What is the meaning of the hadeeth “We are an unlettered nation, we do not write or calculate”?
Question

                What is the meaning of the hadeeth “We are an unlettered nation, we do not read or write”? Does this contradict what the Muslims are doing nowadays of seeking education?
Praise be to Allah.The wording of the hadeeth is not as mentioned 
          in the question. We will quote it here:
It was narrated from Ibn ‘Umar (may Allaah be pleased 
          with him) that the Prophet  (peace 
          and blessings of Allaah be upon him) said:  “We are an unlettered 
          nation, we do not write or calculate. The month is such-and-such or 
          such-and-such – meaning sometimes it is twenty-nine and sometimes it 
          is thirty.” (Narrated by al-Bukhaari, 1814; Muslim, 1080)
This hadeeth was narrated concerning the issue of 
          the beginning of the lunar month, and it indicates that there is no 
          need to resort to astronomical calculations in order to know when the 
          month begins. We should rely on visual sighting of the moon when it 
          is new, then we will know that the month has begun. The hadeeth was 
          quoted to explain that we should rely on sighting of the moon and not 
          on calculations. It did not come to urge the ummah to remain ignorant 
          and not to learn arithmetic and all other useful sciences. So this hadeeth 
          does not contradict what Muslims are doing nowadays of seeking education 
          in different branches of science which will benefit their worldly interests. 
          Islam is the religion of knowledge; it calls for knowledge and obliges 
          every Muslim to learn what Allaah has enjoined upon him and to learn 
          whatever rulings of sharee’ah he needs to know about acts of worship 
          and dealings with others. With regard to worldly sciences such as medicine, 
          engineering, agriculture, etc., Muslims have to learn whatever the ummah 
          needs to know. If the Muslims need to manufacture a needle, there has 
          to be someone among them who can learn how to make this needle.
Shaykh al-Islam Ibn Taymiyah wrote a very useful 
          discussion on this hadeeth; there follows a selection of his comments 
          on it:
“The phrase ‘We are an unlettered nation’ is not 
          telling them to be like that. They were unlettered before Islam came, 
          as Allaah says (interpretation of the meaning):
‘He it is Who 
          sent among the unlettered ones a Messenger (Muhammad) from among themselves’ 
          
[al-Jumu’ah 62:2] 
          
‘And 
          say to those who were given the Scripture (Jews and Christians) and 
          to those who are illiterates (Arab pagans): Do you (also) submit yourselves 
          (to Allaah in Islam)?’ 
[Aal ‘Imraan 
          3:20] 
Although this is how they were before the Prophet 
           (peace and blessings of Allaah 
          be upon him) was sent to them, they were not commanded to become like 
          that. Some of the implications of being unlettered were to remain, but 
          as we shall see, they were not commanded to remain as they were in every 
          sense…
 Among the nation to which Allaah sent 
          him were some who could read and write a great deal, just as there were 
          among his Companions. There were also some who could calculate. The 
          Prophet  (peace and blessings of 
          Allaah be upon him) was sent with some obligations which involve calculation. 
          It was narrated that when the person he had appointed to take care of 
          the zakaah, Ibn al-Latabiyyah, came to him, he  calculated the 
          total amount collected. He had a number of scribes, such as Abu Bakr, 
          ‘Umar, ‘Uthmaan, ‘Ali, Zayd and Mu’aawiyah, who would write down the 
          Revelation, and would write contracts and write his letters to the people 
          to whom Allaah had sent him, the kings of the earth and the leaders 
          of groups, and to his workers, governors, etc. Allaah says in His Book 
          (interpretation of the meaning):
“… that you might 
          know the number of the years and the reckoning” 
[Yoonus 10:5; al-Israa’ 
          17:12] 
This is mentioned in two places in the Qur’aan, where 
          Allaah tells us that He has created [the sun and moon] so that the calculations 
          may be known.  
The word ummi 
          (unlettered or illiterate) comes from the same root as the word ummah 
          (nation). It refers to one who is not distinguished from the rest of 
          the people by knowing how to read or write. It is akin to the word ‘aammi 
          which is used to describe a regular person (one of the ‘aammah 
          or masses) who is not distinguished from them by having knowledge which 
          they do not have. It was also said that the word ummi 
          is connected to the word umm 
          (mother), because he has learned no more than his mother taught him, 
          and so on.  
The distinction which takes him out of the 
          ranks of the regular, unlettered people into the ranks of those who 
          have specialized knowledge may be a virtue in and of itself, as in the 
          case of those who read Qur’aan and understand its meaning, or it may 
          be a means which helps to reach that level of virtue, as when a person 
          is distinguished from them by his being able to write and read. So the 
          one who uses that knowledge to pursue perfection is to be praised, whilst 
          the one who neglects it or uses it for evil purposes is to be condemned. 
          Whoever does away with it in favour of something that is more beneficial 
          is more perfect, and if you can achieve the aim without using these 
          means, then that is even better.  
Thus it is clear that being distinct from 
          the unlettered is of two types. The first nation to which the Prophet 
           (peace and blessings of Allaah 
          be upon him) was sent was the Arabs, through whom the Message was conveyed 
          to all the other nations, because it was sent in their tongue. They 
          were mostly illiterate, and they had no advantage of having knowledge 
          or a scripture etc., although by nature they were more ready to learn 
          than other nations. They were like a plowed field that is ready to be 
          sown, but there was no one to do the task and they had no scripture 
          they could read that had been revealed from Allaah, as the People of 
          the Book had, or any analytical science like the Sabaeans and others 
          had. Writing existed among them, but to a very small extent. They had 
          some knowledge of the type that is acquired by common sense, but which 
          does not make an individual distinct from any other unlettered person; 
          for example, they knew of the Creator, and they held good characteristics 
          in high esteem, and they had some knowledge of astronomy, genealogy 
          and poetry. So they deserved to be called unlettered in all senses of 
          the word, as Allaah said concerning them (interpretation of the meaning):
“‘He 
          it is Who sent among the unlettered ones a Messenger (Muhammad) from 
          among themselves’ 
[al-Jumu’ah 62:2] 
          
‘And 
          say to those who were given the Scripture (Jews and Christians) and 
          to those who are illiterates (Arab pagans): Do you (also) submit yourselves 
          (to Allaah in Islam)?’ 
[Aal ‘Imraan 
          3:20] 
So the unlettered or illiterate were described as being 
          opposite to the People of the Book, for the kitaabi 
          (one of the People of the Book) is something other than the ummi 
          (unlettered).
 When he was sent among them, it became 
          obligatory upon them to follow the Book that he brought and to ponder 
          its meanings, understand it and act upon it. Allaah made this Book an 
          explanation for all things, and their Prophet taught them everything, 
          even (the etiquette of) defecation. They became people of a Book and 
          people of knowledge, indeed, they became the most knowledgeable of people 
          and the best of them in beneficial knowledge. They lost the feature 
          of blameworthy and imperfect illiteracy, which is the lack of knowledge 
          and a revealed Book, and they gained knowledge of the Book and wisdom. 
          They inherited the Book, as Allaah said concerning them (interpretation 
          of the meaning):
“He 
          it is Who sent among the unlettered ones a Messenger (Muhammad) from 
          among themselves, reciting to them His Verses, purifying them (from 
          the filth of disbelief and polytheism), and teaching them the Book (this 
          Qur’aan, Islamic laws and Islamic jurisprudence) and Al-Hikmah 
          (As-Sunnah: legal ways, orders, acts of worship of Prophet Muhammad). 
          And verily, they had been before in manifest error” 
[al-Jumu’ah 62:2] 
            
They were unlettered in every sense of 
          the word, but when he taught then the Book and al-Hikmah, 
          Allaah said concerning them (interpretation of the meaning):
“Then 
          We gave the Book (the Qur’aan) as inheritance to such of Our slaves 
          whom We chose (the followers of Muhammad). Then of them are some who 
          wrong their ownselves, and of them are some who follow a middle course, 
          and of them are some who are, by Allaah’s Leave, foremost in good deeds” 
          
[Faatir 35:32] 
“And this is 
          a blessed Book (the Qur’aan) which We have sent down, so follow it and 
          fear Allaah (i.e. do not disobey His Orders), that you may receive mercy 
          (i.e. saved from the torment of Hell). 
Lest you (pagan 
          Arabs) should say: ‘The Book was sent down only to two sects before 
          us (the Jews and the Christians), and for our part, we were in fact 
          unaware of what they studied.’ 
Or lest you (pagan 
          Arabs) should say: ‘If only the Book had been sent down to us, we would 
          surely, have been better guided than they (Jews and Christians).’” 
          
[al-An’aam 6:155-157] 
          
 And Allaah answered the prayer of al-Khaleel 
          (Ibraaheem) for them, when he said (interpretation of the meaning):
“Our 
          Lord! Send amongst them a Messenger of their own (and indeed Allaah 
          answered their invocation by sending Muhammad), who shall recite unto 
          them Your Verses and instruct them in the Book (this Qur’aan) and Al-Hikmah 
          (full knowledge of the Islamic laws and jurisprudence or wisdom or Prophethood) 
          
[al-Baqarah 2:129]
 So there are kinds of illiteracy which 
          are haraam, kinds which are makrooh and kinds which are a shortcoming 
          and failure to do that which is better. A person who does not know how 
          to read al-Faatihah or 
          any part of the Qur’aan, is called by the fuqahaa’ in their discussion 
          on al-salaah (prayer), ummi 
          (unlettered), the opposite of whom is a qaari’ 
          (one who reads or recites). They say: it is not correct for a qaari’ 
          to be led in prayer by an ummi, 
          but it is permissible for an ummi 
          to lead another ummi in 
          prayer; and they discuss other issues of the same nature. What they 
          mean by ummi here is one 
          who cannot read what is necessary, regardless of whether he can write 
          and calculate or not.
 This illiteracy also includes neglecting 
          what is obligatory, for which a man will be punished if he is able to 
          learn it but he does not do so.
 There is also the kind of illiteracy 
          which is blameworthy, such as that which Allaah described in the case 
          of the People of the Book, when He said (interpretation of the meaning):
“And 
          there are among them (Jews) unlettered people, who know not the Book, 
          but they trust upon false desires and they but guess” 
[al-Baqarah 2:78]  
          
This is a description of one who does not 
          understand the word of Allaah or act upon it; all he does is to recite 
          it. Al-Hasan al-Basri said: The Qur’aan was revealed to be acted upon, 
          so recitation implies acting upon it. The ummi 
          in this sense may read the letters of the Qur’aan, etc., but he does 
          not understand it; when he speaks about matters of knowledge, he speaks 
          superficially, based on conjecture. This person is also regarded as 
          ummi and deserves to be 
          blamed, just as Allaah condemned him for his lack of obligatory knowledge, 
          whether this knowledge is fard ‘ayn 
          (obligatory on each individual) or fard 
          kafaayah (obligatory on the community as a whole but not 
          on each individual)
 There is also the kind of ‘illiteracy’ 
          which is better and more perfect, such as the one who only reads a part 
          of the Qur’aan and he only understands what he has learned. He only 
          understands as much of sharee’ah as he has to know. Such a person is 
          also called ummi (illiterate), 
          and others who learn and act upon the Qur’aan are better and more perfect 
          than him.
 These matters which distinguish a person 
          are virtues, and if a person fails to attain them, he is missing out 
          on something that is obligatory either on him as an individual (fard 
          ‘ayn) or is obligatory on the community (fard 
          kafaayah) or is mustahabb (recommended). These attributes of perfection and 
          virtue may be attributed to Allaah and His Prophets in general terms. 
          Allaah is All-Knowing and All-Wise, and He combines knowledge and beneficial 
          speech in all that He wants, tells and wills. The same is true of His 
          Prophets and our Prophet, the leader of the knowledgeable and wise.
 With regard to the distinguishing features 
          which are means to attaining virtues, but which one can do without and 
          use alternative means, these are things like writing and numeracy. If 
          a person does not have these abilities, knowing that virtue cannot be 
          achieved without them, not having them is a sign of imperfection. If 
          a person acquires them and uses them to perfect himself – like the one 
          who learns how to read and then uses that to read the Qur’aan and read 
          useful books or write other things that will be of benefit to people 
          – then this is a virtue in his case. But if he uses it for purposes 
          that will harm him or other people – like the one who reads misguided 
          books or writes things that will harm people, like forging the writing 
          of rulers, judges and witnesses – then this will be bad for him, and 
          will be a sin and imperfection. Hence ‘Umar forbade teaching women how 
          to write. If it is possible to do without it yet still achieve perfect 
          knowledge, then this is better, and this was the case with our Prophet 
           (peace and blessings of Allaah 
          be upon him), of whom Allaah said (interpretation of the meaning):
“Those 
          who follow the Messenger, the Prophet who can neither read nor write 
          (i.e. Muhammad) whom they find written with them in the Tawraat (Torah) 
          and the Injeel (Gospel)…” 
[al-A’raaf 7:157] 
          
His being unlettered did not mean that he was lacking 
          in knowledge or the ability to recite by heart, for he is the leader 
          of all imaams in that regard. What it meant was that he was not able 
          to write or to read anything that was written, as Allaah said of him 
          (interpretation of the meaning):
“Neither 
          did you (O Muhammad) read any book before it (this Qur’aan), nor did 
          you write any book (whatsoever) with your right hand…” 
[al-‘Ankaboot 29:48] 
          
 [Then he (Ibn Taymiyah – may Allaah 
          have mercy on him) went back to discussing the hadeeth “We are an unlettered 
          nation, we do not write or calculate…” and stated that there is a corroborating 
          report which refers to what is meant by this hadeeth. Then he said:]
 When this is compared with his comment 
          that the month may be thirty or twenty-nine days, it becomes clear that 
          what is meant is that with regard to the new moon (beginning of the 
          month), we have no need for writing or calculations, because sometimes 
          it is (thirty days) and sometimes it is (twenty-nine days). What differentiates 
          between them is the sighting (of the new moon), there is nothing else 
          that differentiates between them, such as writing or calculation.
Thus is becomes clear that the “illiteracy” 
          mentioned here is a characteristic which is praiseworthy in several 
          senses:
it 
          means doing without writing and calculations in favour of something 
          whichis clearer and more apparent, namely, (sighting) the new moon.
-Writing and calculation may involve errors…
Etc.