The Math Myth • Hacker News Board

Re: The Math Myth

#291

Post by kozikow » Sun, Sep 04, 2016, 1:09 PM UTC

ethan_g wrote: post #227

kozikow wrote: post #97

Earlier quoted context omitted.

Only few people in finance really "make it" - and it mostly consists of portfolio managers (quantitative or else). "Superstar economy" analogy discussed in this thread have very strong effect in finance. Luck is also a huge factor. I know cases of International Olympiad gold Medalists, who didn't make it as portfolio managers. Do you really think you are smarter? If you are mathematically inclined software engineer,…

If you define "really make it" as making millions every year, yes that's rare. But if it's making 300k+ per year, there are multitudes of math-types doing that, and not much luck is involved.

> But if it's making 300k+ per year

In Silicon Valley it's not uncommon to see new grads (not even PhD) getting 200K total first year compensation. I was comparing quantitative finance vs silicon valley as a career for mathematically inclined software engineers. You won't end up poor either way.

Re: The Math Myth

#292

Post by jabrown10 » Sun, Sep 04, 2016, 1:27 PM UTC

From my experience, people at the forefront of innovation have mathematics background. Quantitate Portfolio Management has a ton of advanced mathematics and the people designing those strategies definitely use mathematics in finance.

If you look at the requirements to be a software engineer for a company that makes video games these days, the mathematics needed is rigorous in the geometry aspect.

I'm not sure what kind of actuary this guy was interviewing but all the actuaries I know in the industry that are respected have used a significant amount of math in their career before reaching management.

I myself am no expert. I have a MS in applied Mathematics from a regular school and make over $150k in the Reinsurance industry.... I only have 4 years of experience. My superiors are definitely making 7 figures.

These days with emergence of predictive analytics which definitely using above 8th grade math, shows the relevance of advanced mathematics.

Because we can program computers, Of course you don't have to write these formulas/equations etc... Everyday but to initially design these systems, implement, revise, research and innovate, the skills are needed.

That's why at these top companies at the forefront of the industry have a very diverse international makeup of countries that excel in mathematics

Re: The Math Myth

#293

Post by lordnacho » Sun, Sep 04, 2016, 2:06 PM UTC

ar0 wrote: post #43

I don't buy the sports analogy with which he argues that it is "self-serving nonsense" if people state that mathematics education trains your general problem solving skills. His argument that soccer players should only play soccer seems not to be anchored in reality: Of course professional soccer players spend a lot of time in the weights room or go running to enhance their general strength and stamina [1]! They do n…

You're right. In particular, when we train for something, we tend not to train things in the proportion that they occur in during the game.

For instance modern coaching has the kids run around with the ball a lot more than in a real 11-a-side match. That's because it matters a heck of a lot that the kids are comfortable on the ball, and only one of 22 people has the ball during the game.

The same goes for math. You may not have to solve PDEs very often, but if you never do it, you will be stuck when it comes time to do so. I recall writing a Bessel function for an option valuation routine once, and if I hadn't come across it in uni, I'd have been struggling with it.

Re: The Math Myth

#294

Post by dboreham » Sun, Sep 04, 2016, 2:08 PM UTC

This is idiotic nonsense.

I use math all the time, especially when I help my kids with their homework because they don't understand their math assignments properly because the school can't hire anyone with a decent math understanding to teach because those people all took high paid jobs elsewhere..

Re: The Math Myth

#295

Post by ausjke » Sun, Sep 04, 2016, 2:16 PM UTC

ThrustVectoring wrote: post #276

ausjke wrote: post #87

This is not just Math. I learnt chemistry, physics, biology and all that from middle to high school. Now as a software engineer they're totally useless and I have long forgotten all those details that I spent months and years to memorize and master. Even reading a science-101 book in one day now will teach me more than what I can remember. Unless you plan to major in those fields, should we just take some introductio…

Matching people with the professional roles that are best for each other is highly valuable - so even if most people forget chemistry, it's often worth teaching, because the introductory chemistry class is how chemists decided to become chemists.

yes my point is how deep you need learn, maybe have some introduction courses at middle school is a good idea.

Re: The Math Myth

#296

Post by sriram_malhar » Sun, Sep 04, 2016, 2:44 PM UTC

This argument, that "higher math" is only for those few who are interested and capable, is infuriating.

I detest utilitarian arguments, that something is worth learning only because it is useful in my day-to-day. I haven't had the faintest use in my daily life for knowing anything about igneous rocks, sorghum, golgi bodies, Chandragupta Maurya, black holes, playing hockey. Yet, it would be singularly depressing to not know it or something to this level of detail.

Second, regarding the argument that only a select few will be interested in ascending the peak and that the rest are content in the plains. While that is true, it takes a whole community of people interested in an area for there to be a star. A Messi or Usain Bolt comes out of having a sporting culture, in addition to athletic and soccer academies of a high enough standard.

Re: The Math Myth

#297

Post by PunchTornado » Sun, Sep 04, 2016, 2:45 PM UTC

mikebelanger wrote: post #99

jdietrich wrote: post #80

Earlier quoted context omitted.

In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.

I had a philosophy professor who believed evolution was 'just a theory', and routinely dismissed it. I don't think she was religious either. Then again, I had another philosophy teacher who taught logic, which is the most pure use of right/wrong that I can think of.

evolution IS 'just a theory'. like relativity and other scientific theories. it is just a coherent framework to explain observations. today it is our best theory, tomorrow it may not be. you cannot say that evolution is Truth. Truth exists only in mathematics, logics etc.

Re: The Math Myth

#298

Post by kazinator » Sun, Sep 04, 2016, 2:53 PM UTC

iopq wrote: post #290

kazinator wrote: post #150

Earlier quoted context omitted.

The argument is that you cannot get to infinity by adding one by one. (If the argument assumed otherwise, it would only be temporarily, for the sake of setting up a reductio ad absurdum .)

You can't use induction to get to an infinite amount of nines, so induction doesn't work in this case because you never get there. The number of nines is not in the set of natural numbers, yet you're trying to use induction by covering every natural number.

You cannot simultaneously believe that "you never get there" (i.e. an infinite number of nines is not constructible) and believe that the syntax 0.999... denotes an actual infinite string of 9's which has a straightforward value (that happens to be precisely 1).

That simply isn't the basis for how 0.999... is regarded as 1.

Rather, 1 is the supremum ("least upper bound", LUB) of the countably infinite set { 0.9, 0.99, 0.999, ... } as a subset of the reals. We define that 0.9... denotes that supremum: i.e. that the ellipses suffixed to 0.9 denote the expansion of 0.9 into the set { 0.9, 0.99, 0.999, ... } followed by determining the LUB of subset among the reals.

No "infinite string of 9's whose length isn't a natural number" nonsense is involved.

Re: The Math Myth

#299

Post by autokad » Sun, Sep 04, 2016, 2:57 PM UTC

sriram_malhar wrote: post #296

This argument, that "higher math" is only for those few who are interested and capable, is infuriating. I detest utilitarian arguments, that something is worth learning only because it is useful in my day-to-day. I haven't had the faintest use in my daily life for knowing anything about igneous rocks, sorghum, golgi bodies, Chandragupta Maurya, black holes, playing hockey. Yet, it would be singularly depressing to no…

knowing about gogi bodies, hockey, and black holes is a personal choice, and it wouldnt be efficient to teach these topics in depth to everyone.

needing higher level math is absolutely unnecessary for 99% of the working population, so the argument that our economy will fall to pieces unless we force high level calculus and trig on every student seems suspect.

however, it is hurting america in an indirect way. we have an elitism going on that only students from top universities get dibs on the best and important positions out of college, and our graduates are becoming increasingly foreign, as american students aren't prepared to get 165+ math GRE scores.

Re: The Math Myth

#300

Post by nzp » Sun, Sep 04, 2016, 3:12 PM UTC

yequalsx wrote: post #252

ryanmonroe wrote: post #153

Earlier quoted context omitted.

Okay, so it follows from completeness. Now prove that real numbers are complete (or provide a construction of the reals that uses completeness as an axiom) without using concepts foreign or confusing to someone with a middle school level exposure to math.

It depends on where you want to start your axioms. We can go the Whitehead/Russell route or just use this as an axiom. We convince children that 1+1 =2 without delving into the Peano axioms. It's ok to not delve too deeply into the axiomatic structure of the reals.

You're just proving their point. None of the things you talk about are even remotely obvious or “natural” to people we're talking about. You want them to ”choose axioms”? Axiom-a-whaaa? 1+1=2 does not need Peano axioms because it's cognitively fundamentally different than 0.999...=1.0. It is immediately obvious because dealing with simple arithmetic on natural numbers is in everybody's experience constantly. In other words we do not need to convince them. Clever untrained people would be able to get 0.999... thing quickly if you gave them some explanation and let them think a bit, if they cared, but properties of real numbers are far from obvious or basic.