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How do we explain the use of a software on a math paper?
How do you approach your child's math education?How should the Math Subject Classification (MSC) be revised or improved?Applications of Math: Theory vs. PracticeHow To Present Mathematics To Non-Mathematicians?How important is it for one on the job market to have thought about suitable REU projects?Am I allowed to do non-rigorous numerical analysis?Non-computational software useful to mathematiciansLost soul: loneliness in pursing math. Advice needed.Does Pure Mathematics glue Science together?How non-planar is the Math Genealogy Project graph?
$begingroup$
Suppose one is written a math/computer science paper, but more focused in the math part of it. I had a very complicated function and need it to find it's maximum, so I used Mathematica (Wolfram) to do it. How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...".
It's look very sloppy.
soft-question mathematical-writing
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Suppose one is written a math/computer science paper, but more focused in the math part of it. I had a very complicated function and need it to find it's maximum, so I used Mathematica (Wolfram) to do it. How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...".
It's look very sloppy.
soft-question mathematical-writing
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
4
$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago
add a comment |
$begingroup$
Suppose one is written a math/computer science paper, but more focused in the math part of it. I had a very complicated function and need it to find it's maximum, so I used Mathematica (Wolfram) to do it. How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...".
It's look very sloppy.
soft-question mathematical-writing
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Suppose one is written a math/computer science paper, but more focused in the math part of it. I had a very complicated function and need it to find it's maximum, so I used Mathematica (Wolfram) to do it. How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...".
It's look very sloppy.
soft-question mathematical-writing
soft-question mathematical-writing
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
PintecoPinteco
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
PintecoPinteco
1211
asked 4 hours ago
PintecoPinteco
1211
1211
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Pinteco is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
4
$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago
add a comment |
4
$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago
4
4
$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view, can in general be trusted no less than the work of about any human. Others may disagree with this, and so, then you may have to try to obtain the maximum in a way that can be verified by hand. Also, of course, Maximize[] can only solve comparatively easy maximization problems.
On the other hand, if you just used the command NMaximize[] -- which tries to find the maximum numerically, then its output can only be considered a suggestion -- certainly not a proof.
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
$endgroup$
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
add a comment |
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$begingroup$
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view, can in general be trusted no less than the work of about any human. Others may disagree with this, and so, then you may have to try to obtain the maximum in a way that can be verified by hand. Also, of course, Maximize[] can only solve comparatively easy maximization problems.
On the other hand, if you just used the command NMaximize[] -- which tries to find the maximum numerically, then its output can only be considered a suggestion -- certainly not a proof.
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
$endgroup$
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
add a comment |
$begingroup$
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view, can in general be trusted no less than the work of about any human. Others may disagree with this, and so, then you may have to try to obtain the maximum in a way that can be verified by hand. Also, of course, Maximize[] can only solve comparatively easy maximization problems.
On the other hand, if you just used the command NMaximize[] -- which tries to find the maximum numerically, then its output can only be considered a suggestion -- certainly not a proof.
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
$endgroup$
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
add a comment |
$begingroup$
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view, can in general be trusted no less than the work of about any human. Others may disagree with this, and so, then you may have to try to obtain the maximum in a way that can be verified by hand. Also, of course, Maximize[] can only solve comparatively easy maximization problems.
On the other hand, if you just used the command NMaximize[] -- which tries to find the maximum numerically, then its output can only be considered a suggestion -- certainly not a proof.
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
$endgroup$
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view, can in general be trusted no less than the work of about any human. Others may disagree with this, and so, then you may have to try to obtain the maximum in a way that can be verified by hand. Also, of course, Maximize[] can only solve comparatively easy maximization problems.
On the other hand, if you just used the command NMaximize[] -- which tries to find the maximum numerically, then its output can only be considered a suggestion -- certainly not a proof.
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
answered 3 hours ago
Iosif PinelisIosif Pinelis
22k22461
22k22461
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
add a comment |
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
Out of interest, is ball arithmetic implemented in Mathematica? If so, does Maximize[] use this?
$endgroup$
– François Brunault
2 hours ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
$begingroup$
@FrançoisBrunault : There is a command Interval[a1,b1,a2,b2,...] (giving the union of the intervals), and these interval objects can be the values of arguments of a function. This way, interval arithmetic is implemented.
$endgroup$
– Iosif Pinelis
1 hour ago
add a comment |
Pinteco is a new contributor. Be nice, and check out our Code of Conduct.
Pinteco is a new contributor. Be nice, and check out our Code of Conduct.
Pinteco is a new contributor. Be nice, and check out our Code of Conduct.
Pinteco is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
If that's how you did it, that's how you explain it. Of course, the non-believers in the capability of Wolfram Mathematica (like myself) will not consider the proof complete until they verify the statement by alternative means, but the "sloppiness" is not in the explanation but in the approach itself and you won't be able to eliminate it no matter what nice words you say. So, just be straight, concise, and to the point and let the others judge whether such computations are admissible or not for themselves.
$endgroup$
– fedja
4 hours ago
$begingroup$
I would use Mathematica as more of a guide than rely on it entirely. The maximum that Mathematica gave to you is probably very accurate; as such, depending on the precision you need, you might try finding ways to bound your function above by $2$ (or $1.033$, etc.).
$endgroup$
– Clayton
17 mins ago