreover, this is not a one-off: many other councils have observed similar reductions. Does this show that speed cameras improve road safety?

The answer isn’t as straightforward as one might imagine – and the way to understand this is through mathematics. Unfortunately, the way the subject is taught often leaves people with a narrow and misleading view of what maths is. No wonder Simon Jenkins attacked the subject in Thursday’s Guardian.

Mathematics should be a tool for increasing one’s thinking power but for many children it is just a set of rather pointless rules for manipulating symbols. The problem becomes clear if one asks children a question such as the following: a number 35 bus pulls up at a bus stop and eight passengers get on; what is the age of the bus driver? A large percentage of children, their minds numbed by years of symbol manipulation, will give the answer 43. This is a tragedy: rather than being trained to think, these children have been trained to do the opposite.

To return to the speed cameras, the evidence initially seems conclusive. However, the correct answer is neither a clear yes nor a clear no, but rather that more research is needed. Consider what would happen if the locations of accidents were completely random. Then, just by chance, some places would have noticeably more accidents than others while the data was being collected and these places would be identified as blackspots. But since they would not in fact be more dangerous than anywhere else, the later accident rates at these “blackspots” would tend to decrease to more like the average, whether one installed speed cameras or planted apple trees. This phenomenon is known as regression to the mean. Further investigation is needed to determine whether speed cameras make a difference over and above the difference one would have expected anyway. (It turns out that they do.)

Regression to the mean is one of several statistical phenomena that are counterintuitive until you understand them. But once you do, you become better at making decisions. This is important for individuals – whether we like it or not, we all have to take major decisions based on statistical evidence – and it is even more important for people in positions of authority, whose decisions affect other people.

It is therefore good for the health of a country if its population has high standards of mathematical literacy: without it, people are swayed by incorrect arguments, make bad decisions and are happy to vote for politicians who make bad decisions on their behalf.

So how might mathematics education be different? The way it is often taught, children are asked to take a huge leap of faith: that the symbol manipulation that seems pointless now will one day be useful to them. But this is true for only a small minority of children, who enjoy the symbol manipulation for its own sake and later find themselves drawn towards Stem subjects, where it is indeed very useful. The rest know perfectly well that they will never reach this promised land. What can be done for them?

An indication is given by the speed-camera example. It shows that regression to the mean is an important mathematical phenomenon that can be explained without the need for any calculation or symbol manipulation. Why not use examples like this to bring statistics alive? That way we could explain the point of means and standard deviations rather than just asking people to calculate them.

Of course, some proficiency in calculation and symbol manipulation is important – and it improves one’s conceptual understanding – but it should not be all that is taught. We could also ask children open-ended questions, such as whether it is more dangerous to travel by car or by aeroplane. A question like is not explicitly mathematical, so it is less likely to trigger the brain’s off switch. And if it doesn’t, the ensuing discussion will convey why we should care about multiplication, division, averages and probabilities, what we can say about them when we do not have exact numbers handed to us on a plate, and how to frame mathematical questions to help make decisions that are of practical interest.

I am not suggesting that all maths should be introduced this way. But until our mathematics classes encourage people to think, rather than merely play games with marks on paper, the Simon Jenkinses of this world will continue to confuse mathematics with mindless symbol manipulation, attacking the subject itself when their real target should be today’s curriculum.

Failures in Maths Teaching

Pervez Hoodbhoy in The Dawn

Our generals say India’s spy agency RAW is up to its nasty tricks again. No evidence provided but, okay, we’ll buy the story for now. There are two good reasons. First, it’s safer not to question the wisdom of generals. Second, they speak from deep experience, having long played the spy-versus-spy game across borders.

So let’s provisionally assume that India’s spies have engineered the odd bomb blast here and there, and send occasional gifts to the BLF or other militant Baloch movements.

But RAW’s alleged antics are pinpricks compared to the massive and irreversible brain damage that Pakistan’s schools, colleges, and universities inflict upon their students.

Imagine that some devilish enemy has perfected a super weapon that destroys reasoning power and makes a population stupid. One measure, though not the only one, of judging the lethality of this hypothetical weapon would be lower math scores.

No such scores are actually available, but for over 40 years my colleagues and I have helplessly watched student math abilities shrivel.

Only the wealthy customers of elite private schools and universities, tethered as they are to standards of the external world, have escaped wholesale dumbing down. As for the ordinary 99pc, with the rare exception of super-bright students here or there, some form of mental polio is turning most into math duffers.

Does being poor at math really matter? After all there are plenty of intelligent people everywhere, even brilliant ones, who hate math and therefore are bad at it. But this is only because they had dull and uninspiring teachers who never taught them that math is a beautiful exercise of reason, one step at a time. Once on track, you quickly realise that math is the most magnificent, surprising, and powerful of all human achievements.

The success of the human species over other forms of life on planet Earth depends squarely on mathematics. Without math the pyramids could not have been built, navigation would be impossible, electricity could not have been discovered and put to use, factories and industries would not exist, computers and space exploration would be unimaginable, etc.

Here’s how bad our situation is: in a recent math class, I had rather typical 18-20 year-olds from non-elite schools. They had studied geometry but their teachers had not exposed them to the notion of proof — the step-by-step process in which one starts with a proposition, carefully constructs arguments, and then triumphantly arrives at the conclusion.

Instead, they were taught math as a hodgepodge of recipes. A few they remembered, the rest were forgotten.

I nearly wept to see that barely three to four students out of 60 could prove the angles of a triangle add up to 180 degrees. None could prove that similar triangles have proportional sides. Quite a few had difficulty with fractions, some did not know how to take the square root of four or nine or unless armed with a calculator, and translating even simple real-life situations (like compound interest) into equations was difficult. Twelve-year-old kids in Japan or Europe would have done better.

Their teachers are still worse. Earlier I had the misfortune of teaching math courses to college math teachers. In their late 30s or early 40s, most were staid and stable family men who had come to university, expecting to get a higher degree and hence a higher pay grade.

But for all their years of teaching math, they were blanks. Diluting my nominally ‘advanced math’ course to a beginning level course did not help. My conscience could not allow a single teacher to pass.

Could the use of English — a difficult language for all except ‘O’ and ‘A’ level students — reasonably explain this dreadful situation? I am sympathetic to this point of view and therefore use Urdu exclusively in my physics and math lectures, both in distance learning modules and in real-time teaching (except when a university’s regulations require that I teach in English). But this barely solves 10-20pc of the problem.

So then is the math curriculum at fault? It certainly can be improved but almost the same topics in math and science are listed in Pakistani curricula as would expectedly be covered by a similar cohort internationally. In fact, primary school children in Pakistan are expected to carry a bigger burden than overseas kids.

The impediment to learning proper math is just one — wrong learning goals, wrong attitudes. Mathematics does not require labs, computers, or fancy gadgetry. But it does demand mental capacity and concentration. Nothing is true in math unless established by argumentation based upon a rigorous chain of logic, with each link firmly attached to the preceding one. The teacher who cannot correctly solve a math problem by following the defined logic will suffer loss of face before his students.

Contrast this with the madressah model wherein truth is defined by the teacher and prescribed books. The teacher’s job is to convey the book contents, and the student’s job is to appropriately absorb and memorise. There are no problems to be solved, nor is challenging suppositions or checking logical consistency either encouraged or even tolerated.

Limited to religious learning, such learning attitudes are perfectly fine. But their absorption into secular parts of the education system is disastrous. The hafiz-i-science or hafiz-i-math, which are copiously produced, carry exactly zero worth.

Giving logic a back seat has led to more than diminished math or science skills. The ordinary Pakistani person’s ability to reason out problems of daily life has also diminished. There is an increased national susceptibility to conspiracy theories, decreased ability to tell friend from foe, and more frequent resort to violence rather than argumentation. The quality of Pakistan’s television channels reflects today’s quality of thought.

For too long education reform advocates have been barking up the wrong tree. A bigger education budget, better pay for teachers, more schools and universities, or changing instructional languages will not improve learning outcomes. As long as teachers and students remain shackled to the madressah mindset, they will remain mentally stunted. 

The real challenge lies in figuring out how to set their minds free.

India's ancient contribution to science

Shashi Tharoor on NDTV

The unseemly controversy over ancient Indian science at the ongoing Indian Science Congress reflects poorly on all the parties involved, including the conference itself, which is now in its 102nd year without ever having discussed the ancient roots of our indisputable national scientific tradition till yesterday.

First, it reflects poorly on the traditionalists, who have turned revivalism into a form of revisionism with their outlandish claims of improbable Vedic accomplishments. The victory of Narendra Modi in the general elections this year has propelled a number of true believers of Hindutva into positions of unprecedented influence, including in such forums as the Indian Council for Historical Research, the University Grants Commission, and, it now seems, the programme committee of the Indian Science Congress, which scheduled a talk on "Vedic Aviation Technology" that elicited howls of protest from many delegates. 

It has also given a licence to unqualified voices who gain in authority from their proximity to power - none more significant than the Prime Minister himself, who suggested in a speech at a hospital, no less, that Lord Ganesha's elephant head on a human body testified to ancient Indians' knowledge of plastic surgery. Such ideas, because they are patently absurd, except in the realm of metaphor, have embarrassed those who advance them, as well as those who cite them in support of broader, but equally unsubstantiated, claims to past scientific advances, from genetic science to cloning and inter-stellar travel. Petty chauvinism is always ugly, but never more so than in the field of science, where knowledge must be uncontaminated by ideology, superstition or irrational pride.

But the controversy also discredits the modernists who, in their contempt for such exaggerated and ludicrous claims, also dismiss the more reasonable propositions pointing to genuine Indian accomplishments by the ancients. As I pointed out on Twitter yesterday, it is not necessary to debunk the genuine accomplishments of ancient Indian science in order to mock the laughable assertions of the Hindutva brigade.

As I have been repeatedly saying, not everything from the government-sponsored right is necessarily wrong. A BJP government choosing to assert its pride in yoga and Ayurveda, and seeking to promote them internationally, is, to my mind, perfectly acceptable. 

Not only are these extraordinary accomplishments of our civilization, but they have always been, and should remain, beyond partisan politics. It is only if the BJP promoted them in place of fulfilling its responsibility to provide conventional health care and life-saving modern allopathic medicines to the Indian people, that we need object on policy grounds.

Similarly, in asserting that ancient Indians anticipated Pythagoras, Dr Harsh Vardhan was not incorrect and should not have been ridiculed. In fact he could have added Newton, Copernicus, Kepler and Galileo as well, every single one of whom had been beaten to their famous "discoveries" by an unknown and unsung Indian centuries earlier.

The Rig Veda asserted that gravitation held the universe together 24 centuries before the apple fell on Newton's head. The Siddhantas are amongst the world's earliest texts on astronomy and mathematics; the Surya Siddhanta, written about 400 A.D., includes a method for finding the times of planetary ascensions and eclipses. The notion of gravitation, or gurutvakarshan, is found in these early texts. Lost Discoveries, by the American writer Dick Teresi, a comprehensive study of the ancient non-Western foundations of modern science, spells it out clearly: "Two hundred years before Pythagoras," writes Teresi, "philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its centre." 

Aryabhata was the first human being to explain, in 499 A.D., that the daily rotation of the earth on its axis is what accounted for the daily rising and setting of the sun (his ideas were so far in advance of his time that many later editors of his awe-inspiring "Aryabhatiya" altered the text to save his reputation from what they thought were serious errors). Aryabhata conceived of the elliptical orbits of the planets a thousand years before Kepler, in the West, came to the same conclusion (having assumed, like all Europeans, that planetary orbits were circular rather than elliptical). He even estimated the value of the year at 365 days, six hours, 12 minutes and 30 seconds; in this he was only a few minutes off (the correct figure is just under 365 days and six hours). The translation of the Aryabhatiya into Latin in the 13th Century taught Europeans a great deal; it also revealed to them that an Indian had known things that Europe would only learn of a millennium later.

The Vedic civilisation subscribed to the idea of a spherical earth at a time when everyone else, even the Greeks, assumed the earth was flat. By the Fifth Century A.D., Indians had calculated that the age of the earth was 4.3 billion years; as late as the 19th Century, English scientists believed the earth was a hundred million years old, and it is only in the late 20th Century that Western scientists have come to estimate the earth to be about 4.6 billion years old.

India invented modern numerals (known to the world as "Arabic" numerals because the West got them from the Arabs, who learned them from us!). It was an Indian who first conceived of the zero, shunya; the concept of nothingness, shunyata, integral to Hindu and Buddhist thinking, simply did not exist in the West. Modern mathematics would have impossible without the zero and the decimal system; just read a string of Roman numbers, which had no zeros, to understand their limitations. 

Indian mathematicians invented negative numbers as well. The concept of infinite sets of rational numbers was understood by Jain thinkers in the Sixth Century B.C. Our forefathers can take credit for geometry, trigonometry, and calculus; the "Bakhshali manuscript", 70 leaves of bark dating back to the early centuries of the Christian era, reveals fractions, simultaneous equations, quadratic equations, geometric progressions and even calculations of profit and loss, with interest.

The Sulba Sutras, composed between 800 and 500 B.C., demonstrate that India had Pythagoras' theorem before the great Greek was born, and a way of getting the square root of 2 correct to five decimal places. (Vedic Indians solved square roots in order to build sacrificial altars of the proper size). The Kerala mathematician Nilakantha wrote sophisticated explanations of the irrationality of "pi" before the West had heard of the concept. The Vedanga Jyotisha, written around 500 B.C., declares: "Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge." Our mathematicians were poets too! 

Indian numbers probably arrived in the Arab world in 773 A.D. with the diplomatic mission sent by the Hindu ruler of Sind to the court of the Caliph al-Mansur. This gave rise to the famous arithmetical text of al-Khwarizmi, written around 820 A.D., which contains a detailed exposition of Indian mathematics, in particular the usefulness of the zero. It was al-Khwarizmi who is credited with the invention of algebra, though he properly credits Indians for it himself.

But the point is that, alas, we let this knowledge lapse. We had a glorious past; wallowing in it and debating it now will only saddle us with a contentious and unproductive present. We should take pride in what our forefathers did, but resolve to be inspired by them rather than rest on their laurels. We need to use the past as a springboard, not as a battlefield. Only then can we rise above it to create for ourselves a future worthy of our remarkable past. 

The mathematician who loved cricket

 Haider Riaz Khan

The Fenner's ground in Cambridge, where GH Hardy watched a lot of cricket  © Getty Images

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"If I knew that I was going to die today, I think I should still want to hear the cricket scores," GH Hardy is said to have remarked to his sister as he lay dying at the Evelyn Nursing Home in Cambridge in late 1947.

The name GH Hardy is synonymous with pure mathematics, a subject on which he wrote a most insightful book for the layperson, called A Mathematician's Apology, though he is perhaps more well known as the mentor of the Indian mathematical genius Srinivasa Ramanujan. Not many are aware that Hardy, one of the predominant English mathematicians of the pre-war era, was also devoted to cricket. Maynard Keynes, the founder of Keynesian economics and a friend of Hardy's at Cambridge, observed that if Hardy had read the stock exchange for half an hour every day with as much interest and attention as he did the day's cricket scores, he would have become a rich man. 

Hardy did not receive any form of cricket coaching during his formative years, which led to defects in technique later despite having a brilliant eye for the ball. After finishing school at Winchester, he went on to Trinity College, Cambridge, where he began his ritual of watching cricket at Fenner's, Cambridge's picturesque cricket ground. Hardy would saunter to the ground after lunch and settle into his preferred place opposite the pavilion with an umbrella, some sweaters, and a PhD thesis, or a mathematics paper he was refereeing for the Royal Society. Hardy dubbed these items his "anti-God battery", bringing them along in case it rained.

There was often a troop of cricket enthusiasts accompanying him. In particular, during Hardy's second stint at Cambridge, CP Snow, the author ofStrangers and Brothers and The Two Cultures, was his regular companion at cricket games (Snow is the source of much that is known about Hardy's personal life, including his love for cricket). In the foreword of the Apology, Snow recounts the facets of cricket Hardy found most endearing: "Technique, tactics, formal beauty - those were the deepest attractions of the game for him."

Lev Landau, the great Soviet physicist, used a logarithmic scale to rank the productivity of prominent physicists. Hardy had an equally unique way of ranking notable mathematicians and physicists. In a postcard to Snow he wrote, "Bradman is a whole class above any batsman who has ever lived: if Archimedes, Newton and Gauss remain in the Hobbs class, I have to admit the possibility of a class above them, which I find difficult to imagine. They had better be moved from now on into the Bradman class."

Hardy's use of cricket jargon also extended to the types of people he befriended. "He had a great many friends, of surprisingly different kinds," Snow writes in the Apology. "These friends had to pass some of his private tests: they needed to possess a quality which he called 'spin' (this is a cricket term and is untranslatable: it implies a certain obliquity or irony of approach: of recent public figures, Macmillan and Kennedy would get high marks for spin, Churchill and Eisenhower not)."

Even Snow's friendship with Hardy was owed "to having wasted a disproportionate amount of my youth on cricket". Hardy was looking for a cricket companion on his return to Cambridge from Oxford in 1931 and word had reached him that a junior fellow by the name of Snow was a cricket enthusiast. One night, Hardy summoned a nervous Snow after dinner to Christ College's combination room and began a gruelling examination of his cricketing knowledge. Who would he have chosen as captain for the last Test match, a year ago? What would have been his strategy if the selectors had decided Snow was to be England's saviour? And on it went. At the end of the inquisition, Snow recalls Hardy's reaction fondly. "He smiled with immense charm, with child-like openness, and said that Fenner's next season might be bearable after all, with the prospect of some reasonable conversation."

Snow's time with the mathematician is a rich source of Hardy's humorous yet insightful "maxims" on hypocrisy in cricket:

"Cricket is the only game where you are playing against 11 of the other side and ten of your own."

"If you are nervous when you go in first, nothing restores your confidence so much as seeing the other man get out."

The beauty inherent in Hardy's mathematical work is reminiscent of the aesthetic attractiveness of cricket. This love of the game sustained him in his later years when the first love of his life, mathematics, deserted him. As Hardy states in the Apology: "No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." So as his mathematical prowess waned, and his health deteriorated (he had a coronary thrombosis in 1939) and the Second World War raged around him (Hardy was a pacifist and detested anything related to war), he took solace in cricket.

In this gloomy period of Hardy's life, Snow encouraged him to write a cricket book to lessen his despondency. The book was to be called A Day at the Oval, in which Hardy was to write of his experience of watching cricket for a day. It never came to be written, and cricket literature is poorer for it.

Hardy attempted suicide in early 1947 and only survived because he vomited the barbiturates, having taken more than were necessary to kill himself. He was now bedridden at the Evelyn Nursing Home and knew death was imminent. In these last days, he was cared for by his sister. She was aware of her brother's intense fondness for cricket and would search for any cricket story to read to him. As did Snow when he visited Hardy. "Mostly though - about 55 minutes in each hour I was with him - I had to talk cricket. It was his only solace. I had to pretend a devotion to the game which I no longer felt… Now I had to study the cricket scores as intensely as when I was a schoolboy. He couldn't read for himself, but he would have known if I was bluffing."

The last time Snow visited Hardy they discussed the Indian Test team playing in Australia that season. Hardy died early one morning a few days later. His sister had been reading out a chapter from A History of Cambridge University Cricket to him every evening. It seems fitting that that was the last thing Hardy heard.

How internet dating became everyone's route to a perfect love match

The algorithm method: how internet dating became everyone's route to a perfect love match

Six million Britons are looking for their perfect partner online before Valentine's day on Friday, but their chance of success may depend on clever maths rather than charisma

• James Bridle
• The Observer, Sunday 9 February 2014

Six million Britons visit dating sites each month. Photograph: Tom Merton/Getty Images/OJO Images RF

In the Summer of 2012, Chris McKinlay was finishing his maths dissertation at the University of California in Los Angeles. It meant a lot of late nights as he ran complex calculations through a powerful supercomputer in the early hours of the morning, when computing time was cheap. While his work hummed away, he whiled away time ononline dating sites, but he didn't have a lot of luck – until one night, when he noted a connection between the two activities.

One of his favourite sites, OkCupid, sorted people into matches using the answers to thousands of questions posed by other users on the site.

"One night it started to dawn on me the way that people answer questions on OkCupid generates a high dimensional dataset very similar to the one I was studying," says McKinlay, and it transformed his understanding of how the system worked. "It wasn't like I didn't like OkCupid before, it was fine, I just realised that there was an interesting problem there."

McKinlay started by creating fake profiles on OkCupid, and writing programs to answer questions that had also been answered by compatible users – the only way to see their answers, and thus work out how the system matched users. He managed to reduce some 20,000 other users to just seven groups, and figured he was closest to two of them. So he adjusted his real profile to match, and the messages started rolling in.

McKinlay's operation was possible because OkCupid, and so many other sites like it, are much more than just simple social networks, where people post profiles, talk to their friends, and pick up new ones through common interest. Instead, they seek to actively match up users using a range of techniques that have been developing for decades.

Every site now makes its own claims to "intelligent" or "smart" technologies underlying their service. But for McKinlay, these algorithms weren't working well enough for him, so he wrote his own. McKinlay has since written a book Optimal Cupid about his technique, while last year Amy Webb, a technology CEO herself, published Data, a Love Story documenting how she applied her working skills to the tricky business of finding a partner online.

Two people, both unsatisfied by the programmes on offer, wrote their own; but what about the rest of us, less fluent in code? Years of contested research, and moral and philosophical assumptions, have gone into creating today's internet dating sites and their matching algorithms, but are we being well served by them? The idea that technology can make difficult, even painful tasks – including looking for love – is a pervasive and seductive one, but are their matchmaking powers overstated?

 The Kiss, 1901-4, by sculptor Auguste Rodin. Photograph: Sarah Lee for the Guardian

In the summer of 1965, a Harvard undergraduate named Jeff Tarr decided he was fed up with the university's limited social circle. As a maths student, Tarr had some experience of computers, and although he couldn't program them himself, he was sure they could be used to further his primary interest: meeting girls. With a friend he wrote up a personality quiz for fellow students about their "ideal date" and distributed it to colleges across Boston. Sample questions included: "Is extensive sexual activity [in] preparation for marriage, part of 'growing up?'" and "Do you believe in a God who answers prayer?" The responses flooded in, confirming Tarr's suspicion that there was great demand for such a service among the newly liberated student population. Operation Match was born.

In order to process the answers, Tarr had to rent a five-ton IBM 1401 computer for $100 an hour, and pay another classmate to program it with a special matching operation. Each questionnaire was transferred to a punch-card, fed into the machine, and out popped a list of six potential dates, complete with address, phone number and date of graduation, which was posted back to the applicant. Each of those six numbers got the original number and five others in their response: the program only matched women with their ideal man if they fitted his ideal too.

When Gene Shalit, a reporter from Look magazine, arrived to cover the emerging computer-dating scene in 1966, Operation Match claimed to have had 90,000 applications and taken $270,000 in revenue. Even at the birth of the computer revolution, the machine seemed to have an aura about it, something which made its matches more credible than a blind date or a friend's recommendation. Shalit quoted a freshman at Brown University who had dumped her boyfriend but started going out with him again when Operation Match sent her his number. "Maybe the computer knows something that I don't know," she said. Shalit imbued it with even more weight, calling it "The Great God Computer".

The computer-dating pioneers were happy to play up to the image of the omniscient machine – and were already wary of any potential stigma attached to their businesses. "Some romanticists complain that we're too commercial," Tarr told reporters. "But we're not trying to take the love out of love; we're just trying to make it more efficient. We supply everything but the spark." In turn, the perceived wisdom of the machine opened up new possibilities for competition in the nascent industry, as start-up services touted the innovative nature of their programs over others. Contact, Match's greatest rival, was founded by MIT graduate student David DeWan and ran on a Holywell 200 computer, developed in response to IBM's 1401 and operating two to three times faster. DeWan made the additional claim that Contact's questions were more sophisticated than Match's nationwide efforts, because they were restricted to elite college students. In essence, it was the first niche computer-dating service.

Over the years since Tarr first starting sending out his questionnaires, computer dating has evolved. Most importantly, it has become online dating. And with each of these developments – through the internet, home computing, broadband, smartphones, and location services – the turbulent business and the occasionally dubious science of computer-aided matching has evolved too. Online dating continues to hold up a mirror not only to the mores of society, which it both reflects, and shapes, but to our attitudes to technology itself.

The American National Academy of Sciences reported in 2013 that more than a third of people who married in the US between 2005 and 2012 met their partner online, and half of those met on dating sites. The rest met through chatrooms, online games, and elsewhere. Preliminary studies also showed that people who met online were slightly less likely to divorce and claimed to be happier in their marriages. The latest figures from online analytics company Comscore show that the UK is not far behind, with 5.7 million people visiting dating sites every month, and 49 million across Europe as a whole, or 12% of the total population. Most tellingly for the evolution of online dating is that the biggest growth demographic in 2012 was in the 55+ age range, accounting for 39% of visitors. When online dating moves not only beyond stigma, but beyond the so-called "digital divide" to embrace older web users, it might be said to have truly arrived.

It has taken a while to get there. Match.com, founded in 1993, was the first big player, is still the biggest worldwide, and epitomises the "online classifieds" model of internet dating. Match.com doesn't make any bold claims about who you will meet, it just promises there'll be loads of them. eHarmony, which followed in 2000, was different, promising to guide its users towards long-term relationships – not just dating, but marriage. It believed it could do this thanks to the research of its founder, Neil Clark Warren, a then 76-old psychologist and divinity lecturer from rural Iowa. His three years of research on 5,000 married couples laid the basis for a truly algorithmic approach to matching: the results of a 200-question survey of new members (the "core personality traits"), together with their communication patterns which were revealed while using the site.

Whatever you may think of eHarmony's approach – and many contest whether it is scientifically possible to generalise from married people's experiences to the behaviour of single people – they are very serious about it. Since launch, they have surveyed another 50,000 couples worldwide, according to the current vice-president of matching, Steve Carter. When they launched in the UK, they partnered with Oxford University to research 1,000 British couples "to identify any cultural distinctions between the two markets that should be represented by the compatibility algorithms". And when challenged by lawsuits for refusing to match gay and lesbian people, assumed by many to be a result of Warren's conservative Christian views (his books were previously published in partnership with the conservative pressure group, Focus on the Family), they protested that it wasn't morality, but mathematics: they simply didn't have the data to back up the promise of long-term partnership for same-sex couples. As part of a settlement in one such lawsuit, eHarmony launched Compatible Partners in 2009.

Carter says: "The Compatible Partners system is now based on models developed using data collected from long-term same-sex couples." With the rise of Facebook, Twitter, and celebrity-driven online media, have come more personalised and data-driven sites such as OkCupid, where Chris McKinlay started his operation. These services rely on the user supplying not only explicit information about what they are looking for, but a host of assumed and implicit information as well, based on their morals, values, and actions. What underlies them is a growing reliance not on stated preferences – for example, eHarmony's 200-question surveys result in a detailed profile entitled "The Book of You" – but on actual behaviour; not what people say, but what they do.

In 2007, Gavin Potter made headlines when he competed successfully in the Netflix Prize, a $1m competition run by the online movie giant to improve the recommendations its website offered members. Despite competition from teams composed of researchers from telecoms giants and top maths departments, Potter was consistently in the top 10 of the leaderboard. A retired management consultant with a degree in psychology, Potter believed he could predict more about viewers' tastes from past behaviour than from the contents of the movies they liked, and his maths worked. He was contacted by Nick Tsinonis, the founder of a small UK dating site called yesnomayb, who asked him to see if his approach, called collaborative filtering, would work on people as well as films.

Collaborative filtering works by collecting the preferences of many people, and grouping them into sets of similar users. Because there's so much data, and so many people, what exactly the thing is that these groups might have in common isn't always clear to anyone but the algorithm, but it works. The approach was so successful that Tsinonis and Potter created a new company, RecSys, which now supplies some 10 million recommendations a day to thousands of sites. RecSys adjusts its algorithm for the different requirements of each site – what Potter calls the "business rules" – so for a site such as Lovestruck.com, which is aimed at busy professionals, the business rules push the recommendations towards those with nearby offices who might want to nip out for a coffee, but the powerful underlying maths is Potter's. Likewise, while British firm Global Personals provides the infrastructure for some 12,000 niche sites around the world, letting anyone set up and run their own dating website aimed at anyone from redheads to petrolheads, all 30 million of their users are being matched by RecSys. Potter says that while they started with dating "the technology works for almost anything". RecSys is already powering the recommendations for art discovery site ArtFinder, the similar articles search on research database Nature.com, and the backend to a number of photography websites. Of particular interest to the company is a recommendation system for mental health advice site Big White Wall. Because its users come to the site looking for emotional help, but may well be unsure what exactly it is they are looking for, RecSys might be able to unearth patterns of behaviour new to both patients and doctors, just as it reveals the unspoken and possibly even unconscious proclivities of daters.

 Tinder is a new dating app on smartphones.

Back in Harvard in 1966, Jeff Tarr dreamed of a future version of his Operation Match programme which would operate in real time and real space. He envisioned installing hundreds of typewriters all over campus, each one linked to a central "mother computer". Anyone typing their requirements into such a device would receive "in seconds" the name of a compatible match who was also free that night. Recently, Tarr's vision has started to become a reality with a new generation of dating services, driven by the smartphone.

Suddenly, we don't need the smart algorithms any more, we just want to know who is nearby. But even these new services sit atop a mountain of data; less like Facebook, and a lot more like Google.

Tinder, founded in Los Angeles in 2012, is the fastest-growing dating app on mobile phones but its founders don't like calling it that. According to co-founder and chief marketing officer Justin Mateen, Tinder is "not an online dating app, it's a social network and discovery tool".

He also believes that Tinder's core mechanic, where users swipe through Facebook snapshots of potential matches in the traditional "Hot or Not" format, is not simple, but more sophisticated: "It's the dynamic of the pursuer and the pursued, that's just how humans interact." Tinder, however, is much less interested in the science of matching up couples than its predecessors. When asked what they have learned about people from the data they have gathered, Mateen says the thing he is most looking forward to seeing is "the number of matches that a user needs over a period of time before they're addicted to the product" – a precursor of Tinder's expansion into other areas of ecommerce and business relationships.

Tinder's plans are the logical extension of the fact that the web has really turned out to be a universal dating medium, whatever it says on the surface. There are plenty of sites out there deploying the tactics and metrics of dating sites without actually using the D-word. Whether it's explicit – such as Tastebuds.fm, which matches up "concert buddies" based on their Spotify music tastes – or subtle, the lessons of dating research have been learned by every "social" site on the web. Nearly every Silicon Valley startup video features two photogenic young people being brought together, whatever the product, and the same matching algorithms are at work whether you're looking for love, a jobbing plumber, or a stock photograph.

Over at UCLA, Chris McKinlay's strategy seems to have paid off. After gathering his data and optimising his profile, he started receiving 10-12 unsolicited messages every day: an unheard of figure online, where the preponderance of creeps tends to put most women on the defensive. He went on 87 dates, mostly just a coffee, which "were really wonderful for the most part". The women he met shared his interests, were "really intelligent, creative, funny" and there was almost always some attraction. But on the 88th date, something deeper clicked. A year later, he proposed.

Online dating has always been in part about the allure and convenience of the technology, but it has mostly been about just wanting to find "the one". The success of recommendation systems ,which are just as applicable to products as people, says much about the ability of computers to predict the more fundamental attractions that would have got McKinlay there sooner – his algorithms improved his ability to get dates, but not much on the likelihood of them progressing further.

In the end, the development of online dating tells us more about our relationship with networked technology than with each other: from "the Great God Computer", to a profusion of data that threatens to overwhelm us, to the point where it is integrated, seamlessly and almost invisibly, with every aspect of our daily lives.

Economics students aim to tear up free-market syllabus

Undergraduates at Manchester University propose overhaul of orthodox teachings to embrace alternative theories

• Phillip Inman, economics correspondent
• The Guardian, Thursday 24 October 2013 19.17 BST

The Post-Crash Economics Society at Manchester University. Photograph: Jon Super for the Guardian

Few mainstream economists predicted the global financial crash of 2008 and academics have been accused of acting as cheerleaders for the often labyrinthine financial models behind the crisis. Now a growing band of university students are plotting a quiet revolution against orthodox free-market teaching, arguing that alternative ways of thinking have been pushed to the margins.

Economics undergraduates at the University of Manchester have formed the Post-Crash Economics Society, which they hope will be copied by universities across the country. The organisers criticise university courses for doing little to explain why economists failed to warn about the global financial crisis and for having too heavy a focus on training students for City jobs.

A growing number of top economists, such as Ha-Joon Chang, who teaches economics at Cambridge University, are backing the students.

Next month the society plans to publish a manifesto proposing sweeping reforms to the University of Manchester's curriculum, with the hope that other institutions will follow suit.

Joe Earle, a spokesman for the Post-Crash Economics Society and a final-year undergraduate, said academic departments were "ignoring the crisis" and that, by neglecting global developments and critics of the free market such as Keynes and Marx, the study of economics was "in danger of losing its broader relevance".

Chang, who is a reader in the political economy of development at Cambridge, said he agreed with the society's premise. The teaching of economics was increasingly confined to arcane mathematical models, he said. "Students are not even prepared for the commercial world. Few [students] know what is going on in China and how it influences the global economic situation. Even worse, I've met American students who have never heard of Keynes."

In June a network of young economics students, thinkers and writers set up Rethinking Economics, a campaign group to challenge what they say is the predominant narrative in the subject.

Earle said students across Britain were being taught neoclassical economics "as if it was the only theory".

He said: "It is given such a dominant position in our modules that many students aren't even aware that there are other distinct theories out there that question the assumptions, methodologies and conclusions of the economics we are taught."

Multiple-choice and maths questions dominate the first two years of economics degrees, which Earle said meant most students stayed away from modules that required reading and essay-writing, such as history of economic thought. "They think they just don't have the skills required for those sorts of modules and they don't want to jeopardise their degree," he said. "As a consequence, economics students never develop the faculties necessary to critically question, evaluate and compare economic theories, and enter the working world with a false belief about what economics is and a knowledge base limited to neoclassical theory."

In the decade before the 2008 crash, many economists dismissed warnings that property and stock markets were overvalued. They argued that markets were correctly pricing shares, property and exotic derivatives in line with economic models of behaviour. It was only when the US sub-prime mortgage market unravelled that banks realised a collective failure to spot the bubble had wrecked their finances.

In his 2010 documentary Inside Job, Charles Ferguson highlighted how US academics had produced hundreds of reports in support of the types of high-risk trading and debt-fuelled consumption that triggered the crash.

Some leading economists have criticised university economics teaching, among them Paul Krugman, a Nobel prize winner and professor at Princeton university who has attacked the complacency of economics education in the US.

In an article for the New York Times in 2009, Krugman wrote: "As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth."

Adam Posen, head of the Washington-based thinktank the Peterson Institute, said universities ignore empirical evidence that contradicts mainstream theories in favour of "overly technical nonsense".

City economists attacked Joseph Stiglitz, the former World Bank chief economist, and Olivier Blanchard, the current International Monetary Fund chief economist, when they criticised western governments for cutting investment in the wake of the crash.

A Manchester University spokeman said that, as at other university courses around the world, economics teaching at Manchester "focuses on mainstream approaches, reflecting the current state of the discipline". He added: "It is also important for students' career prospects that they have an effective grounding in the core elements of the subject.

"Many students at Manchester study economics in an interdisciplinary context alongside other social sciences, especially philosophy, politics and sociology. Such students gain knowledge of different kinds of approaches to examining social phenomena … many modules taught by the department centre on the use of quantitative techniques. These could just as easily be deployed in mainstream or non-mainstream contexts."