1+ day, 37+ min ago (447+ words) The West African Examinations Council (WAEC) on Saturday, November 29, 2025, released the provisional results for the West African Senior School Certificate Examination (WASSCE) for School Candidates, triggering alarm with a catastrophic decline in performance across key core subjects, particularly Mathematics. Data released by WAEC shows a staggering drop in the percentage of candidates achieving grades A1 to C6 in Core Mathematics, falling by nearly 18 percentage points compared to the previous year. The results also unveiled a disturbing integrity crisis, with over 7,000 candidates penalised and nearly 40 educational personnel facing criminal charges for exam malpractice. The results were contained in a press release by John Kapi, Head of Public Relations at WAEC and represent only the Ghana version. Catastrophic Slump in Core Subjects The comparative statistics from the four-year trend analysis (2022-2025) confirm a sharp reversal of gains made in previous years, casting a shadow over…...

1+ day, 3+ hour ago (521+ words) A zero knowledge proof (ZKP) answers a question without revealing anything more than answer. For example, a digital signature proves your possession of a private key without revealing that key. You can think of Fermat's primality test as a zero knowledge proof. For example, I can convince you that the following number is composite without telling you what its factors are. Fermat's little theorem'says that if'n'is a prime and'b'is not a multiple of'n, then A number'b such that bn1" 1 (mod'n) is a proof that'n is not prime, i.e. n is composite. So, for example,'b = 2 is a proof that'n above is composite. This can be verified very quickly using Python: I tried the smallest possible base [1] and it worked. In general you may have to try a few bases. And for a few rare numbers (Carmichael numbers) you won't be able to…...

1+ day, 18+ hour ago (595+ words) A children's mathematics camp will host part of an international competition on the island next year. Planet Math will hold the trials in February, with successful youngsters getting the chance to compete in the Spirit of Math Global Round in Canada in the summer. Sergio Pitcher, one of the founders of Planet Math, said it meant a lot to host the round in Bermuda because it could showcase the island's talent. He added: "It's going to be an opportunity for young mathematicians to shine not just locally in Bermuda but to shine on an international, global stage. "You'll represent Bermuda and show the world what Bermuda has for mathematicians." Spirit of Math involves children going head-to-head in their home countries and proving their logical mathematical skills before travelling to Ontario, Canada to compete. The competition is open to pupils from…...

1+ day, 22+ hour ago (228+ words) Monero has a way of generating new addresses analogous to the way HD wallets generate new addresses for Bitcoin. In both cases, the recipient's software can generate new addresses to receive payments that others cannot link back to the recipient. Monero users have two public/private keys pairs: one for viewing and one for spending. Let Ks and ks be the public and private spending keys, and let Kv and kv be the public and private viewing keys. Then the user's ith subaddress is given by Here'G is a generator for the elliptic curve Ed25519 and'H is a hash function. The hash function output and kv are integers; the public keys, denoted by capital'Ks with subscripts and superscripts, are points on Ed25519. The corresponding private keys are As with hierarchical wallets, the user scans the blockchain to see which of his addresses…...

1+ day, 23+ hour ago (239+ words) Math Puzzle: The Ancient City The mathematician, who liked to annoy friends with improvised brainteasers, thought for a moment or two, then raised a glass and recited: A rose-red city half as old as Time.One billion years ago the city's ageWas just two fifths of what Time's age will beA billion years from now. Can you computeHow old the crimson city is today? The English professor had long ago forgotten algebra and quickly shifted the conversation to another topic, but readers of this department should have no difficulty with the problem. The rose-red city's age is seven billion years. Let x be the city's present age and y be the present age of Time. A billion years ago the city would have been x " 1 billion years old, and a billion years from now Time's age will be y + 1. The…...

2+ day, 2+ hour ago (236+ words) In spherical geometry, the interior angles of a triangle add up to more than ". And in fact you can determine the area of a spherical triangle by how much the angle sum exceeds ". On a sphere of radius 1, the area equals the triangle excess Area = E = interior angle sum " ". Small triangles have interior angle sum near ". But you could, for example, have a triangle with three right angles: put a vertex on the north pole and two vertices on the equator 90" longitude apart. In hyperbolic geometry, the sum of the interior angles of a triangle is always less than ". In a space with curvature "1, the area equals the triangle defect, the difference between " and the angle sum. Area =D = " " interior angle sum. Again small triangles have an interior angle sum near ". Both spherical and hyperbolic geometry are locally Euclidean. The…...

2+ day, 5+ hour ago (342+ words) What is the value of x in the equation above? For the quadratic function y = f(x), (x " 3) is a factor and'x = k is a positive zero. If (5, c) is the maximum point on the graph of y = f(x), what is the value of k? Which of the following expresses a in terms of b and c? The function f is defined by f(2x " 1) = 4x + 3 and the function g is defined by g(x) = f(x) " 1. What is the value of g(10)? The line shown in the xy-plane passes through the point (0, 0) and the point' (a, b), where a > b. Which of the following could be the slope of this line? A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the…...

2+ day, 5+ hour ago (352+ words) Let " be the upper half plane, the set of complex real numbers with positive imaginary part. When we measure distances the way we've discussed in the last couple posts, the geometry of " is hyperbolic. What is a circle of radius r in "? The same as a circle in any geometry: it's the set of points a fixed distance r from a center. But when you draw a circle using one metric, it may look very different when viewed from the perspective of another metric. Suppose we put on glasses that gave us a hyperbolic perspective on ", draw a circle of radius'r centered at'i, then take off the hyperbolic glasses and put on Euclidean glasses. What would our drawing look like? In the previous post we gave several equivalent expressions for the hyperbolic metric. We'll use the first one here. Here…...

2+ day, 10+ hour ago (948+ words) Introduction: Africa " The cradle of Mathematical wisdom As Africa now stands on the threshold of the Fourth Industrial Revolution, it must reclaim that ancient mathematical genius " and position mathematics once again as the foundation for its transformation through STEAM: Science, Technology, Engineering, Agriculture, and Mathematics. 1. The African roots of Mathematical civilisation The story of mathematics cannot be told without Africa. The Ishango Bone, discovered near the headwaters of the Nile and dated to over 20,000 years ago, is one of humanity's oldest mathematical artefacts " evidence that ancient Africans were already using arithmetic operations and base systems long before Greek or Roman numerals were conceived. In ancient Egypt, mathematics was the foundation of civilisation. Imhotep's design of the Step Pyramid at Saqqara required precise calculation of angles, load distribution, and geometric alignment with celestial bodies. Egyptian scribes mastered algebra and geometry to…...

2+ day, 13+ hour ago (167+ words) We're conducting focus groups to gain a deeper understanding of how people experience mathematics in everyday situations, such as shopping, budgeting, work tasks, or using technology. We want to hear from adults who are not currently studying or teaching. This project is a collaboration between Loughborough University and the University of South Australia. There's no need for maths skills or knowledge; all abilities welcome. We're interested in your stories and feelings about everyday situations where numbers show up. We will offer a "15 voucher as a thank-you gift after the focus groups are completed. If you're eligible, you'll be invited to take part in a 1-hour focus group in Loughborough or at the Loughborough University campus with 45 others. You'll discuss when and how you encounter mathematics in daily life and how it makes you feel. This project has been approved by…...