Math CentralQuandaries & Queries


Question from Maria, a student:

Hello. I am 16-years-old, and I would like to learn as much mathematics as I can and to really understand it. I would like to know what people mean when they say things like "thinking mathematically" or "math is equally beautiful and true".

However, I'm not sure where to start. :-) What do you think of going back to the beginning and working my way through Euclid?
Your help would be very much appreciated. Thank you.

Hi Maria,

Mathematics is such a large subject and the areas of mathematics that interest different people are extremely diverse so it is difficult to advise someone else where to start. For me, when I was a teenager it was Euclid and a very good teacher that really got me interested in mathematics. A quote from Wikipedia helps explain why Euclid's Elements has been so important to many mathematicians.

The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid. Much of the material is not original to him, although many of the proofs are his. However, Euclid's systematic development of his subject, from a small set of axioms to deep results, and the consistency of his approach throughout the Elements, encouraged its use as a textbook for about 2,000 years. The Elements still influences modern geometry books. Further, its logical axiomatic approach and rigorous proofs remain the cornerstone of mathematics.

In my opinion you can't go wrong starting with Euclid,

PS: Euclid's Elements is available online for free (the copyright has long since expired). Click here.

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