Can the entirety of Jesus's teachings be summed up in a few words? A phrase or sentence?

I believe Jesus' own summary of the gospel message is "repentance for the forgiveness of sins" (Luke 24:47; cf Mark 1:15, Acts 2:38).

Obviously this needs a lot of fleshing out e.g. defining sin and repentance.

Can the entirety of Jesus's teachings be summed up in a few words? A phrase or sentence?

Since you reference Albert Einstein, I would like to reference Martin Luther. This way, I am able to give you an historical perspective to your question!

Martin Luther put it in a nutshell centuries ago.

For centuries now, there have been many formidable Bible scholars that would point us to that second-to-last verse of our Gospel lesson today! In his native German tongue, Martin Luther once referred to this passage of John 3:16, as: “Das Evangelium in der Nussschale!” It’s a phrase that, translated into English, means: “The Gospel in a Nutshell!”

“For God so loved the world that he gave his only-begotten Son, that whosoever believes in him should not perish but have eternal life!” - John 3:16

“The Gospel in a Nutshell”

A close second would be the following:

That ye love one another; as I have loved you, that ye also love one another. - John 13:34 (KJV)

The term a New Commandment is used in Christianity to describe Jesus's commandment to "love one another" which, according to the Bible, was given as part of the final instructions to his disciples after the Last Supper had ended, and after Judas Iscariot had departed in John 13:30.

New Commandment

This commandment appears thirteen times in twelve verses in the New Testament. Theologically, this commandment is interpreted as dual to the Love of Christ for his followers. The commandment can also be seen as the last wish in the Farewell Discourse to the disciples.

Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you. 34 A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another. 35 By this shall all men know that ye are my disciples, if ye have love one to another. — John 13:33–35 (KJV)

The "New Commandment" concerns the love for neighbor and is similar to the second part of the Great Commandment, which comprises two commands: love for God and love for neighbor. The first part of the Great Commandment alludes to Deuteronomy 6:4-5, a section of the Torah which is recited at the beginning of the Jewish prayer known as The Shema. The second part of the Great Commandment, which is similar to the "New Commandment", commands love for neighbor and is based on Leviticus 19:18.

According to Scott Hahn, while the Torah commanded human love, Jesus commands divine love for one another that is modeled on his own acts of charity.

The "New Commandment", the Wycliffe Bible Commentary states, "was new in that the love was to be exercised toward others not because they belonged to the same nation, but because they belonged to Christ ... and the love of Christ which the disciples had seen ... would be a testimony to the world".

One of the novelties introduced by this commandment – perhaps justifying its designation as New – is that Jesus "introduces himself as a standard for love". The usual criterion had been "as you love yourself". However, the New Commandment goes beyond "as you love yourself" as found in the ethic of reciprocity and states "as I have loved you", using the Love of Christ for his disciples as the new model.

Sure! The Apostle Paul summed it up quite well at 1 Corinthians 15:1-4.

"Now I make known to you, brethren, the gospel which I preached to you, which also you received, in which also you stand, vs2, by which also you are saved, if you hold fast the word which I preached to you, unless you believed in vain.

Verse 3, "For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, vs4, and that He was buried, and that He was raised on the third day according to the Scriptures."

To verify this the Apostle Paul states at vs5, "and that He appeared to Cephas, then to the twelve. Vs6, After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; vs7, then He appeared to James, then to all the apostles, vs8, and last of all as it were to one untimely born, He appeared to me also."

As a side note the above would be considered a "Creed." "A formal statement of Christian beliefs or a set of beliefs or aims which guide someone's actions."

^{Matthew 22:36-40} Master, which is the great commandment in the law? Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment. And the second is like unto it, Thou shalt love thy neighbor as thyself. On these two commandments hang all the law and the prophets.

^{Matthew 7:12} Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets.

Any such 'summary' would, inevitably, be opinion based.

Any supposed 'summary' of the word of Christ will diminish the whole volume of the words of Jesus and his ministry on earth during the days of his flesh (contained in four, separate accounts) and will diminish the doctrine of the gospel (expressed by six authors).

This diminishing will, invariably, err by its very paucity of expression and the error will be different, depending on who attempts the diminution.

Thus it results in an opinionated summary , as opposed to a body of authentic documentation.

The LAW may be summed up, and is, by Jesus of Nazareth, himself :

Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets. [Matthew 7:12 KJV.]

The Gospel of Jesus Christ and the Person of Jesus Christ : not so.

Many do, indeed, attempt a 'summary' and many (in my experience) express that 'summary' often from pulpit or platform, but starting from a different text each time and padding out the 'summary' appropriately.

But it is always the same (in these instances that I have witnessed) : a diminution of the breadth of the gospel into a much reduced - and 'personalised', opinionated - form.

The epistles and the gospel accounts are the form and the content that they are for there is much to be conveyed of the Person, the Work, the Offices and the Ministrations of Jesus Christ and the Spirit of Christ, and the overseeing of God and the Father.

Like any body of truth, this cannot be diminished - or 'dumbed down'. It must be expressed in its entirety or large parts of the Gospel of Jesus Christ will, generation by generation, be eroded and be let slip, through neglect and through unavoidable ignorance.

One may sum up the focus and the intent of Jesus' teaching - and John the apostle does so :

And this is his commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment. 1 John 3:23.

But in order to fully appreciate these momentous words, one needs all the others - initially - that one might understand the depth, the profundity and the implications of this succinct crystallisation.