Many of us recall the sense of wonder we felt upon learning that there is no biggest number; for some of us, that wonder has never quite gone away. It is obvious that, given any counting number, one can be added to it to give a larger number. But the implication that there is no … Continue reading Degrees of Infinity
Month: July 2014
Invention or Discovery?
Is mathematics invented or discovered? As many great mathematicians have considered this question without fully resolving it, there is little likelihood that I can provide a complete answer here. But let me pose a possible answer in the form of a conjecture: Conjecture: Definitions are invented. Theorems are discovered. The goal is to prove … Continue reading Invention or Discovery?
Digital Dentistry
That’s Maths in The Irish Times this week (TM049, or Search for “thatsmaths” at irishtimes.com) is about applications of computer aided design and computer aided manufacture to making dental crowns. Next time you spot a kid immersed in a video game, pause before uttering a condemnatory remark. The spin-offs from computer gaming are benefiting us … Continue reading Digital Dentistry
Gauss’s Great Triangle and the Shape of Space
In the 1820s Carl Friedrich Gauss carried out a surveying experiment to measure the sum of the three angles of a large triangle. Euclidean geometry tells us that this sum is always 180º or two right angles. But Gauss himself had discovered other geometries, which he called non-Euclidean. In these, the three angles of a … Continue reading Gauss’s Great Triangle and the Shape of Space
Beauty is the First Test
This week, That’s Maths in The Irish Times (TM048: Search for "thatsmaths" at irishtimes.com) is about the beauty of mathematics. “Beauty is truth, truth beauty” wrote John Keats in his Ode on a Grecian Urn. Mathematical theorems have an enduring truth and the truly great ones are profoundly beautiful. Proofs of theorems can be technically … Continue reading Beauty is the First Test
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