Algebraist is a 10 letter English word. It's valid Words with friends word worth 16 points.
You can make 1087 anagrams from letters in algebraist (aabegilrst).
First recorded in 1665-75; algebra + -ist
Like the great French algebraist, Vieta, from whom he drew much of his inspiration, he was an amateur mathematician.
The problem is of course (as any algebraist sees at once) a case of "simultaneous simple equations."