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  • Why mathematicians sometimes get Covid projections wrong | Kit Yates
    by Kit Yates on January 26, 2022 at 3:43 pm

    Modelling may not be a crystal ball, but it remains the best tool we have to predict the futureOfficial modelling efforts have been subjected to barrages of criticism throughout the pandemic, from across the political spectrum. No doubt some of that criticism has appeared justified – the result of highly publicised projections that never came to pass. In July 2021, for instance, the newly installed health secretary, Sajid Javid, warned that cases could soon rise above 100,000 a day. His figure was based on modelling from the Scientific Pandemic Influenza Group on Modelling, known as SPI-M.One influential SPI-M member, Prof Neil Ferguson, went further and suggested that, following the “freedom day” relaxation of restrictions on 19 July, the 100,000 figure was “almost inevitable” and that 200,000 cases a day was possible. Cases topped out at an average of about 50,000 a day just before “freedom day”, before falling and plateauing between 25,000 and 45,000 for the next four months.Kit Yates is director of the Centre for Mathematical Biology at the University of Bath and author of The Maths of Life and Death Continue reading…

  • Did you solve it? The viral maths video that will have you in stitches
    by Alex Bellos on January 24, 2022 at 5:00 pm

    The solution to today’s pro-o-o-o-o-oblemEarlier today I posted the following video, in which I asked Google Assistant to calculate the factorial of 100.The factorial of 100 is the multiplication 100 x 99 x 98 x … x 3 x 2 x 1 in which 100 is multiplied by every whole number below it. Continue reading…

  • Equations built giants like Google. Who’ll find the next billion-dollar bit of maths? | David Sumpter
    by David Sumpter on January 24, 2022 at 10:00 am

    Obscure, generations-old theorems have been transformative in tech, and there are still plenty out there to be usedIn 1998, a computer science PhD student called Larry Page submitted a patent for internet search based on an obscure piece of mathematics. The method, known today as PageRank, allowed the most relevant webpages to be found much more rapidly and accurately than ever before. The patent, initially owned by Stanford, was sold in 2005 for shares that are today worth more than $1bn. Page’s company, Google, has a net worth of well over $1tr.It wasn’t Page, or Google’s cofounder Sergey Brin, who created the mathematics described in the patent. The equation they used is at least 100 years old, building on properties of matrices (mathematical structures akin to a spreadsheet of numbers). Similar methods were used by Chinese mathematicians more than two millennia ago. Page and Brin’s insight was to realise that by calculating what is known as the stationary distribution of a matrix describing connections on the world wide web, they could find the most popular sites more rapidly.David Sumpter is professor of applied mathematics at the University of Uppsala, Sweden, and author of The Ten Equations that Rule the World: And How You Can Use Them Too Continue reading…

  • Can you solve it? The viral maths video that will have you in stitches
    by Alex Bellos on January 24, 2022 at 7:10 am

    Are you smarter than Google Assistant?UPDATE: Read the solution here.“Hey Google, what’s the factorial of 100?”There are several clips doing the rounds of what happens when you ask Google Assistant this question. The response is both hilarious and terrifying. Continue reading…

  • Did you solve it? Gödel’s incompleteness theorem
    by Alex Bellos on January 10, 2022 at 4:59 pm

    The solution to today’s puzzleEarlier today I set you the puzzle below, which is based on Gödel’s incompleteness theorem. As I discussed in the original post, this theorem is one of the most famous in maths and states that in any mathematical system there will always be true statements that cannot be proved.For example, in a formal mathematical setting, the statement ‘This sentence is unprovable” is both true and formally unprovable. When Gödel published his theorem in 1931 it up-ended the study of the foundations of mathematics and its consequences are still being felt today. Continue reading…

  • Can you solve it? Gödel’s incompleteness theorem
    by Alex Bellos on January 10, 2022 at 7:10 am

    The proof that rocked mathsIn 1931, the Austrian logician Kurt Gödel published his incompleteness theorem, a result widely considered one of the greatest intellectual achievements of modern times.The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. The result was a huge shock to the mathematical community, where the prevailing view was an unshakeable optimism about the power and reach of their subject. It had been assumed that maths was “complete”, meaning that all mathematical statements are either provable or refutable. The 25-year-old Gödel demonstrated this was incorrect by constructing a true statement that was not provable. Maths, he announced, has its limits. Continue reading…

  • Did you solve it? Everything you want to know about 2022
    by Alex Bellos on December 27, 2021 at 5:00 pm

    The answers to today’s conundrumsEarlier today I set you the following three puzzles:1. What was the question? Continue reading…

  • Can you solve it? Everything you want to know about 2022
    by Alex Bellos on December 27, 2021 at 6:47 am

    The New Year in numbersUPDATE: Read the solutions hereIf you like number patterns, here’s something to look forward to next year.Shortly after 10pm on February 22, the time and date will consist of a single repeating digit – the last time it will happen this century. Continue reading…

  • Exponential growth is unintuitive and can be frightening | David Spiegelhalter and Anthony Masters
    by David Spiegelhalter and Anthony Masters on December 19, 2021 at 10:00 am

    But, fortunately, it cannot continue indefinitelyThe health secretary impressed parliament last week when he said daily Omicron infections were estimated at about 200,000. This was classic “number theatre” – pulling a big statistic out of a hat without supporting evidence. Although the Health Security Agency (UKHSA) later briefed the press, it only publicly revealed its workings on Thursday: it had estimated 23,000 Omicron infections on 7 December, then assumed exponential growth with a doubling time of 1.9 days. We will have to wait for infection survey estimates to know if this is accurate.Exponential growth simply means something increases in proportion to its current value – the bigger it gets, the more it increases each day. This does not necessarily mean “fast” – a savings account has this kind of growth, even with a 0.1% compound interest rate. Continue reading…

  • Did you solve it? From Russia with logic
    by Alex Bellos on December 13, 2021 at 5:00 pm

    The solutions to today’s problemsEarlier today I set you three questions from a Russian maths competition used to promote the International Congress of Mathematicians, which will be held in July next year in St Petersburg.1. Pet swap Continue reading…

  • Can you solve it? From Russia with logic
    by Alex Bellos on December 13, 2021 at 7:10 am

    Mathematicians get ready to partyUPDATE: The solutions can be read here.The largest and most important event in the mathematical calendar will take place next July in St Petersburg. The International Congress of Mathematicians is a quadrennial gathering at which many of the subject’s most prominent thinkers give lectures and the winners of maths’ most prestigious prize, the Fields Medal, are announced.As part of the build-up to the event – which is expected to attract about 5,000 mathematicians from all over the world – the organisers earlier this year ran an online maths competition for students and the general public. Below are the first three questions from this test. Continue reading…

  • Did you solve it? Yule devour these festive treats
    by Alex Bellos on November 29, 2021 at 5:00 pm

    The solutions to today’s puzzlesEarlier today I set you the following three problems, taken from this year’s Mathigon puzzle advent calendar.1. The seven digits Continue reading…

  • Can you solve it? Yule devour these festive treats
    by Alex Bellos on November 29, 2021 at 7:10 am

    Advent(ures) in numberlandUPDATE: The answers can be read hereEvery year the remarkable maths website Mathigon runs a puzzle advent calendar, publishing a problem a day from December 1 to 24. I’ve had a peek at this year’s puzzles and selected three of the ones I liked the most.1. The seven digits Continue reading…

  • Did you solve it? The man who changed the course of magic
    by Alex Bellos on November 15, 2021 at 5:00 pm

    The solutions to today’s puzzlesProfessor Hoffman was the pen-name of Angelo Lewis, a Victorian barrister whose book Modern Magic, published in 1876, is considered one of the most important and influential magic books of all time.(I read about him recently in David Copperfield’s History of Magic, a stunning book he coauthored with psychologist Richard Wiseman and magician David Britland.) Continue reading…

  • Can you solve it? The man who changed the course of magic
    by Alex Bellos on November 15, 2021 at 7:10 am

    Ten mind-bending riddlesUPDATE: The solutions can be read hereDavid Copperfield’s History of Magic is a beautiful new book by the eponymous magician (coauthored with psychologist Richard Wiseman and magician David Britland), which tells the story of magic through objects in his private museum, the largest and most impressive collection of magic memorabilia in the world.The International Museum of the Conjuring Arts is housed in a gigantic building on the outskirts of Las Vegas, the city where Copperfield, aged 65, still performs 15 shows a week. (His industriousness has helped make him the highest grossing solo entertainer of all time.) Continue reading…

  • On Covid, we need to be careful when we talk about numbers
    by David Spiegelhalter and Anthony Masters on November 14, 2021 at 6:00 am

    A recent wave of mistakes shows how misinterpreting data risks misrepresenting the impact of the virusSince we have just had Maths Week in England, it seems appropriate to look at a wave of recent errors when communicating numbers.First, the statistics may be described wrongly. The chief executive of NHS England recently claimed: “We have had 14 times the number of people in hospital with Covid than we saw this time last year”, a claim repeated on Sky News and ITV. But there were fewer Covid-19 patients in England on 4 November (7,201) than a year earlier (11,037). The intended reference was to last August, when there were about 23,000 admissions within two weeks after a positive test, about 14 times higher than last year. Continue reading…

  • Did you solve it? The playful genius of Hungarian puzzles
    by Alex Bellos on November 1, 2021 at 5:00 pm

    The solutions to today’s 3D logic puzzlesEarlier today I set you the following “three-dimensional” logic puzzles, a genre thought to have emerged decades ago in Hungary. (For more details about the Hungarian link here’s the story.) The idea is that the solution is mapped out on a three-dimensional grid.1. Date night Continue reading…

  • Can you solve it? The playful genius of Hungarian puzzles
    by Alex Bellos on November 1, 2021 at 7:10 am

    Logic puzzles in three dimensionsUPDATE: To read the solutions click hereWhen it comes to the world of mathematical puzzles, Hungary is a superpower. Not just because of the Rubik’s cube, the iconic toy invented by Ernő Rubik in 1974, but also because of its long history of maths outreach.In 1894, Hungary staged the world’s first maths competition for teenagers, four decades before one was held anywhere else. 1894 also saw the launch of KöMaL, a Hungarian maths journal for secondary school pupils full of problems and tips on how to solve them. Both the competition and the journal have been running continuously since then, with only brief hiatuses during the two world wars. Continue reading…

  • The death of Charles Babbage, mathematician and inventor – archive, 23 October 1871
    on October 22, 2021 at 5:30 am

    23 October 1871: Babbage’s calculating machines are seen as the forerunners of modern programmable computersThe death is announced of Mr Charles Babbage, who has long held high rank among the mathematicians of the day. He was born on 26 December 1792, and having been privately educated, proceeded to Trinity College, Cambridge where he took his BA degree in 1814; but, curiously enough, his name does not appear in the mathematical tripos. In the course of his mathematical studies he found fault with the logarithmic tables then in use as being defective and unfaithful; and in order to improve them visited the various centres of machine labour in England and on the continent, and on his return directed the construction of a “difference engine” for the use of the government.Another result of this tour was the production of his work on the Economy of Manufactures. By 1833 a portion of his machine (popularly known as “the calculating machine”) was prepared, and its operations were entirely successful. It was, however, never completed. He next prepared his Table of Logarithms of the Natural Numbers from 1 to 108,000, a work which was so highly esteemed that it was very soon afterwards translated into almost all the European languages. Continue reading…

  • Britain’s Covid numbers show we need to move immediately to ‘plan B’ | Kit Yates
    by Kit Yates on October 21, 2021 at 1:33 pm

    Our comparatively good position has been eroded and now, heading into the winter, the data looks truly alarmingKit Yates is director of the Centre for Mathematical Biology at the University of BathAll the Covid indicators in the UK are going in the wrong direction. They have been for a while now. Cases are surging upwards; hospitals are feeling the strain of increasing numbers of Covid patients, and daily death tolls are rising. At the same time, vaccination delivery is slowing down.On Monday we saw almost 50,000 cases reported. Only on 16 days throughout the whole pandemic have we seen higher numbers. On Wednesday we saw similar numbers. Our seven-day average is more than 45,000 cases a day, and the ONS estimates that one in 60 people are infected – the highest level since January. For comparison, Germany is seeing 165 daily cases per million of its population. In France, the figure is just 71, and in Spain 35. The corresponding rate for the UK is more than 650 per million.Kit Yates is director of the Centre for Mathematical Biology at the University of Bath and author of The Maths of Life and Death Continue reading…