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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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4.4 ★★★★★
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Product Reviews
★★★★★ 5
Foams well, smells good, rinses off nicely, perfect!
Scent: Eucalyptus, Size: 12 Fl Oz (Pack of 1)
Oh five stars easily! I bought some other brand, starts with an M, but no foam! Nothing! Then I ordered this one hoping it would at the very least be foamy. It is, and it smells wonderful, and it cleans hands perfectly. It also rinses off well. FIVE STAR!
I will be buying all of these! The lavender is probably my favorite scent, The Satsuma & Eucalyptus is excellent too, and I will be ordered others when they are available.
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Reviewed in the United States on June 2, 2026
★★★★★ 5
Cleans without any harsh fragrance or residue
Scent: Fragrance Free, Size: 12 Fl Oz (Pack of 1)
I got tired of other overly-scented hand soaps and decided to give this a try. It works well for a quick wash after using the toilet and when you're hands are really dirty. It rinses off easily and quickly. While it's unscented, it does have a smell - it's hard to describe, sort of like a bleach-clean scent but, it definitely does NOT smell like bleach. It just smells "clean."
Since it's in the bathroom, it also gets used to clean up some other adult things. Since it isn't scented and doesn't leave any residue it's perfect for things that are in close contact with sensitive areas.
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Reviewed in the United States on May 12, 2026
★★★★★ 5
Smells nice, foams up. Really good.
Scent: Lavender, Size: 64 Fl Oz (Pack of 1)
Good price, got it for a backup in case we run out of the stuff we normally use. It smells pretty good actually.
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Reviewed in the United States on May 24, 2026
★★★★★ 4
Good smelling soap!
Scent: Lavender, Size: 12 Fl Oz (Pack of 1)
Smells great and is gentle on the hands. No artificial colors and no leaks! It smells good and is a good price! The pump works very well, overall am very happy with this soap!
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Reviewed in the United States on February 2, 2026
★★★★★ 5
Must Use FOAMING SOAP BOTTLE for this soap & you will Love it!
Scent: Fragrance Free, Size: 64 Fl Oz (Pack of 1)
I have been using this soap refill for years and love it. I also use the scented versions when this is out of stock and they are not very strong scent. But if you prefer no fragrance, then this is a great soap. Many reviewers are complaining it is watery and thin. YES, IT IS. It is SUPPOSED to be. If you don't know how foaming soap works, you do need a couple pumps of foaming soap but you are using a fraction of the amount of soap you would use (aka WASTE) with standard soap. Have you ever seen your kid pump soap in the bathroom? Not once, or twice, but three or four times? Well, they can do that with this soap and not waste it because it's half air in each pump. It's SUPPOSED to be for foaming hand soap. Don't get fooled by your costly regular or foaming soap. Buy this and have clean hands and SAVE money! My family has very sensitive skin and nobody gets rough, red hands from this soap. No problems.
HIGHLY RECOMMEND THESE FOAMING SOAP DISPENSERS FOR THIS PRODUCT:
https://www.amazon.com/dp/B07PVFXSVC/ref=sbl_dpx_bath-accessories-countertop-soap-dispensers_B07Z8J57J7_0?th=1
UPDATE ON REVIEW (August 2020): I recently just ordered this item and it was delivered with new packaging. I thought it was the same product, but it seems to have additional ingredients now including alcohol. Hm. Need to look closer into this and will update when figure out what has changed.
UPDATE ON INGREDIENTS (October 2020): The new formula is now showing the ingredients. It has changed. A lot. One ingredient that was removed is PHENOXYETHANOL which is GREAT they removed that! However, if they only removed that, then this would be an amazingly safe hand soap (by EWG standards it would be golden). However, it is a completely different soap with a completely different list of ingredients. I will wait until the EWG rates these ingredients before continuing to purchase this. As other reviewers have noted, it does now have "fragrance" in the ingredients - and misleadingly states "(natural)" next to the word fragrance, which means absolutely nothing in terms of what is allowed and what is not. Do your research on what the word "fragrance" means on labels and what could possibly be in your product under that ingredient. In addition it now does have alcohol in it, which some may like, however I don't think soap needs it. If you are washing, you don't need to sanitize anything. It's overkill ingredient - not needed and dries your hands out.
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Reviewed in the United States on August 18, 2020