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mathematics vocabulary
The present entry presents a list of words you can typically hear in mathematical circles. When used in mathematical writing, these terms often have specific meanings which can differ significantly from their meanings in everyday language.
AB

a posteriori

a priori

abstract

abuse

add, addition

affine

analogous, analogy

applied

approximate

assume, assumption

axiom, axiomatic

azimuth

bundle (as in tangent bundle)
C

Cartesian

circular (as in circular argument and circular reasoning)

circulation

classic

clear, clearly

collapse

concave, concavity

concrete

condition

constrain, constraint

construct, constructible, construction, constructive

contact

contract, contraction

convex, convexity

convergence, convergent

criteria, criterion

cross (as in cross product and cross section)

crystalline

curvilinear
DF

deduce, deduction

dependence, dependent

definition, define

deformable, deformation

different

dilate, dilation

dual

empty

equal

evaluate, evaluation

evident

exact (as in exact sequence)

exhaust, exhaustion

existential

expected

explicit

extend, extension

false

form

formal

formula, formulae
GL

general, generalization

handwaving

heuristics

hyper

if and only if, iff

implication, implies, imply

implicit

identification, identify

independence, independent

inert, inertia

inferior (as in limit inferior)

inject, injection

integrate, integration

invariance, invariant

language

linear
MQ
RS

razor (as in Occam’s razor)

rest

restrict, restriction

self

semi

smash (as in smash product)

space

spectral (as in spectral radius and spectral sequence)

sphere, spherical

split

star, starshaped

subtract, subtraction

superior (as in limit superior)

suppose, supposition

symbol
TZ

tame

term

theorem

theoretical

total

toy (as in toy theorem)

transcend, transcendence, transcendental

transient

triangle, triangular

trivial

true

uniform, uniformly

unique, uniqueness

value

variational (as in variational calculus)

vector, vectorial

wedge (as in wedge product)

well defined, welldefined

word

zero, zeroes, zeros
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Comments
changes
I would like to make changes to this entry (mathematical vocabulary). The main thing that I would like to do is alphabetize the terms. It would be quite difficult for me to do this and change all of the numbers. Thus, I would like to change the ``enumerate'' to ``itemize''. I thought that I would ask before making this change. Any opinions?
Warren
Re: changes
As it has been over a week since I made my previous post and no one has given their opinion, I assume that it is okay for me to implement the changes. If not, this object is worldeditable, so someone can change it back.
questionable words in this entry
This will be a long post, so bear with me.
First of all, there are words in this entry (mathematics vocabulary) that I have never seen before and do not have a link to another PM entry. These include:
aleotropic
anisotropic
azimuth
baricenter
bisectrix
cristallyne (which I suspect should be spelled crystalline)
critery (perhaps "criteria" was meant, which should be on the list)
curvilinear
evolute
homotecy
involute
mediatrix
osculate
Either I'm the dumbest or most illinformed active member of PM, or other people may be confused about these words as well. Also, these do not seem to fall under the stipulations at the beginning of the entry:
>> When used in mathematical writing, these terms often have specific meanings which can differ significantly from their meanings in everyday language.
Since I have never heard of any of these words before, I do not consider them part of "everyday language".
There are other words that either I do not feel are part of "everyday language" or their typical and mathematical usages are so similar that I do not consider them to fall under the stipulations of the >> comment above. These words include:
abelian
affine
arc
area
asymptote
automorphism
biharmonic
bilinear
calculus
classic
codomain
conformal mapping
cosecant
cosine
cotangent
cross product
cross section (perhaps just "cross" should remain)
curvilinear
diffeomorphism
eigenvalue
eigenvector
endomorphism
equal
false
homeomorphism
homomorphism
isomorphism
isoperimeter, isoperimetric
isotropy, isotropic
jacobian
kurtosis
laplacian
Occam's razor (perhaps just "razor" should remain)
ODE (unless confused with the word "ode", which seems unlikely)
orthocenter
orthogonal
orthonormal
PDE
perimeter
pi
rotation
sine
solid angle (perhaps just "solid" should remain)
square root
toy theorem
true
variational calculus (perhaps just "variational" should remain)
vectorial
wronskian
I feel that either the statement >> needs to be amended so that these words fit the stipulations of the entry or they (and others like them) should be removed. I didn't want to make all of these changes myself as it would require a lot of time, and I wouldn't want to put all of the effort into it if someone was just going to change it back to the way it was. (This is currently a worldeditable entry.)
Finally, there are some words that I am curious about, as I am not familiar with their "mathematical usage" (or I've been thinking too hard about creating this post and am mathematically burned out) and they do not have a link to another PM entry:
rest
secular
spectral
Congratulations for making it to the end of this post. :)
Warren
Re: questionable words in this entry
Dear Warren,
Because practically all those words were including by me, I may say the following.
1. I apologize for my limited English.
2. You wrote:
>> When used in mathematical writing, these terms often have specific meanings which can differ significantly from their meanings in everyday language.
However, matte textually wrote in his entry:
>>The present entry presents a list of words you can typically hear in mathematical circles. When used in mathematical writing, these terms often have specific meanings which can differ significantly from their meanings in everyday language.
So, I think that your claim was incomplete. I don't know what matte had in mind though. My particular opinion is that there is a lot of subjectivity in this subject.
3. Why do you think that ``cristallyne'' word may be not included? Or it was simply my evident orthographic error?
4. You wrote:
..."there are words in this entry (mathematics vocabulary) that I have never seen before"...
Very natural! Neither I know all of mathematical words. But believe me, all those words are related to mathematics.
5. About the ``aleotropic'' and ``anisotropic'' words: they are well known (and defined!) in Mathematical Theory of Elasticity.
What do you think about the ``stress'', ``strain'' and ``strenght'' words? (used and/or created by Cauchy, Poisson, Navier, Stokes, etc.). BTW, I forgot to include it.
6. About the ``true'' and ``false'' words: I think that in the "real world" these words could be subjective, in Mathematical Logic are not it.
7. About the ``osculate'' word: I was not that added on there, but evidently it refers to ``osculating''.
8. You wrote:
>>Finally, there are some words that I am curious about, as I am not familiar with their "mathematical usage" (or I've been thinking too hard about creating this post and am mathematically burned out) and they do not have a link to another PM entry:
a)``rest''. Sincerely, it was my lapsus. I would want to say ``substract'' (to substract=restar=substraer,in Spanish). However, incidentally,``rest'' is a very important word in Motion of Continuum and that is mathematics!
b)``secular''(seglar, laic). A very used word in the scientific world. For example, I have taken from H. Goldstein, Classical Mechanics, AddisonWesley, 1964:
``secular determinant'' (pp.119,321)
``secular equation'' (pp.120,154,321,327).
Indeed such a denominations refer to the characteristic determinant equation used to find out certain eigenvalues/eigenvectors.
What these one has to do with seglar/laic? NOTHING!!!
c)``spectral''. Please, look at
http://planetmath.org/?op=search&term=spectral
Sincerely, I appreciate your post in order to clarify the words that I placed in matte's entry.
Regards,
perucho
Re: questionable words in this entry
> Dear Warren,
> Because practically all those words were including by me, I
> may say the following.
> 1. I apologize for my limited English.
Your English is far superior to my Spanish. :)
> 2. You wrote: .....
> So, I think that your claim was incomplete. I don't know
> what matte had in mind though. My particular opinion is that
> there is a lot of subjectivity in this subject.
I definitely agree that there is subjectivity in this entry. The use of the word "everyday" threw me off, but I guess that that does not particularly mean what I thought it originially meant.
> 3. Why do you think that ``cristallyne'' word may be not
> included? Or it was simply my evident orthographic error?
First of all, I think it should be spelled ``crystalline''. Second of all, I have only come across ``crystalline'' once before, and it was not in a mathematical context.
> 4. You wrote:
> ..."there are words in this entry (mathematics vocabulary)
> that I have never seen before"...
> Very natural! Neither I know all of mathematical words. But
> believe me, all those words are related to mathematics.
Then, in my opinion, they should link to other entries on PM. It seems pointless to list words that are used in mathematics and give no explanation how their mathematical usage differs from their common usage.
> 5. About the ``aleotropic'' and ``anisotropic'' words: they
> are well known (and defined!) in Mathematical Theory of
> Elasticity.
Then these should link to a PM entry that uses these words if one exists. I may force this link myself.
> What do you think about the ``stress'', ``strain'' and
> ``strenght'' words? (used and/or created by Cauchy, Poisson,
> Navier, Stokes, etc.). BTW, I forgot to include it.
Yes, I agree that these words should be included (except that the last is spelled ``strength'').
> 6. About the ``true'' and ``false'' words: I think that in
> the "real world" these words could be subjective, in
> Mathematical Logic are not it.
I guess I never thought of it that way. Thanks for explaining this.
> 7. About the ``osculate'' word: I was not that added on
> there, but evidently it refers to ``osculating''.
Okay.
> 8. You wrote:
> >>Finally, there are some words that I am curious about, as
> I am not familiar with their "mathematical usage" (or I've
> been thinking too hard about creating this post and am
> mathematically burned out) and they do not have a link to
> another PM entry:
> a)``rest''. Sincerely, it was my lapsus. I would want to say
> ``substract'' (to substract=restar=substraer,in Spanish).
> However, incidentally,``rest'' is a very important word in
> Motion of Continuum and that is mathematics!
Yet again, I think a link is necessary. Also, I agree that ``subtract'' should be added if it has not been already.
> b)``secular''(seglar, laic). A very used word in the
> scientific world. For example, I have taken from H.
> Goldstein, Classical Mechanics, AddisonWesley, 1964:
> ``secular determinant'' (pp.119,321)
> ``secular equation'' (pp.120,154,321,327).
> Indeed such a denominations refer to the characteristic
> determinant equation used to find out certain
> eigenvalues/eigenvectors.
> What these one has to do with seglar/laic? NOTHING!!!
Would you mind supplying definitions of ``secular determinant'' and ``secular equation'' to PM (if they are not here already) and force the occurrence of ``secular'' in this object to link to one of them?
> c)``spectral''. Please, look at
> http://planetmath.org/?op=search&term=spectral
I might force a link to one of these objects. Also, ``spectrum'' should be added, and I may do this.
> Sincerely, I appreciate your post in order to clarify the
> words that I placed in matte's entry.
Not a problem, and thanks for clarifying these additions.
Warren
Re: questionable words in this entry (crystalline)
http://www.ams.org/msc/14Fxx.html