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If you know what you're doing the axiom bindings make it the most powerful cas in terms of symbolic manipulation. Mathematica is optimized for giving you resul

by antt 8y ago

If you know what you're doing the axiom bindings make it the most powerful cas in terms of symbolic manipulation. Mathematica is optimized for giving you results you need in undergrad classes. Sage is not optimized at all, but can solve problems useful to researchers. It's the difference between osx and linux.

ChrisLomont 8y ago
>Mathematica is optimized for giving you results you need in undergrad classes What makes you think this? Mathematica is used in all sorts research projects, technical fields, finance, and so on. I've seen Mathematica required or recommended in many, many job listings, especially for quants. I've never seen Sage there. For evidence, here [1] is what you get for searching for Mathematica on Indeed.com. Note pretty much every one of those jobs lists several math related packages. Not one mentions Sage. Unfortunately you cannot run the same search on Sage, since there is an ERP package that shows up instead. However, from browsing those listing again I find zero hits for the math package Sage. [1] https://www.indeed.com/jobs?q=Mathematica&l= https://www.indeed.com/jobs?q=Mathematica&l= [1] https://www.indeed.com/jobs?q=Mathematica&l= https://www.indeed.com/jobs?q=Mathematica&l=
- lvh 8y ago
  Despite being the Sage fanboy in the thread, I have to admit that all the use I've seen of Sage has been academic or experimental; I haven't heard of anyone using Sage for statistics in any context, and not for quants or actuarial science or anything of the sort. I'd suggest that Sage is likely less good for those uses since Sage is good at the kinds of things you're likely to find academics use Sage for (e.g. tons of discrete math and most things cryptography). Secondly, since there's very little pressure for high-end uses of commercial packages to worry about the licensing cost of a mathematics package like JMP or Mathematica.
  - williamstein 8y ago
    Indeed. Sage was written by and for academics in academia doing research in pure mathematics. There's also been a fair amount of work to make it usable for undergrad math courses (started originally by some undergrads I hired actually). The only significant overlap with industry in terms of dev support is probably crypto research... But the Python ecosystem overall is pretty strong in industry, and Sage is part of that ecosystem...
- antt 8y ago
  The languages themselves. To evaluate most simple integrals in mathematica you just put them in and all the corner cases are assumed away for you. For sage and the axiom binding you need to make those assumptions explicit. Pretty much everything in mathematica assumes you're working on the real numbers, pretty much nothing in sage does: http://doc.sagemath.org/html/en/tutorial/tour_rings.html http://doc.sagemath.org/html/en/tutorial/tour_rings.html Most math quants use is at the undergrad level, the finance industry in general is pretty backwards. A very large chunk of it is run on spreadsheets that are passed around in emails. I've worked in it and having seem what it takes to run some of the clients spreadsheets still gives me nightmares. Again, the difference between osx and linux. --- To clarify what I mean by undergrad level: Something that is taught to some undergrads in some degree. Someone who specialized in pure symbolic mathematics is likely to see integrals in their last year that other people will not see until they start doing postdoc work.
  - ChrisLomont 8y ago
    >Most math quants use is at the undergrad level, the finance industry in general is pretty backwards Do you have any idea what a quant is? I have a PhD in math, and am decently well versed in the math quants use, and it's nothing like undergrad math. Many of the people I got PhD's with became quants, and we've had plenty of discussions on the math they use. Quants build models using math far beyond what an undergrad learns, including tools such as martingales, stochastic calculus, Black-Scholes (and vast generalizations), Brownian motion, Stochastic differential Equations, numerical methods (usually much more advanced than an undergrad will see), and more. Quant jobs usually want a PhD in math or related field. If an undergrad math degree covered what they needed they'd not require a PhD for most positions. What do you think a quant does? Here's a site [1] for quant jobs. Probably none for someone with only an undergrad math degree. [1] http://www.quantfinancejobs.com/ http://www.quantfinancejobs.com/
    - antt 8y ago
      There's a number of things to disentangle in that post. 1). The domain you posted is for sale and appears to be broken or slow. Given it uses aspx and a Microsoft stack that's ten years out of date I'd say it's perfectly representative of the state of the larger finance industry. 2). What is a quant. Depends on the job. I was hired as a quant for risk management then got switched to algos when the pm found out I have a lot of hard real time experience with Linux. The first job was all discrete math, the second was optimizing x86 assembly. 3). Credential inflation is real. The application of the maths you talked about was something I saw first hand. The assumptions under which the formal models would work were so thread bare a stiff breeze would tear them down quote Keynes: >The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are merely concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols. The above is still excellent advice, most often never followed. Of course the lunch talks we had were very interesting, completely divorced from reality, but very interesting. 4). Most undergrads will never see the mathematics. True. But some will. My numerical methods 4th year project was a symplectic integrator for the gravitational interaction between Jupiter, Mars, the Sun and the asteroid belt. It wasn't new research, the results were known 50 years ago, but it was on par with the state of the art in industry in terms of complexity of implementation (cleanness of implementation was a completely different thing, while not spaghetti code it's rightly never seen the light of day).

by antt 8y ago

ChrisLomont 8y ago

>Mathematica is optimized for giving you results you need in undergrad classes What makes you think this? Mathematica is used in all sorts research projects, technical fields, finance, and so on. I've seen Mathematica required or recommended in many, many job listings, especially for quants. I've never seen Sage there. For evidence, here [1] is what you get for searching for Mathematica on Indeed.com. Note pretty much every one of those jobs lists several math related packages. Not one mentions Sage. Unfortunately you cannot run the same search on Sage, since there is an ERP package that shows up instead. However, from browsing those listing again I find zero hits for the math package Sage. [1] https://www.indeed.com/jobs?q=Mathematica&l= https://www.indeed.com/jobs?q=Mathematica&l= [1] https://www.indeed.com/jobs?q=Mathematica&l= https://www.indeed.com/jobs?q=Mathematica&l=

lvh 8y ago
Despite being the Sage fanboy in the thread, I have to admit that all the use I've seen of Sage has been academic or experimental; I haven't heard of anyone using Sage for statistics in any context, and not for quants or actuarial science or anything of the sort. I'd suggest that Sage is likely less good for those uses since Sage is good at the kinds of things you're likely to find academics use Sage for (e.g. tons of discrete math and most things cryptography). Secondly, since there's very little pressure for high-end uses of commercial packages to worry about the licensing cost of a mathematics package like JMP or Mathematica.
- williamstein 8y ago
  Indeed. Sage was written by and for academics in academia doing research in pure mathematics. There's also been a fair amount of work to make it usable for undergrad math courses (started originally by some undergrads I hired actually). The only significant overlap with industry in terms of dev support is probably crypto research... But the Python ecosystem overall is pretty strong in industry, and Sage is part of that ecosystem...
antt 8y ago
The languages themselves. To evaluate most simple integrals in mathematica you just put them in and all the corner cases are assumed away for you. For sage and the axiom binding you need to make those assumptions explicit. Pretty much everything in mathematica assumes you're working on the real numbers, pretty much nothing in sage does: http://doc.sagemath.org/html/en/tutorial/tour_rings.html http://doc.sagemath.org/html/en/tutorial/tour_rings.html Most math quants use is at the undergrad level, the finance industry in general is pretty backwards. A very large chunk of it is run on spreadsheets that are passed around in emails. I've worked in it and having seem what it takes to run some of the clients spreadsheets still gives me nightmares. Again, the difference between osx and linux. --- To clarify what I mean by undergrad level: Something that is taught to some undergrads in some degree. Someone who specialized in pure symbolic mathematics is likely to see integrals in their last year that other people will not see until they start doing postdoc work.
- ChrisLomont 8y ago
  >Most math quants use is at the undergrad level, the finance industry in general is pretty backwards Do you have any idea what a quant is? I have a PhD in math, and am decently well versed in the math quants use, and it's nothing like undergrad math. Many of the people I got PhD's with became quants, and we've had plenty of discussions on the math they use. Quants build models using math far beyond what an undergrad learns, including tools such as martingales, stochastic calculus, Black-Scholes (and vast generalizations), Brownian motion, Stochastic differential Equations, numerical methods (usually much more advanced than an undergrad will see), and more. Quant jobs usually want a PhD in math or related field. If an undergrad math degree covered what they needed they'd not require a PhD for most positions. What do you think a quant does? Here's a site [1] for quant jobs. Probably none for someone with only an undergrad math degree. [1] http://www.quantfinancejobs.com/ http://www.quantfinancejobs.com/
  - antt 8y ago
    There's a number of things to disentangle in that post. 1). The domain you posted is for sale and appears to be broken or slow. Given it uses aspx and a Microsoft stack that's ten years out of date I'd say it's perfectly representative of the state of the larger finance industry. 2). What is a quant. Depends on the job. I was hired as a quant for risk management then got switched to algos when the pm found out I have a lot of hard real time experience with Linux. The first job was all discrete math, the second was optimizing x86 assembly. 3). Credential inflation is real. The application of the maths you talked about was something I saw first hand. The assumptions under which the formal models would work were so thread bare a stiff breeze would tear them down quote Keynes: >The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish. Too large a proportion of recent 'mathematical' economics are merely concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols. The above is still excellent advice, most often never followed. Of course the lunch talks we had were very interesting, completely divorced from reality, but very interesting. 4). Most undergrads will never see the mathematics. True. But some will. My numerical methods 4th year project was a symplectic integrator for the gravitational interaction between Jupiter, Mars, the Sun and the asteroid belt. It wasn't new research, the results were known 50 years ago, but it was on par with the state of the art in industry in terms of complexity of implementation (cleanness of implementation was a completely different thing, while not spaghetti code it's rightly never seen the light of day).