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Comment by Pyret | Hacker News Reader

> On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results.

How interesting. Usually, it's the math folk who ridicule everyone else for being sloppy with their reasoning. For example, physics = hand-wavery :D

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Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy).

However, they can also be pretty free with their assumptions (which can be wild, though if reasoned from carefully usually turn out to be useful even if nobody anticipated that they would).

People working with mathematicians probably spend a lot of time wondering why they're so persnickety about some things most people would consider obvious ("but how do you really know 2+2=4?") but sometimes not so much about whether the constructions they're working with actually reflect a particular concrete reality.

It's a different kind of hand waving. When presented with a system of ODEs describing a system, a mathematician may be content with some assumptions that make the analytical solution more straightforward, or not be terribly worried about particular values for parameters because they're looking at the more general behavior of the system.

Biologists (or in my case epidemiologists) may, on the other hand, be very concerned about why the value you chose for a particular parameter is 6 instead of 7, and whether or not it's really exponentially distributed.

In my experience mathematicians are definitely concerned whether, say, the assumption of exponential distribution is really justified. But what they are interested in is typically a quite general class of (in this case) distributions, where they typically begin with the "simple" cases (which are often normal or exponential distributions).

nod That example was more to illustrate one of several choices a mathematician might make in order to make a problem analytically tractable that might bother a biologist.

Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."

> Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."

I surely won't disagree, but I want to add the point that when the model turns out to be wrong (and most will), also the biologist will have an interest to know, whether just some parameters (say values of constants, wrong probablility assumption) are wrong or the fundamental model has to be reconsidered.

The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a function with integral 1, and the sum of all positive integers is -1/12, and other such nonsense about "convergent" sequences. They balk at the nuance of mathematics when it actually matters to us.

The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.)

Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.

I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare.

And the Dirac delta is the limit of a function with integral 1, not a function.

Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.

The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist.

On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive.

Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....

Forgetting for a moment that the entire post is an appeal to authority (in other words, ignoring all logic) here's the culprit quote from the post:

> In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+...

If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."

He also says things like

> If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct.

Also not how logic works.

the sum of all positive integers is -1/12, and other such nonsense

Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2].

[1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55

[2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...

Of course I know (I'm a mathematician, I'm the one who cringes at all that). The abuse doesn't stop there though... :(

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