Euclid's Elements

[StJoseph8]

Did St. Thomas Aquinas study Euclid’s Elements? Would it be beneficial for a Catholic who studies St. Thomas as a layman and who is thinking about a college major in Mathematics to read Euclid? Thanks for any comments.

 

[GEddie]

Can’t hurt to read him, provided you have the discretionary time.

Can’t help with Aquinas.

ICXC NIKA

 

[Entwhistler]

If I was a math major I would definitely read it. Many of the Great Books Catholic Colleges (think Wyoming Catholic and Thomas Aquinas in California) read Euclid for their math classes.

 

[Edmundus1581]

Did St. Thomas Aquinas study Euclid’s Elements? Would it be beneficial for a Catholic who studies St. Thomas as a layman and who is thinking about a college major in Mathematics to read Euclid? Thanks for any comments.

Yes, Aquinas studied Euclid. Greek philosophy and mathematics, which were rediscovered towards the end of the first millennium, were core to medieval Scholasticism (Aquinas’ school of thought).

The Summa actually references Euclid, more than once!

eg.

Objection 2. Further, the definition of a thing contains what is known previously, for a definition “proceeds from the first and more known,” as is said Topic. vi, 4. But the indivisible is part of the definition of the divisible; as a point comes into the definition of a line; for as Euclid says, “a line is length without breadth, the extremities of which are points”; also unity comes into the definition of number, for “number is multitude measured by one,” as is said Metaph. x, Did. ix, 6. Therefore our intellect understands the indivisible before the divisible.

However, that doesn’t mean you will get much practical advantage from it during a college major, if any. For the purposes of grades, you’d be best off spending any extra effort on the presented material and more recent related material.

As GEddie says, do it if you have the discretionary time and for personal interest, without expecting any immediate advantage.

 

[Latinitas]

Hi OP,

Okay, I’m a double major in math and theology, so I definitely can speak about this. Euclid’s Elements are interesting, but not exactly as foundational as you’d think in modern mathematics. Modern mathematics has moved so far beyond Euclid that it’s not exactly relevant anymore (this sounds so liberal, but it’s true). The reason is, that the Greeks opposed unifying arithmetic/algebra with geometry, which is a mainstay of modern math (there’s even a branch of math called algebraic geometry).

Consequently, you can read him if you have time, but it’s better to stick with learning modern math.

Benedicat Deus,
Latinitas

 

[StJoseph8]

Thank you for the comments.

Consequently, you can read him if you have time, but it’s better to stick with learning modern math.

What are some books that you would recommend on modern math? By books I don’t mean like textbooks, but more like layman, pleasure reading books. Thanks.

 

[manygift1spirit]

What are some books that you would recommend on modern math? By books I don’t mean like textbooks, but more like layman, pleasure reading books. Thanks.

These are some that an interested high-schooler or early collegian might find good.

Any of the late Martin Gardener’s books on recreational math are likely to have a few chapters that appeal to you.

James Gleick’s Chaos on dynamical systems is great, one doesn’t need much math background.

The Fractal Geometry of Nature by Benoit Mandelbrot requires more math background but has some topics/applications for everyone.

Lady Luck (author escapes me) is a great engaging book about probability.

It’s controversial and some folks hate it, but Steven Wolfram’s A New Kind of Science on cellular autonoma might be a good read, at least certain chapters whose topic appeals to you.

Lastly, Doug Hofstadter’s Eternal Golden Braid has some great material on mathematical logic, as well as many other disciplines. I would encourage anyone interested in logical and scientific literacy to read this book.

 

[Rhubarb]

I don’t know how much Euclid you’ll be reading with an undergrad degree in math. Maybe if you majored in history of math? As others have said, Euclidean geometry is obsolete in terms of cutting edge math and physics.

 

[RPRPsych]

Thank you for the comments.

What are some books that you would recommend on modern math? By books I don’t mean like textbooks, but more like layman, pleasure reading books. Thanks.

They’re pretty basic, but Isaac Asimov’s Realm of Numbers and Realm of Algebra are pretty good.

If you’re up to something a bit more eccentric, try Roger Penrose’s The Emperor’s New Mind, but feel free to disagree with his conclusions at the end.

 

[Sarcelle]

Hi OP,

Okay, I’m a double major in math and theology, so I definitely can speak about this. Euclid’s Elements are interesting, but not exactly as foundational as you’d think in modern mathematics. Modern mathematics has moved so far beyond Euclid that it’s not exactly relevant anymore (this sounds so liberal, but it’s true). The reason is, that the Greeks opposed unifying arithmetic/algebra with geometry, which is a mainstay of modern math (there’s even a branch of math called algebraic geometry).

Consequently, you can read him if you have time, but it’s better to stick with learning modern math.

Benedicat Deus,
Latinitas

Have you taken a course in differential geometry?

I remember taking it as an undergraduate but now all I remember are Riemannian manifolds and the Poincare upper half plane.