You've probably heard stories about him in General Conference and the Ensign, from President Eyring, President Faust, Elder Hales, and others. He was a rather accomplished man.
I won't discuss his childhood, although it was certainly an eventful one.
He was a successful scientist. I don't mean successful in that he taught and did research at a prestigious university (although he did). I mean successful in that he pioneered modern chemistry. He developed the transition state theory. If you've taken a college chemistry class, you probably learned about his discovery.
He was also married to President Kimball's sister and served on the Church's Sunday School General Board (basically the modern version of the church's Sunday School Presidency). Not a general authority, but still in the upper levels of church leadership. His son, of course, is currently in the First Presidency.
Eyring, however, was a bit of a black sheep. I've taken the following account from "Reflections of a Scientist," written by Eyring and published by Deseret Book (out of print, but available on Kindle). President Joseph Fielding Smith, at the time the President of the Twelve, had published his views on some aspects of science, including the age of the earth. Eyring, a prominent chemist, knew how radioactive elements decay. He knew the science behind determining the age of the earth. And he absolutely disagreed with the President of the Twelve's views. President Smith's book was being considered for use as an institute manual at the highest levels. Eyring was worried about educated young members leaving the church over the issue. Eyring recounts, "[T]he next time I went to Sunday School General Board meeting, I got up and bore my testimony that the evidence was strongly in the direction that the world was four or five billion years old."
Not too surprisingly, that same week President Smith invited Eyring in for a little talk. They basically agreed to disagree. Eyring stated of President Smith, "I would say that I sustained President Smith as my church leader one hundred percent. I think he was a great man. He had a different background and training on this issue. Maybe he was right. I think he was right on most things, and if you followed him, he would get you into the celestial kingdom." (Page 53).
Eyring, in his book, then went on to discuss the chemistry and geology supporting an old earth (including discounting "the notion that the earth has been assembled, relatively recently, from the wreckage of earlier worlds"). (Page 54). He also discusses evolution (page 59), but that's an issue for another post.
So what can we take away from this? I think two main things. First, our church leaders are good men, and if we follow them, we will get into the celestial kingdom. And second, that our church leaders aren't necessarily perfect, and may occasionally get things wrong. If we expect them to be perfect, we will ultimately be disappointed.