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Description
What Is Mathematics?: An Elementary Approach to Ideas and MethodsFor more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.Binding Type: Paperback
Publisher: Oxford University Press, USA
Published: 07/18/1996
ISBN: 9780195105193
Pages: 592
Weight: 1.70lbs
Size: 9.02h x 6.05w x 1.06d
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4.9 ★★★★★
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Product Reviews
★★★★★ 5
Excellent all-poly athletic socks for general lifting and HIIT.
Size: Medium, Color: Black/White/Grey
***These are NOT “low” -cut socks as the description in the title states. These are actually “quarter”-cut socks as clearly visible in the picture of the sock itself. “Low” -cut socks are shorter than this height but still visible with a shoe. Also, on the actual UA package of these socks, it clearly states these are QUARTER cut socks.
My review: Gave these UA Performance Tech socks (UAPT) 5 stars since they’re very good but in all reality not the best socks I’ve ever had for lifting and HIIT workouts. That title goes to Nike Dri-Fit MAX socks (DFM)….but these socks are really good. Like Nike’s DFM’s, these UAPT socks come in sizes, halleluah (M, L, and XL). The idea that most athletic sock are sized 6-12 and should therefore fit everyone perfectly is absolutely ridiculous. Your shoes come in whole and half sizes…so socks should at the very least be sized like these UAPT’s and Nike DFM’s…in S/M/L or in this case, M/L/XL. I wear a men’s size 8 shoe and the M (medium) size in these socks was a perfect fit; true to size.
Also, UAPT socks are ALL polyester with Spandex which is ideal and 100% that which you want for athletic socks: wicking with stretch. Cotton socks are the absolute worst thing you could wear to the gym since they’re sponges for sweat and therefore get wet and heavy, cause blisters, tend to stink, stick to skin, etc… IF you prefer cotton socks for athletics, then you don’t understand how performance fabrics work in athletics and training. You do NOT want cotton in your athletic apparel. You want your fabrics that wick sweat away; NOT soak up sweat and hold onto it. Also, the flexibility and stretch of the foot and ankle parts of the sock were both just right. Snug but not too tight. Wicking is perfect, too. Already worn during two 3 1/2 hour workouts and my feet stayed as dry as a desert.
When looking for UA athletic socks on Amazon, I surprisingly continued to find UA “athletic” socks made with mostly cotton which completely surprised me because a serious athletic company should produce an abundance of performance-level socks… i.e. all-poly socks. Thank goodness I finally came across these UA all-poly Performance Techs. The only drawback to these UAPT’s…and it’s a minor drawback…is that unlike Nike DFM’s, these do not come in L & R (left and rights) to specifically match the individual foot shape. Nike DFM socks come in L and R which sets them apart from all other athletic socks…and yet I don’t like supporting a massive monopolistic athletic apparel company like Nike, but they’re the only one that makes THE best athletic sock.
Nonetheless, these UAPT’s are perfect workout/HIIT/lifting socks for the bundle value price of six pair and three colors. If you’re looking to match your new UA or Rock shoes with the appropriate UA athletic sock, then here you go. I chose the black/white/gray mix bundle since I have new pairs of a black and a white version of the same UA-Rock shoe. These UAPT socks are medium thickness so they didn’t take up an exorbitant amount of room in my shoes but they’re thick enough to prevent blisters and provide cushion. Overall they’re very comfortable, hold a good stretch, hold their shape, and seem to be durable but only time will tell.
And since we’re on the black and white sock subject, I couldn’t resist: I read a shoe review about someone angered that his new UA/Rock black shoes (obviously bought for casual wear in lieu of gym use) staining his white cotton socks. First of all, never ever wear white socks (much less cotton white socks) with black athletic shoes! The possibility of staining is always there and the appearance just doesn’t work. However, you can get away with black socks with white shoes in some cases…but never white socks with black shoes. Why? Who knows? It’s just one of those unwritten rules of the gym. And no, I didn’t make the rules…so don’t blame the messenger. LOL!
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Reviewed in the United States on July 28, 2025
★★★★★ 5
Very soft and wears well
Size: Medium, Color: Black/White/Grey
Very nice quality and soft
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Reviewed in the United States on April 18, 2026
★★★★★ 5
Great buy
Size: X-Large, Color: Black/Black/Black
Good socks that fit well.
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Reviewed in the United States on February 20, 2026
★★★★★ 4
Good sock
Size: Large, Color: Black/White/Grey
Great cushion and solid fit. Some days my feet are tired from the compression fit, but they do support my feet well.
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Reviewed in the United States on October 9, 2025
★★★★★ 5
Exceptional!
Size: Large, Color: Black/Black/Black
Best socks I have ever worn. Already bought more.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on March 31, 2026