After graduating from the Grodno gymnasium, in 1839 he entered military service as a non-commissioned officer in the Nizhny Novgorod infantry regiment.

In 1845 he was transferred to the 16th Georgian Line Battalion and attached to the Kabardian Infantry Regiment , and since then, for 20 years, his outstanding combat activities in the Caucasus have continued.

In 1854, he was appointed head of training for the lower ranks in target shooting and participated in several large cases with the highlanders, and on July 13 he was twice wounded by rifle bullets.

In 1857 he was a member of the Kumyk detachment and took an especially active part in the fight against the mountaineers: on January 19, he was during the capture of the village of Ali-Sultan-Kale from the battle, on March 19 - during the assault and occupation of the fortified position of the Goytemir Gate.

When in 1860, after the capture of Shamil, the main actions were transferred to the right wing of the Caucasian line, Geyman was sent there at the head of the combined rifle battalion and the team of hunters of the Kabardin regiment.

During the occupation of the village of Shabanits, his battalion was among the troops of the first line, and during further movement to the upper reaches of the Ili River it was constantly in the vanguard.

Then, as part of the Nizhne-Abadzekh detachment, the battalion of the Kabardin regiment under the command of Geyman participated in the establishment of Russian rule in the region and the ousting of the highlanders.

At the end of April 1862, he, commanding the Nizhne-Abadzekh detachment, skillfully performed difficult and dangerous operations to capture the Dakhovsky gorge, after which he was left there to set up a new Cossack village.

The work on the construction of the Dakhovskaya stanitsa , which lasted until July 12 , was worth tremendous labor and subjected the troops to hourly meetings with the enemy.

On July 18, Geyman raided the valley of the Rufabgo River and destroyed a large aul with all the grain reserves collected there.

On September 25, General Evdokimov , who commanded the troops of the right wing, arrived at the Dakhovsky detachment and made a move with it to the Kurdzhips River.

On February 27, Geyman moved to the ridge along the Tlotz River to meet the new commander-in-chief, Grand Duke Mikhail Nikolaevich .

508 As a reward for the excellent courage and exemplary management shown in the case with the Ubykhs on March 18 between Psezuape and Shakhe and during the occupation of the entire sea coast to the Sochi River.

On May 27, Geyman undertook a reconnaissance of the Shorakh heights and alarmed the Turks, who believed that our troops were marching on an attack, on June 3, Geyman's forces repulsed the Ottoman attack on the Aravartan camp with significant damage, and on June 6 was sent with a detachment to Saganlug to distract Ahmed Muhtar Pasha, who was moving with large forces to the Erivan detachment of Tergukasov .

An attempt, by order of Mikhail Loris-Melikov, to seize on June 13 the Zevin position, at which Mukhtar Pasha stopped, ended in complete failure.

Gaiman was distinguished by outstanding courage and a passionate love for military affairs, but the desire to attack with a bang, insufficient reconnaissance and a certain disdain for the enemy were sometimes the reason for failure.