You're right about the bikeshedness, but that doesn't mean there isn't a clearly better bike shed design. I also find that these sorts of inefficiencies/inelegances compound. One or two are trivial, but when you have 30 of them, suddenly the mental tax becomes noticeable.

Furthermore, the cost falls mostly on the students, while the experts have already paid it and don't see the need to worry about it anymore.

Yeah, but this bikeshed got decided hundreds of years ago.

Its only appealing to internet hipsters who want to brag about their organically grown free range tau.

Making the next generation of math students use "2 pi" in their formulas is going to be vastly easier than literally rewriting all the books.

As a practicing physicist, I found it illuminating and non-trivially useful to know this when it was first introduced to me years ago. This is true even though I will never use in a paper, and even if I only rarely write it in my notes. In my head, 2\pi is a single character, to the point that I often write \frac{1}{2} 2\pi.

I find it worthwhile to think about questions like this, whose answers, on some level, do not matter, but, on another level, can be felt to be more or less in line with insights about the underlying structure.

Examples of other questions in the same category:

- Whether the natural numbers should be defined so as to include zero or not (and, relatedly, whether counting should start on zero or on one).

- How to structure a database or a piece of computer code (including the details of how to formulate individual lines of code).

> If mathematics has a bikeshed, this is it.

In my experience, few professional mathematicians care about this. The question that Bromskloss (https://news.ycombinator.com/item?id=11993750) mentions, of whether or not 0 is a natural number, is likely to incur a far more passionate response. (At the risk of downvotes: it is.)

In therms of practical consequences such as making mathematical expressions look different, it seems to me that 0 vs. 1 makes a smaller difference than does τ vs. π, because many statements about the set ℕ of natural numbers make no mention of what its first element is anyway. Often you can drag along any of the two definitions of ℕ through the argument, without changing it's conclusions. For example, if f:ℕ→ℝ (and ε∈ℝ, N∈ℕ, n∈ℕ), the limit L∈ℝ is given by (∀ε>0)(∃N)(∀n≥N)(|f(n)-L|<ε), regardless of whether one takes ℕ={0,1,2,…} or ℕ={1,2,3,…}.

Well, certainly there is a difference if one wishes to compute, say, `\sum_{n \in \mathbb N} 1/n!`. In that case, it's easy just to say what you mean; but, then again, so is it easy to say what you mean in any occurrence of `\pi` or `\tau`. I spoke only of the passion that the issue evokes, not its practical consequences.

> Well, certainly there is a difference if one wishes to compute, say, `\sum_{n \in \mathbb N} 1/n!`.

Certainly. To be clear, I don't mean to argue against anything you said. I just find it to be an interesting observation that statements quite often are true for both versions of ℕ.

Specifically, I suppose, the two versions work the same when one is concerned with only the most fundamental essence of the natural numbers, as captured by the Peano axioms. https://en.wikipedia.org/wiki/Peano_axioms#Formulation

> Specifically, I suppose, the two versions work the same when one is concerned with only the most fundamental essence of the natural numbers, as captured by the Peano axioms.

I find this statement interesting and plausible, but difficult to formalise. The Peano axioms explicitly name the least element of the natural numbers, so in some sense they foreground, rather than effacing, the issue of whether it is 0 or 1; but, on the other hand, I suppose that one could argue that an argument using "only the most fundamental essence of the natural numbers" is one that, as it were, is allowed only to use a constant naming the least element, without pre-supposing any idea of what that name 'means' in any external axiomatic or intuitive sense.

I think I follow, and I agree. How I view the natural numbers on this fundamental level – and I would say it is the picture that the Peano axioms nail down – is as consisting of a first element and then an infinite chain of elements after it (equivalently: the natural numbers are a chain that extends infinitely in one direction but not in the other). As you say, it does not matter, then, if that first element is called "0", "1", or "17" (until we bestow additional structure on the numbers by introducing addition and multiplication operators).

I have to disagree.

I'm a programmer, but I'm not good at math. I know this. And yet, the Tau Day Manifesto explained the geometry of the circle to me more clearly and understandably than any of the math classes I've ever taken. And it's not just because it's a well-written work; the concept is genuinely simpler to understand.

Pi really is a pedagogical disaster, and tau really does help.

Really? This seems very similar to problems with variable naming and magic numbers, which are far from bike shedding.

No, they aren't.

Mathematics has no shortage of bikesheds.

Let's assume the bikesheds are spherical, with radius r. They'll have surface area 4pi*r^2 and, oh never mind...

I find your interpretation rather benign. Saying, “pi is wrong, tau is right” is the equivalent of mathematical bigotry to me.