Above: HOOVER DAM PLEIADES/ORION/THUBAN STAR CHART
Below: VATICAN SUN DIAL/Disk OBELISK
Carpe diem is a Latin aphorism, usually translated “seize the day”, taken from book 1 of the Roman poet Horace’s work Odes (23 BC).
Carpe is the second-person singular present active imperative of carpō “pick or pluck” used by Horace to mean “enjoy, seize, use, make use of”.  Diem is the accusative case of the noun dies “day”. A more literal translation of “carpe diem” would thus be “pluck the day [as it is ripe]”—i.e., enjoy the moment.
Ask not (’tis forbidden knowledge), what our destined term of years, Mine and yours; nor scan the tables of your Babylonish seers.
Sapere aude is the Latin phrase meaning “Dare to know”; and also is loosely translated as “Dare to be wise”.
Better far to bear the future, my Leuconoe, like the past, Whether Jove has many winters yet to give, or this our last; This, that makes the Tyrrhene billows spend their strength against the shore. Strain your wine and prove your wisdom; life is short; should hope be more? In the moment of our talking, envious time has ebb’d away. Seize the present; trust tomorrow e’en as little as you may. 
In ancient literature
Perhaps the first written expression of the concept is the advice given by Siduri to Gilgamesh, telling him to forgo his mourning and embrace life although some scholars see it as simply urging Gilgamesh to abandon his mourning, “reversing the liminal rituals of mourning and returning to the normal and normative behaviors of Mesopotamian society.” 
In Horace, the phrase is part of the longer “carpe diem, quam minimum credula postero”, which can be translated as “Seize the day, put very little trust in tomorrow (the future)”. The ode says that the future is unforeseen and that one should not leave to chance future happenings, but rather one should do all one can today to make one’s future better. This phrase is usually understood against Horace’s Epicurean background.  The meaning of “carpe diem” as used by Horace is not to ignore the future, but rather not to trust that everything is going to fall into place for you and taking action for the future today. 
The phrase ?ואם לא עכשיו, אימתי “And if not now, then when?” (Pirkei Avoth 1:14).
Gather Ye Rosebuds While Ye May, by John William Waterhouse
An 1898 German postcard, quoting “Gaudeamus igitur”
“Collige, virgo, rosas” (“gather, girl, the roses”) appears at the end of the poem “De rosis nascentibus”  (“Of growing roses”, also called Idyllium de rosis) attributed to Ausonius or Virgil. It encourages youth to enjoy life before it is too late; compare “Gather ye rosebuds while ye may” from “To the Virgins, to Make Much of Time”.
De Brevitate Vitae (“On the Shortness of Life”), often referred to as Gaudeamus igitur, (“Let us rejoice”) is a popular academic commercium song, on taking joy in student life, with the knowledge that one will someday die. It is medieval Latin, dating to 1287.
Horace himself parodies the phrase in his satire “The Town Mouse and the Country Mouse”. He uses the phrase carpe viam meaning “seize the road” to compare the two different attitudes to life of the person (or in this case, a mouse) living in a city and in the countryside.
Related but distinct is the expression “memento mori” (“remember that you are mortal”) which carries some of the same connotation as “carpe diem”. For Horace, mindfulness of our own mortality is key in making us realize the importance of the moment. “Remember that you are mortal, so seize the day.” Over time the phrase “memento mori” also came to be associated with penitence, as suggested in many vanitas paintings. Today many listeners will take the two phrases as representing almost opposite approaches, with “carpe diem” urging us to savour life and “memento mori” urging us to resist its allure. This is not the original sense of the “memento mori” phrase as used by Horace.
A German version of “carpe diem” (Nutze die Zeit) on the face of a turret clock in Germany
In the 1989 movie Dead Poets Society, the English teacher John Keating, played by Robin Williams, famously says: “Carpe Diem. Seize the day, boys. Make your lives extraordinary.” Later, this line was voted as the 95th greatest movie quote by the American Film Institute. 
The American progressive metal band Dream Theater released the 23-minute epic “A Change of Seasons” on their 1995 album of the same name. The song numerously references the “carpe diem” or “Seize the Day” aphorism as part of its storyline. The song also includes audio samples from the 1989 film Dead Poets Society and quotes from the 1648 Robert Herrick poem, “To the Virgins, to Make Much of Time”, all of which are conceived surrounding the concept of “carpe diem”.
The American heavy metal band Metallica produced a song called “Carpe Diem Baby” on their 1997 album Reload. The chorus contains the line “Come squeeze and suck the day. Come carpe diem, baby!”
The soundtrack to the 2011 animated film Phineas and Ferb the Movie: Across the 2nd Dimension includes a track called “Carpe Diem”.
The American punk rock band, Green Day, produced a song called “Carpe Diem” on their 2012 album ¡Uno!. The chorus is “Carpe Diem, a battle cry, are we all too young to die? Ask for reason, and no reply, are we all too young to die?”
The English alternative rock band, You Me at Six, produced a song called “Carpe Diem” on their 2014 album Cavalier Youth. The chorus is “Carpe diem ’til the very end. I have no regrets. Carpe diem ’til the bitter end.”
Bob Catley’s 1999 solo album Legends includes the song “Carpe Diem” with the chorus “seize the day”.
It is also the motto of Marden High School.
Text from Odes 1.11:
Tu ne quaesieris, scire nefas, quem mihi, quem tibi finem di dederint, Leuconoe, nec Babylonios temptaris numeros. ut melius, quidquid erit, pati. seu pluris hiemes seu tribuit Iuppiter ultimam, quae nunc oppositis debilitat pumicibus mare Tyrrhenum. Sapias, vina liques et spatio brevi spem longam reseces. dum loquimur, fugerit invida aetas: carpe diem, quam minimum credula postero.