Paul was the author of Galatians--and Paul testified the Mosaic Law was added because of transgressions:
Galatians 3:19--King James Version
19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.
So--what was the law added to?
Here's some context which might help you understand what Paul is talking about:
"For as many as are of the works of the law ARE UNDER THE CURSE: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them."
The curse of the law is not the commandments, but the consequence of those who do not follow God's commandments.
"11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith."
Here's the topic that Paul addresses repeatedly which most Christians fail to comprehend, i.e. justification was what the legalists of the day were constantly harping on. No one is justified by the works of the law, but just because no one is justified by the works of the law, it doesn't then follow that the law is done away with. However, when one is justified by faith, that faith allows them to keep God's commandments, and as Paul points out, it is only the doers of the law who are justified. He points this out in the very next verse:
"12 And the law is not of faith: but, The man that doeth them shall live in them."
Again, pay careful attention to the fact that Paul is NOT referring to the commandments at all, but the "curse".
"13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
15 Brethren, I speak after the manner of men; Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto."
No man disannulleth? That's what Paul just said, no? Neither you nor anyone else can annul God's commandments.
"16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.
17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect."
Likewise, the promise doesn't do away with the commandments either as it evident in the preceding verses which clearly point out that one lives according to the law.
"18 For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise.
19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.
20 Now a mediator is not a mediator of one, but God is one."
Note again, that he is referring to "transgressions" and one cannot transgress laws that do not exist. Therefore, the law existed already. The law is eternal. Not one jot or title of the law will disappear before heaven and earth pass away. Heaven and earth are still here so it's safe to say the law still exists and is still in effect. Moreover, the "curse" is still in effect for those who continue to sin. Likewise, Christ's sacrifice is still in effect for those who must continue to rely upon his sacrifice to cover their sins. For those who have entered into the new covenant, Christ's sacrifice is no longer relevant as it only covers sins committed under the first testament (Hebrews 9:15) Christ does not mediate a covenant of sin under the second testament.
"23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster."
The Greek word for "schoolmaster" is Paedegagos which as anyone who knows what a schoolmaster is, knows that they do not teach anything. They are administrators, and Paul speaks of the "ministration" which was what was done away with, not the law that was administered. The veil covered Moses' face, not the tablets.
The schoolmaster administered the penalties, punishments, curses, etc. which were what motivated Israel to follow God's commandments, but when those means of motivation are no longer necessary, they are what are done away with, not the commandments which are kept perfectly under the New Covenant.
It is not the law that allows one to keep the law, but God's promise.
Some people believe God's promises, others don't.